Algebra 2: All-In-One Answers (continued)
Chapter 1
23. 186 24. 25 25. 0 26. -25
27. a + (a - b) + c + b +(a - 2c)+ b + c + (a - b); 4a
Practice 1-1
Guided Problem Solving 1-2
1. -4.2 2. 4 3. 7 4. 1 5. 2 6. 1.8 7. 6 8. 0.01 9. 3
All rights reserved.
6
10. = 11. 12. = 13. 14. 15. 16. 17. integer, rational, real 18. whole, integer, rational, real
19. irrational, real 20. rational, real 21. natural, whole,
integer, rational, real 22. rational, real 23. irrational, real
24. integer, rational, real 25. Comm. Prop. of Add.
26. Identity Prop. of Add. 27. Assoc. Prop. of Add.
28. Inv. Prop. of Mult. 29. Dist. Prop.
30. Comm. Prop. of Mult. 31. Identity Prop. of Mult.
32. Inv. Prop. of Mult. 33. Inv. Prop. of Add.
34. Assoc. Prop. of Mult.
35–38.
3
2 1
0.5
2
3
2
1
0
1
2
3
39. 2 1 ; 2 2 40. -3; 1 41. 2 5 ; 9 42. 4; 2 1
10a. about 198 million eligible voters 10b. about 100 million
voters
Practice 1-3
1. h 5 3V2
pr
3
4
9 5
2 5
43. N: natural 44. H: rational; L: rational; n: natural
45. t: rational; n: natural
2S
2. r 5 L L
Guided Problem Solving 1-1
4. x 5 9 g 2 3; no restrictions
h
3. w 5 S 2
1h
be many valid counterexamples for each statement.
4
c(a 1 b)
5. x 5 b 2 a ; a 2 b
3. Answers may vary. Sample: 4 is a whole number, but its
reciprocal 1 is not a whole number. 4. Answers may vary.
4
6. x = t 3 - 3; t 2 0 7. $20 and $35 8. 2.5 in., 6 in., 6.5 in.
9. 41, 42, 43 10. 0 11. 1 12. 6 13. -1 14. 2 74 15. 1
1. An example that makes the statement false. 2. There may
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1. The number of eligible voters in millions in the United
States from 1960 to 2000 2. The number of years since 1960
3. 28; about 180 million voters 4. 52, 60 5. about 242 million
voters; about 263 million voters 6. -0.003y + 0.61
7. -0.0078y2 + 1.265y + 65.27 8. 20; about 87 million voters
9. Answers may vary. Sample: Answers are reasonable.
Year Eligible Voters
1988 180 million
2012 242 million
2020 263 million
Sample: 7 is a natural number, but its opposite -7 is not a
natural number. 5. Answers may vary. Sample: 0 is a whole
number, and since -0 = 0, the opposite of 0 is a whole
number. 6. Answers may vary. Sample: The integer -1 has
-1 as its reciprocal, so -1 is an integer whose reciprocal is an
integer. 7. Answers may vary. Sample: !2 and - !2 are
irrational numbers, but their product -2 is a rational number.
8. Answers may vary. They should be similar to counterexamples in (3) - (7). 9a. Answers may vary. Sample: 2 and
5 are whole numbers but 2 - 5 = -3, which is not a whole
number. 9b. Answers may vary. Sample: 5 is an integer, but
its opposite -5 is not a whole number. 9c. Answers may
vary. Sample: 3 is a whole number but 32 = 9, which is not an
even number. 9d. Answers may vary. Sample: -1 is an
integer, but not a whole number. 9e. Answers may vary.
Sample: 4 is a whole number and !4 is 2, which is not an
irrational number.
Practice 1-2
1. 7x 2. 14t - 5 3. -11a + b - 1 4. 2i + 7j 5. 12xy
6. 13x2 + 5x 7. 4m - 6 8. 1 a 1 1 b 9. 32 t2 1 2t
3
9
2
10. -a - 5 11. -8n - 16m 12. x2 - 2xy + y2
13a. 54 in.2 13b. 13.5 m2 14. $10.06 15. 85 16. 26
17. -42 18. -1421 19. 10 20. 1 21. 32 22. 13
All-In-One Answers
16. 19 17. 15
18. Mike’s bus: 35 mi/h; Adam’s bus: 55 mi/h
2
19. slower train: 50 mi/h; faster train: 100 mi/h
20. 81, 83, 85, and 87 21. length: 17 cm; width: 12 cm
Guided Problem Solving 1-3
1. $5000 2. $2000; $3000 3. 6%; 8% 4. P = 2000, r = 0.06,
t = 1 5. $2120 6. P = 3000, r = 0.08, t = 1 7. $3240
8. $360 9. $746.40 10. Answers may vary. Sample:
I = P(1 + r)t - P; Answers verify. 11. $26; $52.86
Practice 1-4
1. t -5
654321 0 1 2 3 4
2. m 8
0 1 2 3 4 5 6 7 8 9 10
3. x -2
654321 0 1 2 3 4
Algebra 2
75
Algebra 2: All-In-One Answers
(continued)
16. x -1 or x 3
4. a 2 72
7
2
54321 0 1 2 3 4 5
654321 0 1 2 3 4
17. x -1 and x 2, or -1 x 2
54321 0 1 2 3 4 5
6. x 2 12
1
2
54321 0 1 2 3 4 5
18. at least $4500
19. less than 35 ft
20. more than 15 years old
21. at least 1072 questionnaires
22. between 10.3 lb and 12.8 lb
23. at least 7.75 in. and at most 8.25 in.
24. between 4 h and 4.8 h, or between 4 h and 4 h 48 min
Guided Problem Solving 1-4
7. x 12
642 0 2 4 6 8 10 12 14
8. x 3
8
3
8
54321 0 1 2 3 4 5
9. x -16
18 16 14 12 10 8 6
10. -3 x 2
54321 0 1 2 3 4 5
11. x 2 or x 8
0 1 2 3 4 5 6 7 8 9 10
12. x -3 and x 6, or -3 x 6
4321 0 1 2 3 4 5 6
13. x 1 or x 2
54321 0 1 2 3 4 5
14. -3 x 5
4321 0 1 2 3 4 5 6
1. between $700,000 and $750,000 2. $496,000
3. 700,000 x + 496,000 750,000
4. 204,000 x 254,000 5. between $204,000 and $254,000
6. $204,000 + $496,000 = $700,000; $254,000 + $496,000 =
$750,000 7. between 18 hr and 25 hr
Practice 1-5
1. ∆h - 8.3« 2 2. ∆a« 2.5 3. ∆x - 27.5« 5.5
4. x -17 or x 7
17
7
20
10
0
10
20
30
5. k -16 and k 22, or -16 k 22
16
22
20
10
0
10
20
30
6. all real numbers
54321 0 1 2 3 4 5
7. t -2 and t 12, or -2 t 12
42 0 2 4 6 8 10 12 14 16
8. x 2 2 or x 2
3
2
3
54321 0 1 2 3 4 5
15. -2 x -1
54321 0 1 2 3 4 5
76
Algebra 2
All rights reserved.
987654321 0 1
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5. x -8
Algebra 2: All-In-One Answers
(continued)
9. b 2 32 and b 12 , or 2 23 b 12
3
1
2
2
54321 0 1 2 3 4 5
10. w 2 2 or w 2
3
7. Answers may vary.; The experimental probability is expected to be close to the theoretical probability
5 5 0.3125 < 0.31, or 31%
16
8. Answers may vary.; The experimental probability is
expected to be close to the theoretical probability
1 5 0.015625 < 0.02, or 2%
64
1 5 0.03125 < 0.03, or 3%
9. 144p < 0.09, or 9% 10. 32
5000
2
3
Guided Problem Solving 1-6
54321 0 1 2 3 4 5
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
All rights reserved.
11. all real numbers
54321 0 1 2 3 4 5
12. u -3 or u 3
54321 0 1 2 3 4 5
1. 1, 2, 3, 4, 5, 6 2. Answers may vary. Sample: (3,2)
3. (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4),
(2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3),
(4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2),
(6,3), (6,4), (6,5), (6,6) 4. 36 5. 1 6. 1 7. 6 8. 1
6
36
9. Answers may vary. Experimental probabilities should be
close to theoretical probabilities. 10a. (H,H,H), (H,H,T),
(H,T,H), (T,H,H), (T,T,H), (T,H,T), (H,T,T), (T,T,T) 10b. 8
10c. 1 10d. 3
8
8
13. -7, 7 14. no solution 15. 2 16. -27, 3 17. -21, 21
1A: Graphic Organizer
18. 2 11 , 1 19. no solution 20. 2 20 , 4 21. -3, 3
7
5
1
22. -4, 2 23. 2 24. no solution
25. ∆x - 4.2« 0.01; 4.19 x 4.21
26. ∆x - 3.5« 0.002; 3.498 x 3.502
27. ∆x - 10« 1 ; 9 11 x 10 1
12 12
12
28. ∆T - 76« 11; 65 T 87
29. ∆w - 40« 0.25; 39.75 w 40.25
30. ∆d - 13.75« 11.25; 2.5 d 25
1. Tools of Algebra 2. Answers may vary. Sample: properties
Guided Problem Solving 1-5
1. Find a value for b that makes the equation true.
2. distance 3. |4 - 8b| = -12 4. no 5. no solution
6. For any value of b, the left side of the equality is negative.
7. no solution
of real numbers, solving equations, solving inequalities,
probability 3. Check students’ work.
1B: Reading Comprehension
1. temperature scales 2. degrees of temperature 3. 18 years
4. degree 5. 32° (the freezing point of pure water)
6. Fahrenheit used a mixture of salt and ice; Celsius used the
freezing point of pure water. 7. Answers may vary. Sample:
No. There were 96 degrees between 0° F and normal body
temperature. There are almost the same number of degrees
between the freezing and boiling points of water. Since the
difference between the high and low temperatures on the
Celsius scale is greater, Celsius degrees must be significantly
greater than Fahrenheit degrees. 8. b
1C: Reading/Writing Math Symbols
Practice 1-6
1a. 1 , or 20% 1b. 2 , or 40% 1c. 3 , or 60%
5
5
5
1d. 4 , or 80% 2a. 8 < 0.42, or 42% 2b. 4 < 0.21,
19
19
5
7
2
or 21% 2c.
< 0.11, or 11% 2d.
< 0.37, or 37%
19
19
3a. 12 , or 50% 3b. 31 < 0.33, or 33% 3c. 61 < 0.17, or 17%
3d. 56 < 0.83, or 83%
4a. {$6, $11, $15, $21, $25, $30}; 6 outcomes
4b. 61 < 0.17, or 17% 4c. 0 4d. 13 < 0.33, or 33%
47 < 0.67, or 67%
5. 13 < 0.54, or 54% 6. 70
24
All-In-One Answers
1. 5 multiplied by 9 or 5 times 9 2. 1, 2, 3 and the pattern
continues in the same way. 3. 12 divided by 0.4
4. the square root of 7 5. |–3| 6. x 8 or x
7. w = 29
8
5
8. x 9. "5 10. 2, 4, 6, . . .
1D: Visual Vocabulary Practice
1. variable 2. term 3. coefficient 4. opposite 5. absolute
value 6. compound inequality 7. multiplicative inverse
8. algebraic expression 9. experimental probability
Algebra 2
77
(continued)
10.
Opposite: The additive inverse of any number, a, is -a.
Reciprocal: The multiplicative inverse of any nonzero number,
a, is a1.
Absolute value of a real number: The distance from a real
number to zero on the number line.
Variable expression: An expression that contains one or more
variables.
Solution of an equation: A number that makes the equation
true.
2
x
2
1. -8; 2 12 ; 17; 37 2. 1 2 ; 1 1 ; 0; 21 1 3. 7.8; 3.3; -7.2; -19.2
6
3
3
4. not a function 5. not a function 6. function
7.
10
; domain: {1, 2, 3, 5};
range: e 22, 3 , 3 1 , 9 f
4 2
y
6
2
2
8.
4
; domain: {-3, 0, 1};
range: {-2, 4, 5}
6
2
3
3
4
15.
; function
1
0
1
2
3
0
1
4
9
16. 1 17. 3 18. 2 19. 10
3
7
Guided Problem Solving 2-1
1. The radius. 2. 10.5 cm 3. v(r) = 4/3pr3 4. 10.5 or 10.5 cm
5. cm3 6. about 4849 cm3 7. 4849 = 43pr3; r 10.5
8. v(s) = s3; 1520.875 cm3
2
1
1
9. y 2 1 5 2 13 (x 2 0) 10. y 2 3 5 2 2 ax 2 2 b
11. y 1 2 5 2(x 1 3)
12.
x
O
2
1. 2 2. 5 3. 23 4. 2 21 5. 32 6. 2 7. 31 8. 2 72
5
y
2
2
Practice 2-2
x
O
1
5
Chapter 2
Practice 2-1
2
11. not a function 12. function 13. not a function
14.
; not a function
1. multiplicative inverse 2. solution 3. algebraic expression
4. additive inverse 5. theoretical probability 6–8. Answers
may vary. Samples given. 6. The
of a number is the
distance between that number and zero on a number line.
O
2
1F: Vocabulary Review
7. The additive inverse of a number is its
.
8. The
is the multiplicative inverse of a number.
; domain: {0.5};
range: {-1, 0, 1, 3}
y
All rights reserved.
1E: Vocabulary Check
2
13.
y
y
O
4
x
2
4
2
2
9.
; domain: {-1, 2, 3};
range: {2}
y
2
x
2
O
2
x
O
2
14.
4
4
6
y
2
2
x
2
O
2
2
78
Algebra 2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Algebra 2: All-In-One Answers
Algebra 2: All-In-One Answers
(continued)
15. 4x + y = 10 16. 2x - 5y = -17 17. y = -4
Guided Problem Solving 2-3
18. 3 ; (0, -3); (4, 0) 19. 0; (0, -2); none
1. 392 mi 2. 14 gallons 3. k = 28 4. y = 28x 5. 103.6 mi
6. 417.9 gallons 7. $0.056
8a. y = 28x; 392 = 28 3 14
mi
8b. 103.6 = 28x; x = 3.7 8c. y = 28 3 417.9; y ≈ 11,700
9a. y = 58x 9b. 145 mi 9c. 75 gallons
4
20. 4 ; (0, 7); a2 35 , 0b 21. undefined; none; (5, 0)
4
5
22. y = 2x + 5;
23. y 5 53 x 2 43 ;
y
y
2
Practice 2-4
2
x
2
O
x
2
2
All rights reserved.
2
O
2
2
24. x = -3;
9
8
7
6
5
4
3
2
1
25. y = 1;
y
y
2
2
x
2
1. y = 0.6x - 2.1 2. y = -2.04x + 7.548
3. y = 1.2x + 200; $214.40 4. y = 58x; 464 words
5. y = 146x + 5000; 6460 subscribers
6. 10
;
O
x
2
2
O
2
2
y
x
O
2
1 2 3 4 5 6 7 8 9 10
yes; using (3, 3.1) and (7, 5.2): y = 0.525x + 1.525
7. 10
; no
9
8
7
6
5
4
3
2
1
Guided Problem Solving 2-2
1. a 32, 212 b , a223, 13 b 2. The slope of the line through the
points 3. slope = (x2 2 x1) 4. a223, 13 b
2
1
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
(y 2 y )
1 2 (21)
5. slope = 3 2 32
23 2 2
5 7. 2 5 8. 3
6. 2 13
13
O
y
x
1 2 3 4 5 6 7 8 9 10
8.
Practice 2-3
4
9
1. 2 32 ; 2 2 2. 6; 18 3. 9 ; 27 4. yes; 4 5. yes; -1.2
2
9
16 16
6. yes; -4 7. no 8. yes; 3 9. no 10. yes; 3 11. no
5
x
2
O
12. no 13. yes; 3; y = 3x 14. yes; 21 ; y 5 12 x 15. no
2
16. y 5 13 x 17. y = -6x 18. y = -18x 19. y 5 3 x
7
4
20. y 5 23 x 21. y 5 2 35 x 22. y 5 52 x 23. y = 55x
6
24. 10
25. 2 16
26. 11 27. 5
3
3
34
29. 46.08 in.
28. y = 0.06x; 22 min
2
yes; using (-1, -1.8) and (1, 1.9): y = 1.85x + 0.05
9.
; no
y
6
5
4
3
2
1
x
O
All-In-One Answers
;
y
1
2
3
Algebra 2
79
Algebra 2: All-In-One Answers
10a.
(continued)
11.
y
20
18
16
14
12
10
8
12.
y
4
2
O
y
6
x
2
4
2
2
4
x
O
x
13.
10b. using (9.4, 11.2) and (15.1, 19.1): y = 1.39x - 1.83
10c. about 15.5% 10d. yes
14.
y
2
4
x
2
O
2
x
1. Equation 2. Yes
3.
y
y
2
2
Guided Problem Solving 2-4
6
O
2
4
4
40
Fat (g)
15.
16.
y
30
x
4
20
y
4
2
10
x
x
O
200 300 400 500 600 700
Calories
17.
4. slope = 0.076 5. y = 0.076x - 10.04 6. about 15 g
7. Yes, it is a good fit. 8. about 606 Calories
O
18.
y
4
x
2
x
2
O
y
4
2
O
2
20.
2
4
O
10.
y
4
x
2
y
21.
2
x
x
4
2
O
4
2
O
2
O
2
2
4
4
2
2
2
2
9.
2
y
x
x
O
2
6
y
2
x
4
4
19.
2
2
y
2
2
1. E 2. C 3. A 4. F 5. B 6. D
7.
8.
y
O
4
2
4
Practice 2-5
2
2
2
2
O
y
x
O
2
4
2
4
80
Algebra 2
All rights reserved.
8 10 12 14 16 18 20
4
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
O
2
Algebra 2: All-In-One Answers
(continued)
3. vertical;
Guided Problem Solving 2-5
1. Graph the two equations. 2. Compare the graphs. Look for
similarities and differences. 3a. y 2 3 5 P 12x 2 6 P
O
2
2
x
2
1x 2 6 5 2(y 2 3)
2
2
O
2
2
4
5.–6.
y
6
2
12 8
All rights reserved.
y
x
2
3b. 2y 2 3 5 P 12x 1 6 P 4. 12x 2 6 5 y 2 3,
4
2
5. combined;
6. horizontal;
y
O
4
8
x
12
y
4
4
2
2
6
x
O
1 x 1 6 5 –y – 3, 1x 1 6 5 y 1 3
2
2
different vertices, and one points up while the other points
down. 8. Test points should result in true statements.
9.
y
5
4
3
2
1
x
54321
1 2 3 4 5
1
2
3
4
5
2
4
11. y = ∆x + 3« - 2 12. y 5 2u x u 1 3
5
13. y
15. y
17. y
19. y
21. y
= ∆x« - 3 14. y = ∆x - 1«
= ∆x + 2« + 1 16. y = -∆x« + 2
= -∆x + 2« 18. y = -∆x - 1« - 2
= 3∆x« - 4 20. y =
1 ∆x - 2«
2
= 2∆x + 3« - 1
22.
y
2
x
2
O
2
2
Practice 2-6
1. horizontal;
2. horizontal;
y
23.
y
4
4
2
2
O
All-In-One Answers
x
4
2
O
y
2
x
x
2
O
4
9. y = -∆x - 1« + 3 10. y 5 2` x 2 12 ` 2 23
The graphs have the same size and shape. They have different
vertices, and one points up while the other points down.
4
2
x
7. y = ∆x + 2« + 1 8. y = ∆x - 4«
7. The graphs have the same size and shape. They have
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
4. combined;
y
2
O
2
2
Algebra 2
81
17.
y
18.
y
2
2
2
x
x
2
y
O
2
2
O
x
2
2
2
2
19.
Guided Problem Solving 2-6
2
2
20.
y
y
2
2
1. A translation shifts a graph horizontally, vertically, or both.
2. years 3. x-axis 4. horizontal 5. left 6. horizontal
7. The graphs and answers agree. 8. Vertical; the graph is
O
x
x
2
shifted up
O
2
2
O
2
2
2
Practice 2-7
1. y x - 2 2. x - 2y 4 3. y - 2x 4
4. y -2 5. x 2 6. -2x - 3y 6
7. 3x - y 3 8. y - 3x 3
9.
10.
y
y
2
21.
2
2
2
O
O
x
2
2
2
x
2
2
x
2
O
y
2
x
2
22.
y
2
2
12.
y
23.
24.
y
y
2
y
2
2
2
2
2
2
2
O
2
2
2
14.
y
25.
26.
y
y
2
y
x
2
2
2
x
2
O
2
2
x
x
2
2
O
2
27.
O
28.
y
16.
y
y
x
O
x
2
2
82
Algebra 2
2
x
2
O
2
2
2
y
2
O
O
2
2
2
15.
2
2
4
13.
O
2
2
x
O
x
x
x
O
2
2
2
11.
O
2
2
x
2
O
2
2
2
29a. x + y 150, where x represents the number of tuna
sandwiches and y represents the number of ham sandwiches
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
24.
(continued)
All rights reserved.
Algebra 2: All-In-One Answers
Algebra 2: All-In-One Answers
(continued)
29b. 200
y
2D: Visual Vocabulary Practice
1. Constant of variation 2. Slope 3. Scatter plot
4. Translation 5. Standard form of a linear equation
6. Absolute value function 7. Trend line 8. Slope-intercept
form 9. Point-slope form
150
100
50
x
O
50
100 150 200
29c. Yes; the sum of 90 and 80 is more than 150.
30a. 150x + 200y 1800, where x represents the number of
$150 models and y represents the number of $200 models
All rights reserved.
30b. 16
y
12
8
2E: Vocabulary Check
Relation: A set of pairs of input and output values.
Domain: The set of all inputs, or x-coordinates, of the ordered
pairs of a relation.
Range: The set of all outputs, or y-coordinates, of the ordered
pairs of a relation.
Function: A relation in which each element of the domain is
paired with exactly one element of the range.
x-intercept: The point at which a line crosses the x-axis (or the
x-coordinate of that point).
2F: Vocabulary Review Puzzle
4
1
x
O
4
8
12
16
30c. at least four $150 models
Guided Problem Solving 2-7
4
T
R
2
D
R
O
E
M
L
A
N
5
S
L
A
I
L
T
N
O
I
P
O
E
N
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1. Functions, Equations, and Graphs 2. Answers may vary.
Sample: linear equations, direct variation, absolute value
functions and graphs, two-variable inequalities
3. Check students’ work.
2B: Reading Comprehension
1. graph paper, pencil, a ruler, and colored pencils or pens
2. plot; make; classify 3. points plotted on the same graph as
the line 4. three lists of points; one for above, one for on,
and one for below the line 5. a phrase that is one of the
3 choices: on the line, above the line, and below the line.
6. Step IV asks about the equation while Step III asks about
an inequality.
2C: Reading/Writing Math Symbols
1. The theoretical probability of 3 occurring is 1 in 6.
2. the theoretical probability of not taking Spanish
3. a function f of x 4. f of 5, or the value of function f
when 5 is the value of the variable 5. The function A (or
F
U
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O
I
N
C
T
6
L
I
N
E
G
E
A
R
O
7
1. dashed 2. to the right or above 3. x = -3
4. not part 5. > 6. x -3 7. 0 -3; Yes 8. x 2
2A: Graphic Organizer
3
R
A
N
Chapter 3
Practice 3-1
1. Independent 2. Inconsistent 3. Dependent
4. Independent 5. Dependent 6. Independent
7. Independent 8. Inconsistent 9. Independent
10. Inconsistent 11. Independent 12. Dependent
13a. Income: y = 2000x - 500, where x = 1 represents May;
Expenses: y = -2600x + 24000, where x = 1 represents May
13b. October (the sixth month) 14. (6, 4) 15. (5, 2)
16. (12, 1) 17. (2, 1) 18. (1, -2) 19. (2, 3) 20. (-4, 0)
21. (-1, 3) 22. a 23 , 24b 23. (-8, -1) 24. (2, 2)
25. (5, 1)
Guided Problem Solving 3-1
1. 6; 80 2. 4; 100 3. The number of flyers addressed after
x minutes 4. y = 6x + 80 5. y = 4x + 100
Area) of s (or the side of a square) is equal to s2 (or the
z
length of the side squared). 6. x2 2 0 7. z : 7 or
7
4 5 x or 4 : 10 = x : 18 10. g(7)
8. P(red) 9. 10
18
All-In-One Answers
Algebra 2
83
Algebra 2: All-In-One Answers
6.
140
(continued)
Practice 3-3
y
1.
120
100
642
2
4
6
80
2.
y
6
4
6
4
x
O
6
4 6
2
2
4
6
y
x
O
2 4 6
60
20
4
O
x
O
642
2
x
2 4 6 8 1012
4.
y
2 4
y
8
6
4
2O
x
642
2 4 6
4
7. (10, 140) 8. 10 minutes 9. Yes; y = 6(10) + 80 = 140
and y = 4(10) + 100 = 140
5.
10. y = 3x + 5; y = 2x + 20;
80
70
60
50
40
30
20
10
y
6.
y
After 15 minutes, the
numbers of newspapers is
the same at 50.
6
4
2
O
2
2
x
5
10
15
7.
6
4
20
Practice 3-2
x
O
42
2
1. (6, 4) 2. (4, 1) 3. (5, 2) 4. (1, 2) 5. (4, 3) 6. a5, 2 1 b
8.
y
8
2 4
y
x
O
42
2
4
6
x
2
All rights reserved.
8
8
4
y
6
4
2O
x
42
2 4 6 8
2
5
7. (1, 1) 8. (2, -2) 9. (5, -2) 10. C = 525 + 150p;
I = 325p; three performances 11. (2, 3) 12. (4, 6)
13. (0, 3) 14. (-3, 5) 15. (4, 1) 16. (6, 3) 17. (2, -2)
18. (3, 0) 19. (-4, -4) 20. 8r + 1g = 4.60,
6
6
9.
6r + 3g = 4.80, where r represents number of oranges and
g represents number of grapefruits; oranges = $.50,
grapefruits = $.60 21. (1, 4) 22. (-2, 3) 23. (0, 3)
24. (1, -2) 25. e (x, y): y 5 2 15 x 1 15 f 26. (-4, 5)
10. y
y
2
2
x
2
O
x
O
2
2
4
6
2
27. (-3, 2) 28. No solution 29. (2.25, 0)
Guided Problem Solving 3-2
1. $40,000 plus $2800 per performance 2. $3675
3. y = 40,000 + 2800x 4. y = 3675x
5. 40,000 + 2800x = 3675x 6. x ≈ 45.7
7. 46 performances 8. Yes; y = 40,000 + 2800(46) = 168,800,
y = 3675(46) = 169,050 9. 612 trips
11.
12.
y
2
2
x
2
O
2
y
2
O
x
2
2
4
6
84
Algebra 2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
3.
40
Algebra 2: All-In-One Answers
(continued)
x1y$6
2x 1 5y # 20
13a. µ
,
x$0
y$0
where x represents number of spiral notebooks and y
represents number of three-ring notebooks
13b.
y
19.
20.
y
6
4
6
4
x
O
642
4
6
4
21.
y
x
O
4
22.
x
O
2 4 6
y
2
2
4
All rights reserved.
642
2
4
6
2 4 6
y
x
6
Solutions correspond to points in shaded region with integer
coordinates.
x 1 y # 30
14a. • x $ 10
,
y$5
where x represents number of campers on the low trail and y
represents number of campers on the high trail
14b.
y
4
2
x
2
O
2
23.
O
2
2
y
2
x
4
2
O
2
40
20
O
20
Guided Problem Solving 3-3
x
40
1. 7, 8, 9, 10 2. more (or greater) 3. j 0; s 0; s j;
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
j + s 7; j + s 10
Solutions correspond to points in shaded region with integer
coordinates.
15.
6
16.
y
4. s
y
4
O
642
2
x
x
4 6
4
3
1
18.
y
6
O
y
4
O
642
2
5
4
4
6
17.
O
x
2 4 6
O
642
4
6
x
2 4 6
1
3
5
j
5. (1, 6), (1, 7), (1, 8), (1, 9), (2, 5), (2, 6), (2, 7), (2, 8), (3, 4),
(3, 5), (3, 6), (3, 7), (4, 5), (4, 6) 6. Yes, substituting each
combination listed in (8) into the inequalities of the system
results in a true statement.
7a. x 0; y 0; x + y 5; x + y 8; x y or y x
7b. y
(3, 2), (4, 1), (4, 2), (4, 3),
8
(5, 0), (5, 1), (5, 2), (5, 3),
7
(6, 0), (6, 1), (6, 2), (7, 0),
6
(7, 1), (8, 0)
5
4
3
2
1
x
1 2 3 4 5 6 7 8
All-In-One Answers
Algebra 2
85
Algebra 2: All-In-One Answers
6.
Practice 3-4
; (2, 1)
y
(2, 2)
2
O
1
2.
(4, 1)
(2, 1)
3 4 5 6
x
; (0, 4)
y
7
6
5 (0, 4)
(2, 3)
3
Guided Problem Solving 3-4
1. corn muffins: 4 c; bran muffins: 2 c; baker has 16 c
2. corn muffins: 3 c; bran muffins: 3 c; baker has 15 c
3. P = 3c + 2b
4. c 0, b 0, 4c + 2b 16 (milk), 3c + 3b 15 (flour)
5.
y
2
1 O
(5, 0)
x
1 2 3 4 5
3.
b
; (5, 0)
y
7
(0, 6)
6
5
4
3
(4, 2)
2
1 O
(5, 0)x
1 2 3 4
6 7
4.
7
6
5
7. (0, 10); 30 8. (4, 0); 4 9. (8, 8); 32 10a. Four loaves of
Irish soda bread and two Kugelhopf cakes 10b. $14
11a. 10 qt regular, 4 qt extra-rich 11b. $132
; (2, 0)
y
(0,5)
(3,2)
(0,0)
(4,0)
c
(0, 0), (0, 5), (4, 0), (3, 2) 6. At (0, 0), P = 0; At (0, 5),
P = 10; At (4, 0), P = 12, At (3, 2), P = 13 maximized at (3, 2)
7. 3 trays of cranberry muffins and 2 trays of bran muffins
8. Yes, other points in the feasible region result in P 13.
9. 40 Q, 60 R
Practice 3-5
3 (0, 2)
6 ,6
1 O 5 5(2, 0)
x
1 2 3
5 6 7
( )
5.
; (1, 0)
y
3
2
(0, 1)
2 ,2
3 3
(1, 0)
O
1
2
3
1. From the origin, move forward three units. 2. From the
origin, move right two units. 3. From the origin, move forward three units, left two units, and down 4 units. 4. From the
origin, move back six units, left four units, and down one unit.
5. From the origin, move up four units. 6. From the origin,
move forward one unit, right two units, and up three units.
7. From the origin, move forward three units, left one unit,
and up six units. 8. From the origin, move right four units,
and down one unit.
( )
86
Algebra 2
All rights reserved.
7
6
5
4
; (0, 0)
y
7
6 (0, 5)
5
(1, 4)
4
3
2
1 O (2, 0)
x
1
3 4 5 6 7
x
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1.
(continued)
Algebra 2: All-In-One Answers
9.
(continued)
13.
z
z
5
5
5
5
5
5 y
5
5
x
5 y
5
x
5
5
10.
14.
z
z
5
All rights reserved.
5
5
5
5
5
5 y
5 y
5
x
5
x
5
5
11.
15.
z
z
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5
5
5
5
5
5 y
5
5
x
5 y
5
x
5
12.
5
16.
z
z
5
5
5
5
5
5 y
5
x
5
5 y
x
5
All-In-One Answers
5
Algebra 2
87
Algebra 2: All-In-One Answers
(continued)
17. (0, 0, 0) 18. (0, 0, 1) 19. (0, 2, 0) 20. (3, 0, 0)
21. (0, 4, -2) 22. (0, -2, 3) 23. (-5, 0, 3) 24. (1, -1, -3)
25.
z
28.
z
5
5
5
5
5
5
5 y
5
x
5 y
5
x
z
29.
5
26.
5
z
5
5
5
5 y
All rights reserved.
5
5
x
5
5 y
5
x
30.
z
5
5
27.
z
5
5
5
5
5 y
5
x
5
5 y
5
x
31.
z
5
10
10
10
10 y
10
x
10
88
Algebra 2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5
Algebra 2: All-In-One Answers
32.
(continued)
36. x + 2y = 6, x + 3z = 6, 2y + 3z = 6;
z
z
5
5
5
5
5
5 y
5
x
5
5 y
5
x
5
33.
5
z
37. x + 3y = 6, x + 2z = 6, 3y + 2z = 6;
All rights reserved.
5
z
5
5
5
5
y
5
x
5
5
5
x
34.
5
z
38. 2x + 3y = 6, 2x + z = 6, 3y + z = 6;
3
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5 y
4
z
5
y
6
5
x
6
5
35. x + y = 3, x + z = 3, y + z = 3;
z
5
5 y
5
x
5
5
5
5 y
5
x
5
All-In-One Answers
Algebra 2
89
Algebra 2: All-In-One Answers
39. -4x + 2y = 8, -4x - 4z = 8, 2y - 4z = 8;
(continued)
42. 7x - 3y = 21, 7x + 7z = 21, -3y + 7z = 21;
z
z
5
5
5
5
5
5
y
5 y
5
5
x
5
x
5
40. 4x - 2y = 12, 4x + 6z = 12, -2y + 6z = 12;
43. 4x - 3y = -12, 4x + 6z = -12, -3y + 6z = -12;
z
z
5
5
5
5
5
5 y
5
5
x
All rights reserved.
5
5 y
5
x
5
Guided Problem Solving 3-5
1. y and z 2. x and z 3. x and y 4. x-intercept: (6, 0, 0);
y-intercept: (0, 6, 0); z-intercept: (0, 0, -3) 5. x + y = 6
6. x - 2z = 6 7. y - 2z = 6
8.
z
z
5
6y
5
6
3
x
5
5 y
5
x
9. The results are the same.
10.
z
xy-trace: 4x + 9y = -36;
xz-trace: 4x - 9z = -36;
yz-trace: 9y - 9z = -36
5
y
x
90
Algebra 2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
41. 6x - 3y = 6, 6x + z = 6, -3y + z = 6;
Algebra 2: All-In-One Answers
(continued)
Practice 3-6
3E: Vocabulary Check
1. No unique solution 2. (4, 0, -1) 3. (3, 3, 3)
4. No solution 5. (-1, 1, -1) 6. (4, 1, 3) 7. (5, -1, -2)
8. (-3, -2, -1) 9. (2, -2, 2) 10. (2, -1, -3)
11. (-2, 0, 5) 12. (4, -1, -2) 13. (1, 1, 2) 14. (3, 1, -6)
Linear system: This is a set of two or more linear equations
that use the same variables.
Dependent system: This is a system that does not have a
unique solution.
Linear programming: A technique that identifies the
minimum or maximum value of some quantity. This quantity is
modeled with an objective function. Limits on the variables in
the objective function are constraints, written as linear
inequalities.
Objective function: In linear programming, this is a model
of the quantity that you want to make as larger or as small as
possible.
Trace: This is a set of ordered pairs that results from
substituting 0 for one of the variables in the equation of a
plane.
15. a21, 4, 1 b 16. a 2 , 2 1 , 1 1 b 17. (-2, -1, -2)
2
3
2
2
18. (-1, -3, -4) 19. (0, 5, 0) 20. (8, -1, -2) 21. (1, 2, 3)
22. (2, -3, -2) 23. No unique solution 24. (1, 1, 1)
All rights reserved.
25. µ
x 1 y 1 z 5 22
3x 1 2y 1 z 5 9
,
1
y 2 z 5 10
2
where x represents the first number, y represents the second
number, and z represents the third number; 3, 5, -10
x 1 5y 1 10z 5 96
26. • x 1 1 5 y 1 z
,
x 1 y 1 z 5 23
where x represents the number of $1 bills, y represents the
number of $5 bills, and z represents the number of $10 bills;
Eleven $1 bills, seven $5 bills, five $10 bills
Guided Problem Solving 3-6
1. weight of tail, weight of head, and weight of body
2. 9 lb 3. t = 9 4. h = t + 12b 5. b = h + t
6. (h, b, t) = (27, 36, 9) 7. 72 lb (27 + 36 + 9) 8. Yes, the
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
three weights satisfy each of the statements in the original
problem. 9. 11 hours (mathematics 1 hr, history report 4 hr,
speech 6 hr)
3A: Graphic Organizer
1. Linear Systems 2. Answers may vary. Sample: graphing
systems of equations, solving systems algebraically, systems of
inequalities, graphs in three dimensions 3. Check students’ work.
3B: Reading Comprehension
1. alphabetical order 2. where to find the word in the text
3. It repeats the word being defined. 4. an example of what is
being defined 5. See if it is defined in the glossary. If not,
look it up in a dictionary. 6. a
3C: Reading/Writing Math Symbols
1. The most commonly used letter is f, but accept all
reasonable responses. 2. The most commonly used letters
are x and y, but accept all reasonable responses. 3. m 4. w
5. l 6. the measure of angle A, usually in degrees 7. P(7)
3D: Visual Vocabulary Practice/High-Use
Academic Words
3F: Vocabulary Review Puzzle
1. consistent 2. dependent 3. equivalent 4. inconsistent
5. independent 6. three
E
T
D
E
P
E
N
D
E
N
T
T
E
D
N
E
P
E
P
P
E
N
N
S
O
R
D
E
R
E
D
T
E
E
C
T
E
E
R
H
T
C
E
D
T
H
Q
N
I
R
D
N
F
S
N
S
R
T
E
I
H
S
E
P
I
E
I
H
A
R
S
A
I
Q
D
N
P
S
O
S
E
E
N
R
P
E
I
E
N
A
D
O
N
D
H
T
A
N
D
O
P
A
L
N
I
O
E
S
D
N
C
N
O
Q
E
D
L
R
C
N
I
N
E
L
B
I
S
A
E
F
P
O
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E
Q
U
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V
A
L
E
N
T
C
Chapter 4
Practice 4-1
1. 3 1; -3 2. 3 4; 5 3. 2 3; 12 4. 3 3; q
5. 3 2; 4 6. 1 4; -4
7. c
17.6 8.3 5.4 8.7 4.0 6.6 3.5
d
9.5 5.1 4.5 6.4 2.6 5.1 2.7
8. 2 7 9. 9.5; percent unemployment in construction in
June, 1996 10. 6.6; percent unemployment in services in
June, 1992 11. Answers may vary.
3900 3300
Sample: M 5 £ 400 150 § 12. 3 2
100
50
13. number of days lost to strikes per 1,000 employees in
Greece in the given years 14. number of days lost to strikes
per 1,000 employees in the United States from 1990 to 1994
1. Define 2. Evaluate 3. Approximate 4. Interpret
5. Model 6. Set 7. Compare 8. Property 9. Test
All-In-One Answers
Algebra 2
91
Algebra 2: All-In-One Answers
(continued)
Guided Problem Solving 4-1
Guided Problem Solving 4-2
1. table 2. matrix 3. weeks
4. Estimates may vary. Sample:
1. 2, 3 2. 2
Types of CD
Rock
R&B
Rap
Classical
Wk 1
165
100
96
98
Wk2
150
94
90
97
Wk3
200
110
110
97
Wk4
180
98
100
102
Plastic Rubber
500
700 ;
R
B
3– color 1300 1900
3. Plant 1: 1– color
Plastic Rubber
Plant 2: 1– color 400
1200
R
B
1600
3– color 600
5.
Vanilla
Chocolate
Strawberry
8b.
Day 1
50
175
25
Day 2
75
125
50
Day 3
25
150
25
Day 1 Day 2 Day 3
Vanilla
50
75
25
Chocolate C175
125
150S
Strawberry
25
50
25
Columns represent the days of Labor Day Weekend and
rows are the flavors of ice cream.
Practice 4-2
1. a = 5; b 5 2 7 ; c = 12; d = 7 2. c 5 5 ; y = -7;
2
3
x = 4; z 5 7 ; a = -3; b = 0 3. x = 3; z = -2
2
37 56
23 58
0 76
93 82
4. M 5 ≥
¥;F 5 ≥
¥
87 102
0 34
6 27
18 29
14 22
293 26
22 3
¥ 6. c
d
5. M 2 F 5 ≥
87 68
2 0
212 22
8 25 26
22
2
27
12 § 8. £ 26
5 § 9. £ 24 §
7. £ 3 28
4 212 218
24 22
23
8 11
227 101 22
21 24
d
10. £ 13 14 § 11. £ 219 93 21 § 12. c
0
4
4 11
28 21 20
13. c
0 24 3
d 14. not equal; dimensions are different
24 22 5
Plastic Rubber
Plant 2: 1– color 1200
3600
R
B
3– color 1800 4800
5. c
All rights reserved.
8a. Flavor
Plastic Rubber
4. Plant 1: 1– color 1000 1400 ;
R
B
3– color 2600 3800
2200 22200
d
800 21000
6. Plant 1; 800
7. Plant 2; 2200
8. The answers check.
Big
Small
270 ;
R
B
60 108
9a. Carrier A: Envelopes 120
Boxes
Big Small
Carrier B: Envelopes 160 300
R
B
25 100
Boxes
9b. c
240 230
d ; B; A
35
8
Practice 4-3
1. product undefined 2. c
6 22
4
d 3. c
6
0
23
4 21
1
4. difference undefined 5. c
d 6. c
3
1
3
1
d
7
21
d
22
0 2
7. product undefined 8. £ 22 1 § 9. product undefined
21 0
16
3 23 21
10. c d 11. c
d
2 22
4
20
12. product undefined 13. c
7 3
2 0
d 14. c
d
0 2
0 2
0 0.4
15. product undefined 16. £ 20.4 0.2 §
20.2
17. ≥
3 23 21
4
4
4
1 21
2
2
1
¥ 18. c
0
0.5 20.5 22.5
d
2.5 22.5 25.5
15. equal; dimensions and corresponding elements are equal
92
Algebra 2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Week 1 Week 2 Week 3 Week 4
Rock
165
150
200
180
R&B
100
94
110
98
T
D
Rap
96
90
110
100
Classical
98
97
97
102
6. Columns represent the weeks in August and rows are the
type of CDs sold.
7. The new bar graph should be the same as the one given.
Algebra 2: All-In-One Answers
(continued)
12.
19. product undefined 20. product undefined
72
4 5
23. 2 3 2; c
d 24. £ 60
5 4
0
213 19 28
25. £ 224 42 214 § 26.
25 8 23
All rights reserved.
y
6
4
x
x
6
24
72 §
212
O
6
4
6
11 10
21 1 1
c
d 27. £ 11 10 §
26 5 5
11 10
23
8 14 14 12
51 24
28. £ 16 8 8 10 § 29. c
d 30. D
T
117 55
5 22
18 18 20 14
3
2
2
31. C 20 S
4
3
O
4
4
14.
15.
y
y
4
4
x
4
8
3
x
4
4
O
4
16.
O
4
4
y
4
x
4
Guided Problem Solving 4-3
150 130 160
5. £ 125 130 175 § 6. 3 3 7. 1 3
60 52 80
Thurs Fri Sat
8. Revenue [2100 1950 2570] 9. The answers check.
Cost
10. Summer 1,270,000
Winter
B
R
1,010,000
Practice 4-4
1. c
44
44 233
5 5 22
d
d 2. c
22 222
0
6 2
4
6
6 24.5
6
6 21
d
d 4. c
3. c
3 23
0
24 28 26
2 22
0
2 22 0
5. c
d 6. c
d
4
4 23
24 24 3
22 2
0
3
3 24
1
1 26
7. c
d 8. c
d 9. c
d
4 4 23
0 24 22
3 21
1
2
2 21.5
4 4 23
10. c
d 11. c
d
1 21
0
22 2
0
4
17. 17 c
21
0 214 0
3
0
d 5 c
214 27
0 7
22 21
2
0 22
0
0
0
18. c
d 1 c
d 5
0 22
0
22 22 22
0 21 2
0 22
0 2
19. c
dc
d 5 c
21
0 0 22
0
22 0
22 0
d
0 1
2
0 22
c
d
22 24 22
0
d
2
Guided Problem Solving 4-4
1. 5 2. 1 3. subtract 5 from each x-coordinate
4. add 1 to each y-coordinate
5. c
25 25 25 25
28 28 23 23
d 6. c
d
1
1
1
1
21 23 21 23
7. Yes, the graphs verify the answers.
8. c
All-In-One Answers
O
4
1. no 2. yes 3. [7 6 5] 4. 1 3
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
13.
y
1 2 3 4
71 34
21. 3 3 4; £ 2 4 6 8 § 22. 2 3 2; c
d
49 56
3 6 9 12
7
2 8
d
26 28 0
Algebra 2
93
Algebra 2: All-In-One Answers
(continued)
Practice 4-5
Guided Problem Solving 4-6
2
0 1
21
3
¥ 3. c
d 4. c
d
21 2
1 22
1
2
1 21
6
6
23
4
25
7
d 6. c
d 7. ≥
¥
5. c
1 21
3 24
1
1
8
8
8. No inverse; the determinant of the matrix is zero.
22
2 3 22
10
5
1
§ 10. ≥
¥
9. £ 3
21
2
2
2 5 23
2
11. no inverse, cannot be solved 12. c d 13. c d
1
2
3
4
14. -1 15. -21 16. 14 17. -29 18. 9 19. 36
20. yes 21. yes 22. yes
a determinant.
3. (a1b2c3 + a2b3c1 + a3b1c2) - (a1b3c2 + a2b1c3 + a3b2c1)
4. -30 5. Yes, the determinant is the same. 6. 52
Practice 4-7
1. (0.251, 0.3, 0.07) 2. (0.7, -0.3, -0.2) 3. (1, 5, -5)
4. (2, 1) 5. (2, 1, -9) 6. (3, 2) 7. (-5, 15, 21) 8. (-1, 0)
9. (0, 6, 2.8) 10. (-2, -1) 11. (-1, 7, -3) 12. (4, 2, -8)
coefficient
variable
constant
6 9
13. c
d
4 13
x
c d
y
=
c
36
d
2
14. c
x
c d
y
=
c
29
d
24
3 24
d
0
7
Guided Problem Solving 4-5
4
0 21
x
9
15. £ 12
2
0§
£y§ =
£ 17 §
1 21 12
z
3
x1
y 5 548,303
16. e
;
0.2553415x 1 0.1167209y 5 110,017
(331,975.0482, 216,327.9518); about 331,975 doctors
1. subtract c
17. e
2 7
d from both sides of the equation
23 4
4 7
4 25
dX 5 c
d 4. 1
2. A-1 3. c
1 2
1 21
2 27
1 23
d 6. c
d
5. c
21
4
0
1
7. Yes, the equation is true.
5
1
d
8. c
2 22
Practice 4-6
3 10
6
3 21 21
3
2§
1. £ 21 25 23 § 2. £ 26
22 27 24
4 22 21
29 11
19
3. £ 1 21 22 § 4. no inverse
5 26 210
0.65 21.45 20.2
5. £ 20.8
1.4
0.4 § 6. no inverse
0.4 20.2 20.2
x1
y5
50
; (20, 30);
425x 1 550y 5 25,000
20 one-bedroom and 30 two-bedroom apartments
3 , 233 b 19. a8, 4 b 20. no unique solution
18. a 17
3
17
21. (4, –32) 22. det A = 10, has a unique solution
23. det A = 0, no unique solution 24. det A = -5, has a
unique solution
Guided Problem Solving 4-7
1. l = 2w 2. 840 ft
3. c
2 21
0
dX 5 c
d 4. 6
2
2
840
1
3
1
6
5. C 1 1S 6. c
d
280
23 3
140
7. width = 140 ft, length = 280 ft 8. The answers check.
9. 6 yards; 14 yards
Practice 4-8
9. £ 25 § 10. £ 1 § 11. no inverse, cannot be solved
4x 2 2y 5 3
12x 1 6y 5 24
2. e
6x 1 11y 5 9
2x
5 2
22x 1 9y 2 2z 5 20
3. • 3x 2 y 1 2z 5 29 4. (2, -3) 5. (6, 2)
6x 1 5y 1 5z 5 24
6. (-3, 2) 7. (0.9, 0.08, 0.3) 8. (0.25, 0.75, 0.5) 9. (3, 1, -2)
12. 39 13. -47 14. -7 15. 9 16. 26 17. -42
18. no 19. yes
10. c
20.6
0 20.2
20.4 20.4 20.1
7. £
0 20.5
0 § 8. £ 0.2
0.5
0.2 §
20.4
0
0.2
20.1
0.2 20.1
94
4
23
3
22
Algebra 2
All rights reserved.
1. £ 1
§ 2. ≥
1
2
21
1. No, the determinant is a number. 2. Any square matrix has
1
2
1. e
23
4 28
1 3 230
` d 11. c
`
d
2 28 16
4 1
1
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1
2
1 1
Algebra 2: All-In-One Answers
(continued)
1 24
1 29
2 23 † 9 § 13. (-6, -8, 14) 14. (9, -3, -6)
4
0
2 24
15. (7, 1, 0) 16. (2, 6, -4) 17. (-1, 7, 0.5) 18. (-4, 3, 9)
19. (5, 8, -2) 20. (1, 7, -9) 21. (-2, 3, 5)
12. £ 3
Guided Problem Solving 4-8
All rights reserved.
1. 5 erasers and 2 pencils 2. 7 erasers and 5 pencils
3. 5e + 2p = 0.23; 7e + 5p = 0.41
5 2
0.23 2
5 0.23
` 5 11 5. `
` 5 0.33 6. `
` 5 0.44
4. `
0.41 5
7 0.41
7 5
7. e = 0.03, p = 0.04; one eraser is $0.03 and one pencil is
$0.04 8. Yes, the prices match. 9. adult: $8; child: $5.50
4A: Graphic Organizer
1. Matrices 2. Answers may vary. Sample: organizing data
into matrices, matrix multiplication, geometric transformations
with matrices, inverse matrices and systems
3. Check students’ work.
4B: Reading Comprehension
1. They are to be taken together as a system. 2. 4 inequalities
3. 6 elements 4. 2 rows 5. 3 columns 6. 2 by 3 or 2 3 3
7. -1 8. b
4C: Reading/Writing Math Symbols
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
4
3
b 6. "a 1 b
1. exponent 2. base 3. amn 4. a3 5. "
7. a2 + b2
4D: Visual Vocabulary Practice
1. matrix 2. zero matrix 3. matrix addition 4. dilation
5. matrix multiplication 6. scalar multiplication
7. matrix element 8. matrix equation 9. rotation
4E: Vocabulary Check
Square matrix: A matrix with equal numbers of columns
and rows.
Determinant: A real number ad – bc of a 2 2 matrix
c
a b
d.
c d
Coefficient matrix: When representing a system of
equations with a matrix equation, this is the matrix containing
the coefficients of the system.
Variable matrix: When representing a system of equations
with a matrix equation, this is the matrix containing the
variables of the system.
Constant matrix: When representing a system of equations
with a matrix equation, this is the matrix containing the
constants of the system.
All-In-One Answers
4F: Vocabulary Review
3
2 5
1. Answers may vary. Sample: £ 7 22 8 §
4 21 12
2. Answers may vary, but must have 3 rows and 2 columns.
3. 9 4. Answers may vary.
11
7
21 0
10 7
Sample: c
d 1 c
d 5 c
d
26 21
2 5
24 4
5. Answers may vary, but the two must be identical in every
way. 6. Answers may vary and can be of any dimensions, but
every element is zero.
Chapter 5
Practice 5-1
1. ƒ(x) = x2 2. ƒ(x) = x2 + 4x + 8
3. ƒ(x) = -2x2 + 12 4. ƒ(x) = 2x2 - 1
5. ƒ(x) = x2 + 6x + 9 6. ƒ(x) = x2 - 4x + 7
7. (0, 1); x = 0 8. (3, 0); x = 3 9. (-1, -2); x = -1
10. quadratic; quad: x2; lin: 2x; const: -8 11. quadratic;
quad: 3x2; lin: 15x; const: none 12. linear; quad: none;
lin: -25x; const: none 13. linear; quad: none; lin: 22x;
const: -14 14. quadratic; quad: 3x2; lin: -4x; const: 8
15. quadratic; quad: 3x2; lin: -6x; const: -7
16. quadratic; quad: 3x2; lin: none; const: -12 17. quadratic;
quad: 2x2; lin: x; const: -6 18. linear; quad: none; lin: 3x;
const: -5 19. P9(0, 4), Q9(3, 1) 20. P9(-2, -2),
Q9(-5, -5) 21. P9(2, 2), Q9(-1, -1)
22a. h = -16t2 + 272t 22b. 372 feet
Guided Problem Solving 5-1
1. 1974 2. (0, 10), (4, 15), (7, 18), (9, 20), (14, 25), (21, 32),
(27, 34), (28, 37) 3. y = -0.0112x2 + 1.24x + 9.97
4. Answers may vary. Sample: Domain: whole numbers from
0 to 50, Range: whole numbers from 0 to 44. 5. x = 18; year
1992 6. Answers may vary. Sample: The maximum value of the
function is about (55, 44), so the first-class postage never reaches
50¢. The quadratic model is useful over a limited number of
years, but because it increases and then decreases, it does not
model the data after 2021. 7. The quadratic model is useful
over a limited number of years, but because it increases and then
decreases, it does not model the data after 2021. 8. The answers
are verified by the graph. 9a. y = -0.016x2 + 3.99x - 41.94
9b. Answers may vary. Sample: Domain: real numbers from 0 to
100, Range: whole numbers from 0 to 200. 9c. 51 °F
9d. 118 °F; The sales may not follow this pattern when the
temperature gets so hot people do not leave their airconditioned homes.
Algebra 2
95
Algebra 2: All-In-One Answers
6.
Practice 5-2
1.
2
(1 ,4)
4
O
4
7.
; min. (-1, -5)
y
x
x
2
y
O
2
2
O
2
4
4
( 1 , 92 )
(1,5)
; max. a 2 , 4 b
3 3
y
(
2
2,4
3 3
8.
O
2
)
O
2
8
9.
(1, 9)
; min. (2, -16)
y
x
O
2
2
2
16
4
(2, 16)
2
(2, 3)
5.
4
( 12 , 54 )
10.
6
5
4
; max. a2 1 , 5 b
2 4
y
2
1
2
x
2
O
2
321
2
12.
321
Algebra 2
11.
y
y
3
x
O
1 2 3
6
5
4
3
2
1
96
4
8
x
4
4
; min. (2, -3)
y
O
2
4
2
4.
; min. (1, -9)
y
x
x
2
4
2
2
3.
; min. a1, 2 9 b
2
All rights reserved.
2.
(0, 3)
4
1O
1
1
2
3
4
5
13.
y
4
3
2
1
x
O
1 2 3
321
1
2
x
1
3
y
x
O
1 2 3
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
2
O
4
x
2
2
x
2
; min. (0, -3)
y
2
; max. (1, 4)
y
6
(continued)
Algebra 2: All-In-One Answers
14.
4
3
2
1
All rights reserved.
1
1
2
15.
y
6
4
O
8 42
x
O
1 2
4 5
29.
y
2
24.
x 3
27.
2
4
6 (0, 6)
8
10
1
2
5. y 5 2 x 1 10 6. Yes, the graph verifies the model.
10
7. y 5 2 1 x 2 1 40
250
c
y
4
2 O
x
8642
2 4
2
4
x 1
(1, 7)
y
x4
3 O
x
3
3 6 9 12 15
3
6
9
12
15
(4, 16)
26.
y
x 1
10
(1, 8)
6
4
2 O
x
8642
2 4
2
28.
All-In-One Answers
x
4 6
x0
1. 10 ft 2. 10 ft 3. (0, 10), (10, 0) 4. a = 2 1 , c = 10
18. $3.25 19. 81.125 ft; 156.25 ft 20. 20 fixtures per day
21.
22.
y
y
6
1 Ox1 x
(4, 4)
4
2
1 2
4
1
x
O
2
2 4 6 8 10
3
4
4
(1, 4)
6
5
x4
25.
y
4
2 O
Guided Problem Solving 5-2
; $6
1 2 3 4 5 6 7 8
y
3
2
1 O x
5 3 1
1
1
2
(3, 2) 3
64
x
4
6
16. 1.2 s; 24 ft
17.
p
2500
2000
1500
1000
500 O
23.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
(continued)
Practice 5-3
1. y = x2 - 5 2. y = x2 + 2 3. y = (x - 2)2
4. y = -2x2 + 4 5. y = 2(x - 3)2 + 2
6. y = -2(x + 3)2 + 5
7.
8.
y
y
10
1O
x
8
1
1 2 3 4 5
6
1
(6, 6)
4 x6
2
2O
3
x
(2, 3)
4
2
2 4 6 8 10
2
5
x2
9.
8
y
6
3
x
129 3 O 6
3
6
9
12
(3, 13)
x 3
11.
x 1
12.
y
x 1 3
2
1O
4 2
(1, 1)
2
3
14.
x
y
x
O
1 2
y
6
(2, 4) 4
x
x 2 2 O
8642
2 4
2
x1
13.
4
3
4321
1
(1, 2)2
y
3
(1, 3)
2
1O
x
21
3 4
1
1
y
4
(0, 3) x 0
2
1 O
x
321
1 2 3
1
2
10.
y x1
4
3
2
1O
x
21
3 4
1 (1, 1)
2
y
x 6 8
6
4
2O x
8 42
2
2
(6, 2) 4
Algebra 2
97
15.
y
2
1O x
5 3 1
1
1
2
3
(3, 3) 4
x 3
16.
x 1 y
2O x
8642
2
2
(1, 5)
18.
17.
8
10
y
(continued)
x2
4
3
2
1O
(2, 0) x
1
1 2 3 4 5
1
3
2
y
x
O
21
1
2
3
1 2 3 4
(1, 2)
x1
19. y = (x + 2)2 - 4 20. y = 2(x + 2)2 - 5
21. y = -2(x + 2)2 + 8 22. y = -(x - 2)2 + 8
2
23. y = (x - 2)2 - 8 24. y 5 ax 1 52 b 2 25
4
2
95
25. y = 2(x - 0)2 - 6 26. y 5 23ax 1 16 b 2 12
2
27. y 5 ax 1 72 b 2 45
28. y = (x + 4)2 - 13
4
2
29. y 5 2ax 1 32 b 1 11
30. y = (x + 2)2 - 7
2
28. (x + 4)(x + 1) 29. (x - 22)(x + 1)
30. (x + 5)(x + 8) 31. (2x + 1)(x - 3)
32. (x + 11)(x - 1) 33. (x - 12)(x - 2)
34. (x + 2)(5x - 6) 35. (x + 1)(2x - 7)
36. (x + 5)(2x + 3) 37. (x - 3)(3x + 2)
38. (x + 3)(3x + 7) 39. (x + 8)(x - 3)
40. (x + 36)(x - 2) 41. x(x - 11) 42. 3x(x + 7)
43. (x + 2)(x + 6) 44. (x - 6)(x - 4)
45. (x + 10)(x - 3) 46. (x - 14)(x + 12)
47. (x - 9)(x + 8) 48. (2x + 5)(2x - 5)
49. (x + 11)(x - 11) 50. (x + 16)(x + 1)
51. (5x - 1)(2x - 3) 52. (2x + 3)(2x + 3)
53. (2x - 5)(2x + 3) 54. (3x + 2)(3x - 2)
55. (x + 10)(x - 4) 56. 2(x + 2)(x - 2)
57. (x + 11)(x + 7) 58. 2(x + 7)(x - 7)
59. (x + 14)(x + 7) 60. (x + 6)(x + 14)
61. (3x + 2)(3x + 8) 62. (2x + 3)(4x - 9)
63. (x - 9)(x + 6) 64. (x + 13)(x - 13)
65. (5x + 3)(5x - 3) 66. 7(x2 + 7) 67. 2(x - 7)(x + 2)
68. (x + 6)(x + 2) 69. (x + 5)(x - 7)
70. (x + 9)(x - 7) 71. (5x + 1)(4x - 3)
72. (2x - 1)(6x + 5) 73. (4x + 3)(x - 2)
74. (4x - 3)(2x + 7) 75. 3(x + 7)(x - 8)
All rights reserved.
Algebra 2: All-In-One Answers
Guided Problem Solving 5-4
1. x + y 2. y 3. (x + y)2 4. y2 5. (x + y)2 - y2
6. x(x + 2y) 7. The expressions are correct. For example,
4(4 + 2 2) = 32 and 62- 22 = 32. 8. (x + y)2 - 4y2;
(x - y)(x + 3y)
31. (2, -4); 8 32. (-6, 5); -7 33. (1, -1); 1
Practice 5-5
38. (-5, -3); -53 39. (-2, 5); -15
1. 20, -2 2. 0, 27 3. 0, 3 4. 7, -1 5. 7, -7 6. -1
Guided Problem Solving 5-3
7. 1, -1 8. 4, -1 9. -4, -5 10. -9, 216 11. 1, -11
1. price of a bagel in dollars 2. bakery’s daily profit in dollars
3. The domain is all nonnegative numbers. 4. x cannot be
negative because that would mean the bakery pays people to
take the bagels. 5. $277.50; $210.00 6. (0.55, 300) 7. $.55
8. $300 9. The graph verifies the answers. 10a. The domain
is all nonnegative numbers. x cannot be negative because
that would mean the theater pays people to see a movie.
10b. 140, 74.375 or about 74 10c. $6.50 10d. 150
Practice 5-4
1. (x + 2)2 2. (x - 5)(x - 2) 3. (x + 8)(x - 1)
4. x(x - 6) 5. (2x - 1)(x - 4) 6. (x + 7)(x - 5)
7. (x + 5)(x + 1) 8. (x + 3)(x - 3) 9. (x - 16)(x + 3)
10. (x + 2)(x - 2) 11. x(4x + 1) 12. (x - 25)(x - 4)
13. (x - 3)(x + 2) 14. (3x + 1)(3x - 1) 15. x(3x - 2)
16. (x + 8)(x - 8) 17. (x + 5)(x - 5)
18. (x + 9)(x - 9) 19. (x + 6)(x - 6)
20. (x + 10)(x - 10) 21. (x + 1)(x - 1)
22. (2x + 1)(2x - 1) 23. 4(x + 3)(x - 3)
24. (3x + 2)(3x - 2) 25. (x - 8)(x + 1)
26. (x + 9)(x + 4) 27. (x - 3)(x - 2)
98
Algebra 2
12. 0, 23 13. 2, 225 14. 1, 214 15. 1, 1 16. -1, 213
5
1
1
1
1
17. 2, 22 18. 2 , 3 19. -1, 2 20. -2, 31 21. 4, 2
22. -6, -1 23. 0, -3 24. 21 , 5 25. 2, 31 26. 12 , 1
27. 2, 232 28. 12, -12 29. 21 , 1 30. -1, 22 31. -1, 17
5
1 34. -1, 21 35. -9, -1
32. 1, 2 33. 1, 11
7
36. 6.24, -2.24 37. 7, 1 38. 4, -4 39. -2, -4 40. 3, 1
41. -2, 232 42. 12 , 32 43. 221
, 235 44. 1, 21
4
4
9
45. 212 , 21 46. -2, 241
5
47. 2, 23 48. -1, 254
1
49. -1, 219 50. -4, 212 51. -2, -1 52. -1, 11
53. 12 , 212 54. 0, 2 55. 3 , 23 56. 21 , -6 57. 12 , 14
5 5
58. -11, -1 59. 2, 61 60. 11, -11 61. 3, 241 62. 212 , 214
63. -8, -1 64. -2, -6 65. 4, -10 66. 2, -2 67. 3, -2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
34. (-4, -3); 23
35. (1, 2); 3 36. (2, 4); -8 37. (5, 1); 101
3
Algebra 2: All-In-One Answers
(continued)
68. 1.65, -3.65 69. 3.46, -3.46 70. 0.9, -2.23
18. y = -2(x - 1)2 + 5; (1, 5)
71. 3.87, -3.87 72. 9 , 2 9 73. -1, -4 74. -4, -9 75. 3, 2
19. y 5 ax 1 52 b 2 5; a252 , 25b
4
4
2
2
Guided Problem Solving 5-5
1. 24 ft by 16 ft 2. 384 ft2 3. 276 ft2 4. length: (2x + 24),
width: (2x + 16) 5. (2x + 24)(2x + 16) - 384 = 276
6. x = -23 or x = 3 7. 3 ft 8. Yes, the area of the border
is 276 ft2. 9. 5 ft
All rights reserved.
2
23. y 5 3ax 1 32 b 2 43 ; a232 , 234 b
24. 26 4 4"2 25. 12 4
Practice 5-6
1. 2i, -4 + 2i, 12 - 14i 2. 1 + i, 1 + 3i, -7 + 7i
3. -2 - 3i 4. 4 - i 5. -2i 6. 1 + i 7. 6i 8. -5 + 2i
9. 2 - 3i 10. -4 11. 2 12. 13 13. "2 14. "5 15. 5
16. "29 17. "13 18. "5 19. 3"2 20. 3 21. 2
22. "17 23. 3"5 24. "10 25. 4 26. 2"10
27. 2i"22 28. -6i 29. 2 30. 0 31. 4 - 5i 32. -5 - 3i
33. 26 34. 21 + 27i 35. 18 - 46i 36. -7 + 24i
37. 13 38. 8 39. -9 + 7i 40. -1 + 6i 41. 4i"3
42. 10i"3 43. 5i"3 44. 2 + 4i 45. 15 - 8i
46. 18 - 26i 47. 22 - 4i 48. 2 - 16i 49. 265
50. -2 + 8i 51. -5 + 16i 52. 169 53. 11 - 2i
54. 10 - 10i 55. -144 - 130i 56. 2i"11 57. 23i"7
58. 2i"2 59. -7 + 22i 60. 6 + 6i 61. 3 - 4i
62. 7 + 6i 63. 7 64. 5 + 12i 65. 2 + 8i 66. -3 + 14i
67. 26 68. 44i"5 69. 410i 70. 42i"5 71. 42i"3
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
20. y 5 22ax 2 52 b 1 23 ; a 52 , 32 b
21. y = 6(x - 1)2 - 5; (1, -5)
22. y = -2(x - 2)2 - 1; (2, -1)
72. 45i 73. 46i"2 74. 420i 75. 4 12 i 76. 4i"5
77. 45i 78. 43i 79. 4i"10
x2 +
"5
"3
"10
i"14
27. 12 4 2 28. 1 4 2 29. 4 4
30. 1 4 2
5
5
31. 0, -11 32. 7, -2 33. 21 , -1 34. 232 4
35. 22 4
38. 1, -3 39. 27 4
42. 232 4
- 9i2
x2 -
9i2
1. Yes 2.
3.
3ix - 3ix
or
4. x2 + 9 5. 25 6. ±5 7. Yes, - 5 and 5 check and are both
solutions. 8. x = ±7
Practice 5-7
1. 9 2. 49
3. 36 4. 94 5. 16 6. 64 7. 441
8. 1
4
4
2
9. y = (x + 2) - 10; (-2, -10)
10. y = (x - 3)2 - 3; (3, -3)
11. y = 4(x + 1)2 - 8; (-1, -8)
2
12. y 5 4ax 1 12 b ; a212 , 0b
13. y = 2(x + 1)2 - 7; (-1, -7)
"23
2
"106
"5
36. 2 3 4 i"3 37. 241 4 4
2
2
2
"97
"37
40. 32 4 2 41. 1 4 i"2
2
"17
"41
3"5
43. 272 4 2 44. 238 4 8
2
"65
"19
45. 1 4 i"6 46. 54 4 4 47. 23 4 2 48. 0, 3
2
"11
49. 0, 8 50. 2 1 4 i"11 51. 212 4 2
4
4
52. 254 4
55. 67 4
"37
i"15
53. 256 4 6 54. 2, -1
4
"145
"17
"13
56. 232 4 2 57. 272 4 2
6
58. 0, 52 59. 0, -14 60. 21 4
Guided Problem Solving 5-6
a2 + b2
"21
26. 22 4 "3
2
62. 212 4
"14
61. 1, 254
2
"21
"17
63. 4, -1 64. 21 4 2 65. -1, 34
6
66. 2, -4 67. 3 1
5" 15
"13
68. 2 4 "5 69. 232 4 2
3
"41
"53
70. 2 3 4 i"15 71. 232 4 2 72. 272 4 2
2
2
73. 232 4
"29
74. 3 4 "7
2
Guided Problem Solving 5-7
1. height in feet 2. horizontal distance from the base of the
left side of the arch in feet
3.
600
y
2
14. y 5 23 ax 1 32 b 1 31 ; a223 , 13 b
2
15. y 5 23ax 2 12 b 2 41 ; a 12 , 214 b
16. y = (x + 1)2; (-1, 0)
17. y = -5(x - 1)2 + 6; (1, 6)
All-In-One Answers
300
x
O
300 500
Algebra 2
99
Algebra 2: All-In-One Answers
(continued)
4. (315, 630) 5. The domain is real numbers from 0 to 630
and the range is real numbers from 0 to 630. The distances
and heights must be nonnegative real numbers. 6. 630 ft
2 (x 2 315) 2 1 630; Yes,
7. 630 ft 8. vertex form: y 5 2315
the answers verify.
9a.
Guided Problem Solving 5-8
1. the year 1985 2. the amount of carbon monoxide released
in a year in millions of tons
3.
y
200
y
60
100
50
40
30
x
20
10
x
200
vertex (100, 50)
9b. 50 ft 9c. 200 ft
Practice 5-8
1. 200; 2 real 2. 60; 2 real 3. 576; 2 real 4. 0; 1 real
5. 9; 2 real 6. -7; 2 imaginary 7. -7; 2 imaginary
8. 61; 2 real 9. -31; 2 imaginary 10. 9; 2 real 11. 0; 1 real
12. -8; 2 imaginary 13. 225; 2 real 14. -44; 2 imaginary
23 4 i"31
15. 0; 1 real 16. -3 17. 7, 8 18. 23 , 1 19.
4
20. 32 , 4 21. 254 , 1 22. -3, -5 23.
5
24.
31.
23 4 2i"3
3
23 4 "3
29 4 "133
32. -10, -8 33.
34. 4 4 3i
2
2
35. -4, 34 36.
38.
21 4 i"2
3
21 4 i"79
3 4 "17
25. 6, -2 26.
27. 2, 12
8
2
28. 23 4 "13 29. 1 4 2i 30.
5 4 i"119
22 4 i"11
37.
3
6
3 4 i"47
21 4 i"59
39. 21 4 2i 40.
4
10
5
21 4 " 61
41.
10
30
40
50
1 4 i"34
42.
43. 1 4 i"2
5
3 4 i" 183
5 4 i"71
45.
46. -5, -1 47. 4, 2
4
8
48. 3 4 "3 49. No; When p = 4000, the discriminant is
negative, so there are no real solutions. 50. 3, -1
44.
6 4 "15
; 1.41, 0.30
7
25 4 3"5
54.
; 0.17, -1.17 55. -1, 21 56. 1 , 24
4
2 3
10
51. -1, -4 52. 4, -2 53.
y = 100 is when less than 100 million tons were released.
5. 0.0721x2 - 2.8867x + 117.061 < 100 6. Subtract 100
from each side. Then use the quadratic formula to solve.
7. Answers may vary. 8. The results are the same.
9a. Wherever y 5 22x2 1 100x 1 4000 is above y = 4500
is when profit was greater than $4500. 9b. Solve -2x2 + 100x
+ 4000 4500 by first subtracting 4500 from each side. Then
use the quadratic formula to solve.
5A: Graphic Organizer
1. Quadratic Equations and Functions 2. Answers may vary.
Sample: properties of parabolas, transforming parabolas,
quadratic equations, completing the square 3. Check
students’ work. Chapter: Quadratic Equations and Functions;
Modeling Data with Quadratic Functions: using quadratic
functions to model data; Properties of Parabolas: identifying
properties of parabolas; Transforming Parabolas: translating
parabolas in the coordinate plane; Factoring Quadratic
Expressions: factoring quadratic expressions; Quadratic
Equations: working with quadratic equations; Complex
Numbers: defining and understanding complex numbers;
Completing the Square: factoring quadratic expressions by
completing the square; The Quadratic Formula: using the
quadratic formula to solve quadratic equations
5B: Reading Comprehension
1. factoring 2. ax2 + bx + c = 0 where a 2 0
3. because you need factors that have product ac and sum b
4. (2x - 5) 5. Answers may vary. Sample: a(b + c) =
ab + ac 6. Answers may vary. Sample: If two quantities
have a product of zero, then one of them must be zero.
7. Answers may vary. Sample: The Zero-Product Property
states that one quantity must be zero. This means that one
solution or the other gives zero. “And” would mean both
solutions satisfy the equation at the same time. 8. b.
57. -3, 2 58. 16, -3 59. 0, 252
60.
62.
23 4 "21
; 0.79, -3.79 61. 2 4 "3; 3.73, 0.27
2
1 4 2" 2
; 1.28, -0.61 63. 7, -5 64. -5, -2
3
100
Algebra 2
All rights reserved.
100
20
4. Wherever y = 0.0721x2 - 2.8867x + 117.061 is below
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
10
Algebra 2: All-In-One Answers
(continued)
5C: Reading/Writing Math Symbols
5F: Vocabulary Review Puzzle
1. Answers may vary. Sample: (2, 3) means 2 units to
the right along the x-axis and then 3 units up along the y-axis.
(3, 2) means 3 units to the right along the x-axis and then
2 units up along the y-axis. The x distance is always listed first.
y
(2, 3)
2
(3, 2)
x
2
O
2
2
1
V
E
R
2
T
E
X
N
O
3
R
4
5
6
F
B
P
A
I
T
T
O
M
I
A
L
N
N
C
S
R
D
R
M
A
I
A
R
B
A
D
O
L
All rights reserved.
L
1 2 3
2. Answers may vary. Sample: c
d is a 2 3 3 matrix
4 5 6
with 2 rows and 3 columns.
1 2
£ 3 4 § is a 3 3 2 matrix with 3 rows and 2 columns.
5 6
3. 12 4 3 means 12 divided by 3, which equals 4, while 3 4 12
means 3 divided by 12, which equals one-fourth. 4. 15 - 5
means to subtract 5 from 15 to get 10, while 5 - 15 means
5 minus 15, which is -10. 5. No; by the Symmetric Property of
Equality, a = b means b = a.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5D: Visual Vocabulary Practice
1. absolute value of a complex number 2. parabola
3. difference of two squares 4. imaginary number
5. Quadratic Formula 6. vertex form of a quadratic function
7. standard form of a quadratic equation 8. complex number
plane 9. perfect square trinomial
5E: Vocabulary Check
Quadratic function: A function that can be written in the
form f(x) 5 ax2 1 bx 1 c , where a 0. Its graph is a
parabola.
Axis of symmetry: The line that divides a parabola into two
parts that are mirror images.
Vertex of a parabola: The point at which the parabola
intersects the axis of symmetry.
Factoring: Rewriting an expression as the product of its
factors.
Greatest common factor (GCF) of an expression: The
common factor of each term of the expression that has the
greatest coefficient and the greatest exponent.
A
Chapter 6
Practice 6-1
1. y = -0.0439814815x3 + 0.6507936508x2 - 2.935185185x
+ 24.84126984; 21.098 2. y = 0.0130787037x3 -
0.1743055556x2 + 0.7951058201x + 3.125396825; 4.6362
3. 5x + 2; linear binomial 4. -3; constant monomial
5. 6x4 - 1; quartic binomial 6. 5s4 - 2s + 1; quartic
trinomial 7. 2m2; quadratic monomial 8. -4x3 + x2 + 3x;
cubic trinomial 9. 2x2 - 1; quadratic binomial 10. -3m3
+ 5m2; cubic binomial 11. -7x2 + 5x; quadratic binomial
12. 3x3; cubic monomial 13. -x3 + 2; cubic binomial
14. -x; linear monomial 15. a5 + a4 + a3; quintic trinomial
16. x2 - 25; quadratic binomial 17. p2 - 5p + 6;
quadratic trinomial 18. 9c4; quartic monomial
19. b - 3; linear binomial 20. 12x - 6; linear binomial
21. s2 1 32 ; quadratic binomial 22. 21 x4 1 x 2 54 ; quartic
trinomial 23. 21 z5 1 1; quintic binomial 24. 3x + 5 units
3
25. 0.0008797x3 + 0.2229900x2 - 3.1465532x + 29.0544437;
about $1203.18
26. 0.0000006x3 - 0.0005101x2 + 0.1270416x + 2.0612682;
about 12 yr
Guided Problem Solving 6-1
1. h = 10 cm 2. They are the same. 3. pr2h
4. V 5 10pr2 5. 34pr3 6. V 5 23pr3
7. V 5 23pr3 1 10pr2 8. Answers may vary.
9. 12pr2 1 48r
Practice 6-2
1. 5, multiplicity 3 2. 0; 8, multiplicity 2 3. 2; -7, multiplicity
3 4. 0, multiplicity 2; 4, multiplicity 2 5. -3, 0, 3
6. 252 ; 3, multiplicity 2 7. y = 2x3 - x2 - 50x + 25
All-In-One Answers
Algebra 2
101
(continued)
8. y = -2x3 + 15x2 - 22x - 15
9. V = x3 + 54x2 + 936x + 5184
10. y = x3 - 6x2 + 5x + 12
11. y = x3 - 4x2 + 5x - 2 12. y = x4 - 2x3 - 15x2
13. y = x3 + 6x2 + 12x + 8 14. x3 - 2x2 + x
15. x3 + 7x2 + 15x + 9
16. 2x4 + 23x3 + 60x2 - 125x - 500
17. y = 2x(x + 2)(x + 3)
18. y = x2(x + 2)(x - 3) 19. y = -3x(x - 3)2
20. -1, 1, 3;
y
2
Guided Problem Solving 6-3
1. x + 3 2. 3x3 1 10x2 2 x 2 12 3. 0 4. -3
5. 23k 3 10 21 212 6. 0 7. yes
3
(1, 0) x
2 (3, 0)
O
29 23
1 24
12
0
8. (x + 3)(3x2 + x - 4) + 0 = 3x3 + 10x2 - x - 12
9. 3(-3)3 + 10(-3)2 - (-3) - 12 = 0 10. no
2
Practice 6-4
21. -2, 3;
2
4
4. 2(x - 5)(x2 + 5x + 25); 5,
O
y (3, 0) x
2
25 4 5i"3
2
5. 4(x - 2)(x2 + 2x + 4); 2, 21 4 i"3
1 4 i"3
6. (3x + 1)(9x2 - 3x + 1); 213 ,
6
6
22. -5, 0, 2;
7. (4x - 1)(16x2 + 4x + 1); 41 ,
y
8. (x - 3)(x2 + 3x + 9); 3,
10
(5, 0) (0, 0)
4 O
(2, 0)
4
x
23. rel. max.: 4.06; rel. min.: -8.21; zeros: 0, 2, 5
24. rel. max.: 16.9; rel. min.: -5.05; zeros: -3, 1, 3
25. x(x + 2)(x - 8) 26. x(x + 3)(x + 4)
27. x(x - 3)(x - 5) 28a. V = x2(20 - x)
28b. about 1185 in. 3
Guided Problem Solving 6-2
1. 4 ft 2. The volume will be twice as much. 3. x ft 4. 60 ft3
5. 120 ft3 6. V(x) 5 (x 1 5)(x 1 4)(x 1 3) 7. 1
8. 1 ft 9. Answers may vary. 10. 2 in.
Practice 6-3
1. yes 2. yes 3. no 4. yes 5. x2 - 3x + 2
6. x2 + 3x - 7, R 5 7. -2x2 + 9x + 5 8. x2 + 6x + 9
9. x2 - x + 8, R -12 10. x2 - 7, R -10 11. x3 + x, R 1
12. x3 + 2x2 + 6 13. x3 - x2 + x + 11, R 32
14. 2x3 + 15x2 - 125 15. -1 16. -13 17. 0 18. 39
Algebra 2
21 4 i"3
8
23 4 3i"3
2
9. (x + 1)(x - 1)(x + 2)(x - 2); -2, -1, 1, 2
20
102
23 4 3i"3
4
2. (x + 4)(x2 - 4x + 16); -4, 2 4 2i"3
3 4 3i"3
3. 2(x + 3)(x2 - 3x + 9); -3,
2
(2, 0)
2
1. (2x - 3)(4x2 + 6x + 9); 23 ,
10. (x + 1)(x - 1)(x2 - 11); -1, 1, 2"11, "11
11. (x2 - 2)(x2 - 8); 2"2, "2, 2"8, "8
12. (x + 2)2(x - 2)2; -2, 2
13. (x2 - 7)(x2 - 2); 2"7, "7, 2"2, "2
14. (x2 + 4)(x2 + 9); -2i, 2i, -3i, 3i
15. (x + 1)(x - 1)(x + 3)(x - 3); -1, 1, -3, 3
16. (x + 1)(x - 1)(x2 + 4); -1, 1, -2i, 2i
17. 5.52% 18. -2, 2, -0.71, 0.71 19. 0.06, 15.94 20. 0
21. -0.59, 0, 0.42 22. -0.67, 0, 1.4 23. -9, 0, 9
24. (n - 1)n(n + 1) = -336; -8, -7, -6
25. (x - 5)(x2 + 5x + 25) 26. (x2 - 3)(x2 - 5)
27. (x + 1)(x - 1)(x2 + 2) 28. (x + 1)(x2 - x + 1)
29. (x2 - 6)(x2 + 4) 30. (x2 + 1)(x2 + 9)
31. (x + 3)(x2 - 3x + 9) 32. (x2 - 2)(x2 + 9)
21 4 i"3
33. 0, 1,
34. 21, 1, 2"6, "6
2
35. 2"14, "14, 2i, i 36. 2i"2, i"2, 22i"2, 2i"2
37. -3, 3, -3i, 3i 38. 2"5, "5, 2i"5, i"5
39. 0, -2, 2, 2i"3, i"3 40. 0, 2, 6
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
(1, 0)
2
19. x - 16 20. 2x + 11, R 48 21. x2 + 6x + 3, R 2
22. 3x2 - 7x + 7, R -8 23. (x + 1)(x - 3)(x + 5)
24. (x - 2)(x + 3)(x - 4) 25. 2x2 - 2x - 1, R 16
26. x3 + 3x2 + 3x + 4, R 1 27. x3 + 2x2 - x, R 1
28. x4 + x3 + x2 + x + 1 29. x3 + 2x2 + x + 2, R -6
30. 3x2 - 3x + 3 31. width: x - 3; height: x - 5
All rights reserved.
Algebra 2: All-In-One Answers
Algebra 2: All-In-One Answers
(continued)
Guided Problem Solving 6-4
m3
1. 60
2. the length of the box 3. width = x - 2
4. height = x - 1 5. V(x) = x(x - 1)(x - 2)
6. x(x - 1)(x - 2) = 60 7. (5, 60). The length of the box
when the volume is 60 m3. 8. 5 meters 9. 5 4 3 = 60
10. 10 years old
Practice 6-5
All rights reserved.
1. 2 2 3i, 2"7 2. 3 1 "2, 1 2 "3 3. 4i, 6 1 i
4. 5 1 "6, 22 2 "10 5. x4 - 8x3 + 21x2 - 32x + 68
6. x4 - 4x3 - x2 + 8x - 2 7. x4 + 3x2 - 54
8. x4 - 6x3 + 9x2 + 6x - 20 9. 4, 2, -1 10. 3, 1, -5
2343"5
11. -4, -3, 21 12. 7, -2, -4 13. 3;
2
14. -2, -1, 1, 2 15. 2, 2 4 i 16. -1, 3 4 i 17. 1, 2 4 3i
18. -2, 1 4 2i 19. 1, -1, 5 20. -4, 2 21. -2, 1, 3
22. 10, 21 4 i"19 23. 1, -3 24. 3, 12 , 212
234"13
25. 2,
26. -3, 23 , 214
2
Guided Problem Solving 6-6
1. three 2. three 3. 41, 42, 43, 44, 46, 49, 412,
418, 436 4. 4 5. x 2 1 9 6. 3i, -3i 7. 4, 43i
8. Answers may vary. 9. Answers may vary.
10. -1, 42i
Practice 6-7
1 1 1 2 4
1 , 4 1 , 4 1 ; -4, 21 , 1
4 6 9 9 9 12 18 36
6 6
1
1
1
2
1
29. 41, 4 2 ;-1, 22 30. 41, 42, 44, 4 2 , 4 3 , 4 3 , 4 43 , 4 41 ,
1
1
1 1
4 , 4 ; none 31. 41, 4 ; ; 1 32. 41, 47, 449; none
6 12
5 5
33. x3 - 7x2 + 17x - 15 = 0 34. x3 - 5x2 + 4x - 20 = 0
35. x3 - 5x2 + 4x + 10 = 0 36. x3 + 7x2 + x + 7 = 0
37. x3 + 4x2 + 16x + 64 = 0 38. x3 - 12x2 + 49x - 78 = 0
1. combination 2. permutation 3. permutation 4. combination 5. 12 6. 66 7. 792 8. 12 9. 1 10. 15 11. 1 12. 84
13. 1 14. 252 15. 2002 16. 2,118,760 17. 40,320 18. 110
19. 17,280 20. 360 21. 479,001,600 22. 239,500,800
23. 95,040 24. 12 25. 3024 26. 455 27. 60 28. 360
29. true, comm. prop. of mult. 30. false; Let a = 2. (22)! =
24 2 4 = (2!)2 31. false, Let a = 2 and b = 3. 2 ? 3! =
12 2 720 = (2 ? 3)! 32. true; identity prop. of add.
33. false; Let a = 2 and b = 3. (2 + 3)! = 120 2 8 =
2! + 3! 34. false; Let a = 2. (2!)! = 2 2 4 = (2!)2
Guided Problem Solving 6-5
Guided Problem Solving 6-7
27. 41, 43, 45, 415; none 28.41, 42, 44, 4 12 , 4 13 , 4 23 ,
4
3
4 ,4 ,4 ,4 ,4 ,4 ,4
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1 2 3 6 9 18 17. 5; 5, 3, or
7 7 7 7 7
7
1; 41, 45 18. 5; 5, 3, or 1; 41, 42, 43, 46, 4 1 , 4 3 , 4 1 , 4 3 ,
2 2 4 4
1 3 19. 3 20. 4, -3i, 3i 21. 22, 1 4 "7
4 ,4
8 8
21 4 i"5
22. 2, 1 4 "5 23. 1,
24. -3, 1, 4
2
25. -4, 2i"7, i"7 26. -1, 21 4 i"3 27. -3, 3, -2i, 2i
2 2
28. -2, 2, 2"3, "3 29. 23 , 3 , 2i, i
30. 2"3, "3, 212 i, 12 i
43, 46, 49, 418, 4 , 4 , 4 , 4 , 4 , 4
1. two 2. four 3. 3 - i 4. 2i
5. (x - 2i)(x + 2i)(x - 3 + i)(x - 3 - i)
6. (x - 2i)(x + 2i)(x - 3 + 1)(x - 3 - i) =
(x2 + 4)(x2 - 6x + 10) = x4 - 6x3 + 14x2 - 24x + 40
7. x4 - 6x3 + 14x2 - 24x + 40 = 0
8. Check students’ work. 9. Answers may vary.
10. x4 1 10x2 1 9 5 0
Practice 6-6
1. -1, 0, 1 2. -4, 0, 4 3. 213 , 0, 12 4. 212 , 0, 13
5. -1, 21 , 0 6. -5, 0, 5 7. 2; 2 or 0; 41, 43, 4 12 , 4 32
5
8. 2; 2 or 0; 41, 42, 45, 410, 4 13 , 4 23 , 4 53 , 4 10
3
9. 4; 4, 2, or 0; 41, 45, 4 12 , 4 52 10. 3; 3 or 1; 41, 43, 49,
1 3 9 1 3 9 11. 5; 5, 3, or 1; 41, 43, 45,
2 2 2 4 4 4
1 3 5 15 1 5 1 5
415, 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 12. 3; 3 or 1;
2 2 2
2
3 3 6 6
41, 47 13. 3; 3 or 1; 41, 42, 43, 44, 46, 412
14. 4; 4, 2, or 0; 41, 42, 43, 46, 4 12 , 4 23 15. 5; 5, 3, or 1;
1 3 1 3
41, 42, 43, 46, 4 , 4 , 4 , 4 16. 6; 6, 4, 2 or 0; 41, 42,
2 2 4 4
4 ,4 ,4 ,4 ,4 ,4
All-In-One Answers
1. 2; 5; 3; 2 2. the number of different ratings possible
3. No; a particular television set will fall into one price range
or the other. 4. 1 5. the Multiplication Counting Principle
6. 2 5 3 2 7. 60 8. Answers may vary. 9. 240
Practice 6-8
1. x4 + 8x3 + 24x2 + 32x + 16 2. a7 + 14a6 + 84a5
+ 280a4 + 560a3 + 672a2 + 448a + 128 3. x7 + 7x6y
+ 21x5y2 + 35x4y3 + 35x3y4 + 21x2y5 + 7xy6 + y7
4. d9 - 18d8 + 144d7 - 672d6 + 2016d5 - 4032d4
+ 5376d3 - 4608d2 + 2304d - 512 5. 256x8 - 3072x7
+ 16128x6 - 48384x5 + 90720x4 - 108864x3 + 81648x2
- 34992x + 6561 6. x9 - 9x8 + 36x7 - 84x6 + 126x5
- 126x4 + 84x3 - 36x2 + 9x - 1 7. 64x12 - 384x10y2
+ 960x8y4 - 1280x6y6 + 960x4y8 - 384x2y10 + 64y12
8. x35 + 14x30y + 84x25y2 + 280x20y3 + 560x15y4
+ 672x10y5 + 448x5y6 + 128y7 9. about 1%
10a. about 99% 10b. about 95% 10c. about 5%
11. about 3% 12. about 3% 13. about 8%
14. about 0.6% 15. n3 - 9n2 + 27n - 27
16. 16n4 + 64n3 + 96n2 + 64n + 16 17. n5 - 30n4
+ 360n3 - 2160n2 + 6480n - 7776 18. n6 - 6n5
+ 15n4 - 20n3 + 15n2 - 6n + 1
Algebra 2
103
(continued)
3584x5 + 17920x4 + 57344x3 + 114688x2 + 131072x
+ 65536 29. x6 - 18x5y + 135x4y2 - 540x3y3
+ 1215x2y4 - 1458xy5 + 729y6
30. x5 + 10x4 + 40x3 + 80x2 + 80x + 32
31. x10 - 5x8y2 + 10x6y4 - 10x4y6 + 5x2y8 - y10
32. y5 + 15y4 + 90y3 + 270y2 + 405y + 243
33. x12 + 18x10 + 135x8 + 540x6 + 1215x4
+ 1458x2 + 729 34. x7 - 35x6 + 525x5 - 4375x4
+ 21875x3 - 65625x2 + 109375x - 78125
35. x4 - 16x3y + 96x2y2 - 256xy3 + 256y4
Guided Problem Solving 6-8
1. 0.5 2. 5 3. 0.5 4. 2 5. b3g2 6. 5C3 5 10 7. 10b3g2
8. about 31% 9. 1 10. 5b4g1 11. about 16% 12. 5b1g4
13. about 16% 14. Answers may vary. 15a. 37.5%
15b. 25% 15c. 25%
6A: Graphic Organizer
1. Polynomials and Polynomial Functions 2. Answers may
vary. Sample: polynomials and linear factors, dividing
polynomials, solving polynomial equations, the Fundamental
Theorem of Algebra 3. Check students’ work.
6B: Reading Comprehension
1. x 2. y 3. 1 unit 4. parabola 5. y-axis 6. downwards
7. (0, 0) 8. upper right 9. a
6C: Reading/Writing Math Symbols
1. subtract 2. inverse 3. zero 4. inverse; 18 5. 1
6. inverse 7. identity
6F: Vocabulary Review Puzzle
1. absolute 2. opposite 3. term 4. variable 5. evaluate
6. complex
Chapter 7
Practice 7-1
1. 12 2. -5 3. not a real number 4. 0.1 5. 0.3 6. 3
7. -3 8. 0.3 9. 6 10. -7 11. -0.4 12. 10
13. -20, 20
3
14. no real square roots 15. -100, 100 16. -0.25, 0.25
17. no real fourth roots 18. -4, 4 19. -0.1, 0.1 20. -5, 5
21. 9x2 22. 11 ∆y5« 23. 2g2 24. 5x3 25. 3xy3
3
26. x - 9 27. 5(x + 2)2 28. 4x
29. -2, 2 30. -3, 3
7
4
4
31. -0.4, 0.4 32. 27 , 7 33. 20 cm 34a. about 25.30 ft/sec
34b. about 10.48 ft/sec
Guided Problem Solving 7-1
1. K and L, respectively 2. length, L 3. K 5 1.35"L
4. 8 5 1.35"L; L 35 ft 5. 10 5 1.35"L; L 55 ft
6. 20 ft longer 7. The answers check. 8a. 72,000 cars
8b. 6,500 cars
Practice 7-2
3
6x2 4. 48x 5. 2xy
1. 2"6 2. 9xy2"y 3. 5yz2"
3
4
"
9x2y2
"3y
"
54x3
6. 27"2y 7. 3"2x 8.
9. 3y
10. 3x
2
3
3
2
"2xy
11.
12. "6abc 13. 10 14. 54 15. 9 16. -3
4y
2bc
3 2
y z
17. 3x2"2 18. 2xy3 19. 6x"x 20. 5z"
3
4 3
21. 3k3"2 22. 22a4"
2 23. xy5"z 24. 4st3"
s
3
3
4
25. 6xy"
x 26. 5r"3r 27. 5uv2"
u 28. "2 29. "4x
3 31. 2x 32. "12y 33. 3"3
30. k
a
2
2
3
25y
6D: Visual Vocabulary Practice/High-Use
Academic Words
1. symbol 2. always 3. table 4. explain 5. graph
6. formula 7. common 8. never 9. simplify
6E: Vocabulary Check
Polynomial: A monomial or the sum of monomials.
Degree of a polynomial: The largest degree of any term.
Remainder Theorem: If a polynomial P(x) of degree n 1
34a. r 5
3
3V ; r 5 "6p2V 34b. 2.88 in.
2p
Å 4p
3
Guided Problem Solving 7-2
1. distance in miles from the satellite to the center of Earth
2. 3950 mi 3. r = 3950 + 100 = 4050 4. 17,498 mi/h
5. r = 3950 + 200 = 4150 6. 17,286 mi/h 7. 212 mi/h
greater 8. The answers are reasonable. 9. 0.22 gram
is divided by (x - a) where a is a constant, then the remainder
is P(a).
Multiplicity: The number of times the related linear factor is
repeated in the factored form of the polynomial.
Relative maximum: The y-value of a point on the graph of a
function that is higher than other nearby points.
104
Algebra 2
All rights reserved.
19. 8a3 + 24a2 + 24a + 8 20. x8 - 4x6y2 + 6x4y4 4x2y6 + y8 21. 32x5 + 240x4y + 720x3y2 + 1080x2y3 +
810xy4 + 243y5 22. 64x12 + 192x10y2 + 240x8y4 +
160x6y6 + 60x4y8 + 12x2y10 + y12 23. x6 - 3x4y2 +
3x2y4 - y6 24. 16b4 + 32b3c + 24b2c2 + 8bc3 + c4
25. 243m5 - 810m4n + 1080m3n2 - 720m2n3 + 240mn4
- 32n5 26. x18 - 6x15y4 + 15x12y8 - 20x9y12
+ 15x6y16 - 6x3y20 + y24 27. x7 + 7x6 + 21x5 + 35x4
+ 35x3 + 21x2 + 7x + 1 28. x8 + 32x7 + 448x6 +
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Algebra 2: All-In-One Answers
Algebra 2: All-In-One Answers
(continued)
Practice 7-3
1. -63 2. -6 3. 73 4. 11"3 5. 5"2 + 2"3
3
3
x 7. 11"xy 8. -2 - "3 9. 10 - 5"3
6. 3"7 - 7"
22 1 14"3
3 1 "5
10. - 2
11.
12. 22"2 13. 4"2
13
All rights reserved.
Guided Problem Solving 7-5
4
14. 0 15. 13"
3 16. -3 - "5 17. -38 + 7"10
18. 67 - 15"7 19. 28 - 16"3 20. 9 + 2"14
21. 30 + 12"6 22. 12"7 23. 18"10
3
3
24. 41"3 - 3"6 25. 6"
3 + 4"
9 26. 105"x
27. 26y"5 28. 6y + 13"5y - 25 29. x - 3
3
"3
1. s"
2. 2A ; 2A9"3 ; #2A
3. about 8.8 in.
2
3
3"3
4. about 15.2 in. 5. Yes, the answer checks. 6a. about 10.7
in. 6b. about 11.5 in.
30.
1a. ƒ(x) = 1.8x 1b. g(x) = 0.75x 1c. g(f(150)) = $202.50
1d. No; it doesn’t matter whether you first multiply by 0.75
or by 1.8. 2. 2x2 + 4x + 2; all real numbers
3. -2x2 + 4x - 4; all real numbers
4. 8x3 - 2x2 + 12x - 3; all real numbers
Practice 7-6
3 2
x 1 2"
"5 2 2"2
x
31. "2 32.
x
3
33a. (900 1 300"3 1 300"6) ft or about 2154 ft
33b.
270,000 1 90,000"3 2
ft or about 212,942 ft2
2
5. 4x2 2 1 ; all real numbers 6. 2x2 - 4x + 4; all real
Guided Problem Solving 7-3
1.
1 1 Í5
2
2. subtract 3.
2
1 1 Í5
2x 1 3
4. 1 2 Í 5 5.
21 1 Í 5
2
6. 1 7. Yes, it equals the reciprocal of the golden ratio.
8. 224Í 35 1 52
Practice 7-4
1. 3 2. 81 3. 32 4. 256 5. 1 6. 4 7. -1 8. 9 9. 2
10. x 6 11. 2y2 12. 4 13. 1 14. 21 15. 49 16. 0
5
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
22. -27, 27 23. 64 24. 0, -1 25. no solution 26. 64
27. 23 28. 0 29. no solution 30. -2 31. 1 32. -123
33. 8 34. 12 35. 1 36. 16 37. 8 38. -6, 2 39. 2
3
3
7
31
2
17. 12x6 18. 31 19. 9ab 3 20. 16 21. b 4 22. y 40
a
y
y6
2
3
13
3x
1
1
23. 2 24. 8a 4 25.
26. 12x 20 27. y
9
x 21
Guided Problem Solving 7-6
1. cost in dollars to produce x violins; income in dollars from
selling x violins 2. profit earned when he makes and sells x
violins 3. I(x) = 5995x 4. C(x) = 1000 + 700x 5. P(x) =
5295x - 1000 6. 157,850 7. He made a profit of $157,850
when he makes and sells 30 violins. 8. The answers match.
9a. P(x) = 56x -30 9b. $13,970
3 4
3
5
x 30. "
2y 31. "a3 32. "
b
28. 10.1% 29. "
3 2
4
5 12
z 34. "
ab 35. "
m 36. 71 37. 51
33. "
"t2
"a8
3
1
1
1 2
2
numbers 7. 2x 1 3 ; all real numbers except 1 8. -4
4
4x 2 1
9. -2 10. 7 11. 23a 1 2 12. -4x + 7
5
13. 2x2 - 3x - 7 14. 17 15. 16 16. -8x + 6 17. 2 4
5
5
5
18. 23x 1 2 19. 7 20. 3x2 - 13
5
5
21. 3x3 + 2x2 - 15x - 10 22. -2x2 + 3x + 12
23a. ƒ(x) = 0.75x 23b. g(x) = x - 5
23c. g(ƒ(50)) = $32.50 23d. Yes; multiplying by 0.75 and
then subtracting by 5 is different than subtracting by 5 and
then multiplying by 0.75.
3
1
38. x 2 39. m 3 40. (5y) 2 41. 23y3 42. b 4 43. (26) 2
4
Practice 7-7
3
44. 36a2 45. n5 46. (5ab) 4
1.
6
4
2
Guided Problem Solving 7-4
1. 39% 2. number of years ago that the organism died
T
R 5 (2.7) –8033
3. fraction of A left after T years 4. A
5. 78% 6. 61% 7. 37% 8. Yes, the answers check.
9. 81%; 65%; 12%
4 O
2.
y
x
2 4 6
y
6
4
2O
642
2
2
4
6
x
6
Practice 7-5
1. 127 2. -8, 8 3. 9 4. 3 5. no solution 6. 25 7. 9
8. -14 9. 1 10. 27 11. 4, 2 12. 9 13. 7 14. 2 15. 4
16. 29,-25 17. 10 18. 16 19. 4 20. 13 21. 4
All-In-One Answers
Algebra 2
105
Algebra 2: All-In-One Answers
4.
y
5
4
3
2O
642
2
4
6
3
2
1
32 O
x
–3
–2
–1
0
y
–2
–1
0
1
y
x
x
2
4 5
O
x
6.
y
x
1 2 3
2
3
4
3
2
1
2
y
2 O
O
2
2
x
1 2 3 4
26.
2
x
–3
–1
0
–2
y
0
1
2
3
y
7. y 5 4"x 2 2; no 8. y = x - 2; yes
2
9. y 5 13 x 2 1; yes 10. y 5 4"2x 2 3; no
x
2
x ; no
11. y 5 12 x 1 12 ; yes 12. y 5 4 1 2
Ä 3
17. y 5 4"x 1 4 2 4; no 18. y 5 4"4 2 x; no
19. f21(x) = 6x; The domain and range of f and f21 is the
set of all real numbers; f21 is a function.
20. f21(x) 5 25x 1 10; The domain and range of f and
f 21 is the set of all real numbers; f 21 is a function.
21. f21(x) 5 4"x 1 2; Domain of f = all real
numbers = range of f 21; Range of f = the set of real
O
2
2
13. y 5 4 x ; no 14. y 5 4"x 2 3; no
Ä5
4 ; no 16. y 5 4 x 1 2 ; no
15. y 5 4 x 1
Ä 6
Ä 3
27. -1 28. 3 29. 2 12 30. f21(x) 5
22.
f21 (x)
5 4"x 2 4; Domain of f = all real
numbers = range of
f 21; Range
of f = all real numbers
greater than or equal to 4 = domain of f 21; f 21 is not a
function.
23. f 21 (x) 5 x 2 1 1; Domain of f = all real numbers
greater than or equal to 1 = range of f 21; Range of f = all
real numbers greater than or equal to 0 = domain of f 21;
f 21 is a function.
x 2 635,600
; in 2009
198,900
Guided Problem Solving 7-7
1. v is the velocity of the water in feet per second; g is the
acceleration due to gravity (32 ft/s2); x is the height of the
2 2
water in feet. 2. v2; v ; v 3. 25 4. 25 ft 5. 6.25 6. 6.25 ft
2g 64
7. Yes, the answers check. 8. r 5
numbers greater than or equal to -2 = domain of f 21;
f 21 is not a function.
All rights reserved.
5.
4
25.
y
S 2 1; r 8.4%
ÅP
Practice 7-8
1.
y
6
4
2O
x
642
2 4 6
2
4
6
2.
y
6
4
2O
x
2
2 4 6 8 10
2
4
6
24. f 21 (x) 5 31 x 2; The domain and range of f and f 21 is
the set of all real numbers greater than or equal to 0; f 21 is
a function.
106
Algebra 2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
3.
(continued)
Algebra 2: All-In-One Answers
3.
All rights reserved.
5.
7.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
9.
11.
13.
y
6
4
2O
x
2
2 4 6 8 10
2
4
6
4.
y
6
4
2O
x
2
2 4 6 8 10
2
4
6
6.
y
4
2O
x
42
2 4 6 8
2
4
6
8
8.
y
6
4
2O
x
2
2 4 6 8 10
2
4
6
10.
2
y
6
4
2O
14.
16.
x
1
321
18.
y
19.
6
2 3
3
2
1
21
O
2
2
4
6
y
x
1
x
O
2 3 4 5
24.
y
3
2
1
x
O
1 2
4321
2
3
4
2
3
4
5
y
2
3
4321
1
x
O
1 2 3 4 5 6
3
2
1
x
O
1 2 3 4
2
1
1
y
y
22.
y
23.
25.
2 4 6 8
5
4
3
2
1
2
3
y
6
4
2O
x
2
2 4 6 8 10
2
4
6
6
4
20.
y
x
O
21 1 2 3 4
x
x
O
1 2 3 4 5
x
O
1 1 2 3 4 5
4
3
2
1
21.
5
4
3
2
1
x
O
2
3
y
6
4
2O
4
2 4 6
2
4
6
y
2
3
2
1
6 8
4
3
2
1
x
2 4 6 8 10
17.
y
6
4
2O
x
2
2 4 6 8 10
2
4
6
y
6
4
2O
x
2
2 4 6 8 10
2
y
6
4
2O
2
2
4
6
4
6
12.
All-In-One Answers
15.
y
6
4
2O
x
2
2 4 6 8 10
2
4
6
y
6
4
2O
x
2
2 4 6 8 10
2
4
6
6
(continued)
x
1 2 3 4 5
x
O
1 2
2
3
26.
y
O
y
4
3
2
1
y
x
O
321 1 2 3
2
Algebra 2
107
Algebra 2: All-In-One Answers
27.
(continued)
43.
y
5
4
3
2
1
y
2
2
x
O
1 1 2 3 4 5
2
O
4
x
2
2
2
28b. about 10.6 ft
r
O
2x
2
Guided Problem Solving 7-8
12
1. length, in feet, of the trapeze 2. time, in seconds, for a
trapeze to complete one full cycle
3.
4
4
A
O
y
All rights reserved.
8
2
100 200 300
29. 75 30. 7 31. no solution; 3 is extraneous 32. 2.36
O
2
2
4
x
6
33. y 5 9"x 1 2; graph of y 5 9"x shifted left
2 units 34. y 5 22"x 1 5; graph of y 5 22"x
4. 4.3; about 4.3 s 5. 6.1; about 6.1 s 6. Yes, the answers
3
3
shifted left 5 units 35. y 5 5"
x 2 2; graph of y 5 5"
x
shifted right 2 units 36. y 5 28"x 1 3; graph of
7a.
3
y 5 28"x shifted left 3 units 37. y 5 22"
x 2 7 1 4;
3
graph of y 5 22"
x shifted right 7 units and up 4 units
38. y 5 5"x 1 3 2 1; graph of y 5 5"x shifted left
40.
y
2
x
2
x
2
O
2
4
2
4
O
42.
y
2
7B: Reading Comprehension
x
O
2
7b. about 9.1 nautical miles; 11.7 nautical miles
1. Radical Functions and Rational Exponents 2. Answers
may vary. Sample: roots and radical expressions, binomial
radical expressions, rational exponents, inverse relations and
functions 3. Answers may vary. Sample: packaging, art, space
travel, solar energy 4. Check students’ work.
y
2
2
6
7A: Graphic Organizer
4
41.
4
2
2
2
4
y
2
x
y
2
3 units and down 1 unit
39.
check.
2
2
O
2
2
x
1. cube 2. 12 edges 3. 8 vertices 4. sphere
5. They are not actually visible. 6. cube or polyhedron
7. inscribed 8. circumscribed 9. b
7C: Reading/Writing Math Symbols
1. f, h 2. a 3. g 4. c 5. d 6. b 7. f 8. j 9. i, k
108
Algebra 2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
28a.
44.
y
Algebra 2: All-In-One Answers
(continued)
7.
7D: Visual Vocabulary Practice
1. nth root 2. like radicals 3. composite function
4. inverse relation 5. square root equation 6. radical
equation 7. square root function 8. radical function
9. inverse functions
4
2
x
7E: Vocabulary Check
2
Radicand: The number under a radical sign.
Index: With a radical sign, this indicates the degree of the root.
Principal root: When a number has two real roots, this is the
All rights reserved.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
2
x
Rational exponent: If the nth root of a is a real number and
n
n
1. index 2. inverse 3. left 4. principal 5. radical
6. rational
L
O
N
O
E
G
R
V
E
I
A
C
T
E
V
I
E
T
N
R
N
R
V
N
N
E
L
D
E
I
O
V
A
R
N
A
E
E
O
E
I
C
O
R
C
X
D
R
I
H
T
G
R
I
T
S
D
A
E
L
A
T
D
E
N
N
I
E
E
I
R
A
2
m
7F: Vocabulary Review Puzzle
N
G
R
O
H
F
N
R
R
E
E
X
E
G
T
I
I
R
; y=0
y
4
an expression so there are no radicals in any denominator and
no denominators in any radical.
m
2
6
Rationalize the denominator: Rewrite the denominator of
1
n
m
n
m is an integer, then an 5 Í a and a 5 Í a 5 Q Í a R .
If m is negative, a 0.
O
8.
positive root.
P
R
I
N
C
I
P
A
L
; y=0
y
6
O
2
9. y = 18,000(0.75)x; $5695.31 10. y = 29,000(0.88)x;
$11,851.59 11. y = 1573(1.02)x; 1917 bears
12. y = 75,000(1.125)x; $2,568,247.87
13. y = 200,000(0.9925)x; 94,207 birds 14. y = 2(0.65)x
15. y = 10(0.8)x 16. y = 0.7(1.2)x 17. 1.45 18. 0.9
19. 0.6 20. 3 21. 25% decrease 22. 37.5% decrease
23. 73% increase 24. $300,000
Guided Problem Solving 8-1
1. the intensity of sunlight beneath the surface of the ocean
2. the depth beneath the ocean surface, in feet 3. percent of
sunlight that reaches a depth of x feet 4. 50
5. y 5.63976205 6. about 5.6% 7. 370 8. y 0.00170898
9. about 0.0017% 10. Answers may vary. 11. about 91.8%
Practice 8-2
Chapter 8
1. 7.3891 2. 0.0821 3. 1.3956 4. 4.1133 5. $39,624.12
1
Practice 8-1
1. growth 2. decay 3. growth 4. decay
5.
;y = 0
y
8. y 5 8a 12 b
1
64.9 x
; about 2.7 mg
1
13.2 x
4
9. y 5 45a 12 b
; about 34.6 mg 10. decay 11. growth
12. decay 13a. $9948.90 13b. $19.68 14. 9.9 yr
2
15.
6
O
6.
6
16.
y
x
2
x
64.1
6. $21,557.68 7. y 5 12a 21 b
; about 5.5 mg
y
4
4
2
2
2
; y=0
y
2
O
2
x
2
O
2
x
4
2
x
2
O
2
All-In-One Answers
Algebra 2
109
Algebra 2: All-In-One Answers
2
O
4
2
2
2
2
x
y
x
4
2
O
2
2
2
O
21.
O
20.
y
2
15. log8512 = 3 16. log13169 = 2 17. log2512 = 9
2
4
19.
1 11. 2-10 = 1
9. 560 = 1 10. 12-2 = 144
1024
12. 38 = 6561 13. log981 = 2 14. log25625 = 2
y
x
2
22.
y
56. 6.3 3 10-9 57. 6.3 3 10-7 58. 2.5 3 10-6
y
2
25
1
23. log8 8 = -1 24. log111 = 0 25. log66 = 1
1 = -3 27. log 1 = 0 28. log 17 = 1
26. log6 216
17
17
29. 5 h 30. 4 31. 3 32. 2 33. 1 34. 0 35. -1 36. -2
45. 1 46. 1 47. 5 48. -2 49. -3 50. -2 51. 52
52. -2 53. 12 54. 6.3 3 10-8 55. 5.0 3 10-8
x
4
1 = -3 22. log 1 = -2
20. log100.001 = -3 21. log4 64
5
37. -3 38. 1 39. 3 40. 2 41. -1 42. 0 43. 0 44. 3
4
x
18. log41024 = 5 19. log5625 = 4
O
2
59. 2.5 3 10-5 60. 1.0 3 10-7 61. 1.3 3 10-3
62.
2
2
O
23.
2
4
x
24.
y
4
2
2
3
2
1
1
1
2
3
y
4
O
25.
2
x
2
O
26.
y
O
O
1 2 3 4
1
1
2
3
3
2
1
65.
4
3
2
x
O
1 2 3 4 5
x
O
1
1
2
3
x
y
y
1 2 3 4 5
y
x
O
1
1
2
1 2 3 4 5
4
2
66.
2
4
x
y
x
2
2
3
2
1
63.
y
64.
2
All rights reserved.
18.
y
67.
y
y
2
x
4
2
x
2
O
x
O
O
2
2
4
2
4
4
2
Guided Problem Solving 8-2
1. to save $8000 2. 5 yr 3. a single deposit 4. continuously
5. 0.052 6. 8000 5 Pe0.052(5) 7. $6168.41 8. $6497.65,
$6844.47, $7209.80, $7594.63, $8000. Answers may vary.
9. Answer may vary. 10. $2556.43
Practice 8-3
68.
69.
y
y
2
2
x
2
O
2
2
O
2
4
6x
2
1. 44 = 256 2. 70 = 1 3. 25 = 32 4. 101 = 10
1 7. 95 = 59,049 8. 172 = 289
5. 51 = 5 6. 8-2 = 64
110
Algebra 2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
17.
(continued)
Algebra 2: All-In-One Answers
70.
(continued)
Practice 8-5
y
1. 3.58 2. 3.36 3. 1.5 4. 0.68 5. 0 6. 1.43 7. 3 8. 1.63
9. 0.5 10. 0.53 11. 7.92 12. 1.28 13. 0.93 14. -0.47
15. 2.79 16. 0.39 17. 2.52 18. 2.04 19. 33.33 20. 10
21. 334 22. 0.22 23. 40 24. 4 25. 100 26. 100 27. 25
28. 125 29. 10 30. 16.67 31. 2.26 32. 1.19 33. 0.48
34. -0.32 35. 1.48 36. 1.19 37. 3.85 38. 1.72
39. about 19 mo 40. about 27 yr 41. 3.16 42. 0.4 43. 0.04
44. 4000 45. 20 46. 497.5 47. 47.5 48. 0.03 49. 5.48
50. 0.48 51. 0.23 52. 3.30 53. 0.86 54. 0.75 55. -2.54
2
x
O
2
4
6
2
All rights reserved.
Guided Problem Solving 8-3
1. log273 2. log273 = x; yes 3. 3 5 27x 4. The error is
in the second line. It should read 3 5 27x . 5. 31 5 (33) x
6. 31 5 33x 7. 1 = 3x 8. log273 5 31 9. Answers may
vary. 10. The error is in the third line. It should read
23 5 (22) x; the correct answer is 23.
E ? 30
log11,600
; 5.1 10. Answers may vary.
log30
11. Answers may vary. 12. after 2 hours
9. M 5 7.9 2
1 1
2
2 3
14. log7x3 15. log415x 16. log 14 17. log x 3 18. log r s1
y
t4
3
2
19. log3100xy 20. log 8 21. log 3x 22. log 64 23. log 8
24. log x11 25. log6 21 26. log 8 27. log3 2x5
7
y
1 1
1
3
x 2y 3
y
30. log t24 31. log5 4 8
2
z
r t
y3
32. log x + log y + log z 33. log2x - log2y - log2z
34. log 6 + 3 log x + log y 35. log 7 + 2 log (3x - 2)
36. 21 log 2 + 12 log r + 12 log s + 21 log t - 12 log 5 - 12 log w
37. log 5 + log x - log 4 - log y
38. log55 - 5 log5x, or 1 - 5 log5x
39. log 2 + 2 log x + log y - log 3 - 3 log k
40. 2 log43 + 2 log4x + 2 log4y + 2 log4z 41. Quotient
Prop. 42. Power Prop. 43. Product Prop. 44. Power Prop.
45. Power Prop. 46. Power and Quotient Prop.
28. log2 x 1 29. log
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
7.9
3. E ? 307.9 4. E ? 30M 5. E ? 30 M 5 11,600
8. (7.9 2 M)log30 5 log11,600
1. about 377.7 decibels 2. about 2.6 decibels 3. 1.0792
4.1.2042 5. -0.2219 6. -0.0969 7. 1.8751 8. 0.5052
9. 0 10. 1.7782 11. log512 12. log65 13. log21 = 0
Guided Problem Solving 8-4
1. 1024 W/m2 2. 6.31 3 1026 W/m2 3. decibels
4. the decrease in apparent loudness
24
5. L1 5 10 log 10I
0
1026
6. L2 5 10 log 6.31 3
I
0
24
7. L1 2 L2 5 10 log 10I
0
8.
1. 7.9 2. the magnitude of the Pennsylvania earthquake
6. 307.92M 5 11,600 7. log(307.92M) 5 log11,600
Practice 8-4
10(log1024
Guided Problem Solving 8-5
26
2 10 log 6.31 3 10
I0
2 logI0) 2 10flog(6.31 3 1026) 2 logI0g
9. 10 log1024 2 10 log(6.31 3 1026)
10. 20 - 10 log 6.31 12 dB
11. L1 5 80dB, L2 68dB; L1 2 L2 < 80 2 68 5 12dB
12. about 15 dB
All-In-One Answers
Practice 8-6
1. 40.2 days 2. 35.7 days 3. 31.8 days 4. 6.36 km/s; no
5. 22.65 6. 25.79 7. 2.71 8. 0.92 9. 1.91 10. 0.41
11. 4.69 12. -1.15 13. 0 14. 17.33 15. 2.60 16. -2.28
17. -0.02 18. 6.44 19. 1.61 20. 4 21. 21 22. no solution
23. 0.61 24. 12.37 25. 1.58 26. 29,937.07 27. -0.11
28. 633.14 29. 2.12 30. 1.85 31. 1.84 32. 3 33. 2
34. 12 35. 1.83 36. 7.36 37. -0.93 38. 48.14 39. 151.48
a
z
40. 4.19 41. ln 2 42. ln 243 43. ln 4b 44. ln 3 45. ln 9x
x
4 3
46. ln x y
Guided Problem Solving 8-6
1. maximum velocity of the rocket, in kilometers per second;
the time in seconds that the booster rocket fires; velocity of
the exhaust, in kilometers per second; the mass ratio of the
rocket 2. 6.9; 50; 3.1; unknown
3. 6.9 5 20.0098(50) 1 (3.1)ln R
6.9 1 0.0098(50)
6.9 1 0.0098(50)
3.1
5 ln R 5. e
4.
5R
3.1
6. R 10.8 7. Answers may vary. 8. Answers may vary.
9. Answers may vary. 10. R 20.0
8A: Graphic Organizer
1. Exponential and Logarithmic Functions 2. Answers may
vary. Sample: properties of exponential functions, logarithmic
functions as inverses, properties of logarithms, natural
logarithms 3. Reading Data 4. Testing Multiple Choices
5. Answers may vary. Sample: population, depreciation,
medicine, investments 6. Check students’ work. Chapter:
Exponential and Logarithmic Functions; Exploring
Exponential Models: modeling exponential growth and decay;
Properties of Exponential Functions: exploring properties of
exponential functions; Logarithmic Functions as Inverses:
Algebra 2
111
(continued)
write, evaluate, and graph logarithmic functions; Properties of
Logarithms: use properties of logarithms; Exponential and
Logarithmic Equations: solve exponential and logarithmic
equations; Natural Logarithms: evaluate natural logarithmic
expressions and solve equations using natural logarithms
26. z 5 3x3 ; 9
8B: Reading Comprehension
Guided Problem Solving 9-1
1. the current use of logarithms 2. common and natural
3. Answers may vary. Sample: The phrase “In the twentieth
century” 4. 500 5. 39 6. log 500 x = 39 7. a
1. directly 2. inversely 3. y = 8 4. the value of x when
1. 1; 13; no 2. 1; 5; no 3. (2, -3); (-3, 2); no 4. 5; -1; no
5. 64; 64; yes 6. -9, -9, 9; yes and no, -(b2) is the same as
(-b2), but it is not the same as (-b)2.
k(48)
y = 12 and z = 2 5. y 5 kx
6. 8 5
7. k = 1.5
z2
(3) 2
8. y 5 1.5x
9. x = 32 10. Answers may vary.
z2
11. Answers may vary. 12. a = 4
Practice 9-2
8D: Visual Vocabulary Practice
1. common logarithm 2. change of base formula
3. exponential equation 4. growth factor 5. logarithmic
equation 6. continuously compounded interest
7. logarithmic function 8. decay factor 9. natural
logarithmic function
3
x2
3. y 5 2 3
x2
6. y 5 2 3
x2
8. y 5 2 3
x1
1. y 5 2
9.
8E: Vocabulary Check
1 1 2. y 5 2
4
2O
x
642
2 4 6
2
4
6
Asymptote: A line that a graph approaches but never
reaches.
Logarithmic function: The inverse of an exponential
function.
Exponential function: The general form is y = abx,
where x is a real number, b 0, and b 1.
Common Logarithm: A logarithm that uses base 10.
Growth factor: The value b in y = abx, where b 1.
3 13
x11
3 1 6 5. y 5 2 3
2 2 4. y 5 2 x
x23
4
1 2 7. y 5 2 3 2 1
x13
1
11
2
; x = 1, y = 2
y
2
10.
; x = -1, y = 0
y
8F: Vocabulary Review
1. e 2. d 3. f 4. b 5. c 6. a 7. g 8. h
6
Chapter 9
x
O
2
4
2 4 6
Practice 9-1
36
1. 1 2. 1.2 3. 50 4. 2 5. 4.2 6. y 5 14
x 7. y 5 x
7
0.8
30
4
8. y 5 2 24
x 9. y 5 2 x 10. y 5 x or y 5 5x
8 12. y 5 3 13. y 5 6.3 or y 5 63
11. y 5 x
x
x
10x
3
14. y 5 2 0.3
x or y 5 2 10x 15. I varies inversely with R.
16. A varies jointly with b and h. 17. h varies directly with V
and inversely with B. 18. V varies directly with the cube of r.
8 ; 1 23. y 5 2 1 ; 2 1
19. 4 20. -4 21. 2 22. y 5 x
x 8
11.
; x = -3, y = -3
y
12963
3
6
9
12
O
x
3
36
24. y 5 7.2
x or y 5 5x ; 0.9 25. z = 2xy; 48
112
Algebra 2
All rights reserved.
8C: Reading/Writing Math Symbols
27. inverse; y 5 20
x 28. neither
y 32
29. direct; y = 6x 30. direct; y = 125x 31. neither
32. inverse; y 5 15
x
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Algebra 2: All-In-One Answers
Algebra 2: All-In-One Answers
12.
6
4
; x = 2, y = -2
y
13.
18.
8
6
4
x
O
2
4
6
(continued)
2 4 6
42
2
4
; x = 0, y = 3
y
All rights reserved.
14.
;x
y
1O
x
4321
1 2
1
2
3
4
5
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
15.
4
3
2
1
y
16.
O
y
3
2
1O
321
1 2
; x = 2, y = 1
21.
; x = 1, y = -1
22.
; x = 0, y = 0
2
All-In-One Answers
x
x
;x
y
6
4
2O
x
8642
2 4
2
4
6
23.
4
2
4
6
8
= -3, y = -1
; x = 5, y = 0
y
6
4
2O
4
x
; x = 3, y = -2
y
x
O
2
; x = 0, y = 0.5
3
642
2
4
6
2
; x = -1, y = 2
y
x
y
2
20.
2 3 4 5
y
2
1O
21
1 2
1
2
3
4
17.
= -1, y = -2
x
1 O
1
2
6 8
4
2O
x
642
2 4 6
2
x
O
1 2 3
321
x
O
2
19.
4
3
2
; x = 3, y = 1
y
2 4 6 8
Algebra 2
113
Algebra 2: All-In-One Answers
24.
(continued)
; x = 0, y = 0
y
Guided Problem Solving 9-2
2
1. 10,000 mi 2. mi/gal 3. g, gallons of gasoline used to drive
O
10,000
g
5. Check student’s table.
10,000 miles 4. m 5
x
25.
;x
y
4
3
2
1O
x
21
1 2 3 4
1
2
= 1, y = 1
Mileage (mi/gal)
2
100
80
60
40
20
O
100
200
300
Gasoline Used (gal)
400
6. This will translate the graph 50 units to the right.
26.
; x = 0, y = 0
y
10,000
7. m 5 g 2 50 ;
2
O
2
x
2
27.
; x = 4, y = -2
y
4
2O
2
4
6
8
28.
3
2
O
1
1
2
3
100
80
60
40
20
O
x
4 6 8 10
100
200
300
Gasoline Used Later (gal)
400
8. 25 mi/gal; 28.57 mi/gal 9. Check students’ work.
10,000
10,000 m 5 20,000
or
g ; The graph of
g ;m 5 1
g
2
the new mileage is a strech of the graph of the old mileage by
a factor of 2.
10. m 5
; x = 2, y = -0.5
y
Practice 9-3
x
1 2 3 4 5
29. 2.25 ft 30. 412.5 Hz 31. 825 Hz 32. 165 Hz 33. $7.50
34. 324 keepsakes 35. $4.50 36. $36.00
114
Mileage (mi/gal)
2
Algebra 2
All rights reserved.
2
1. -3, 4 2. 42 3. 2 4. 0, -2 5. -1 6. 0, 43 7. y = 0
8. y = 1 9. y 5 12 10. y = 2 11. y = 0 12. y = 1.5
13.
14.
y
y
6
6
4
4
2O
2
x
x
O
4
642
2 4 6 8
2 4 6
2
2
4
4
6
6
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
2
Algebra 2: All-In-One Answers
15.
All rights reserved.
17.
y
6
4
2O
x
2
2 4 6 8 10
2
4
6
16.
y
6
4
2O
642
2 4
2
4
6
18.
19.
x
6 9 12
y
9
6
3O
x
63
3 6 9 12
3
6
9
20.
y
Guided Problem Solving 9-3
y
9
6
3O
63
3
6
9
x
x
2
21.
x
2
2
O
2
2
x
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5. Answers may vary. 6. 6 free throws
7. 70%; answers may vary; 100%; answers may vary
1 6
27
3
8. 21
9. 20 assignments
30 1 6 5 36 5 4 5 75%
1 1 ; x 2 0 or -2 6. 3 ; x 2 -2
4. 43 ; x 2 -5 5. x
x12
5
2 ; y 2 0 or -6 8. x ; x 2 5 or -5
7. y 1
6
x15
1 8 ; x 2 7 or -5
9. x 2 3 ; x 2 6 or -6 10. x
x27
x26
2x 1 1 ; x 2 -5 or 22 14. 2x 1 3 ; x 2 1 or 2
13. 3x
12
3
3
x21
2
O
WINDOW FORMAT
Xmin=0
Xmax=100
X s c l =10
Ymin=.5
Ymax=1
Y s c l =.1
26
4x 2 12
11. 3x
; x 2 3 or -2 12.
; x 2 -3 or -7
x17
x23
y
2
4.
1. 2x x1 1 ; x 2 0 2. 2; x 2 232 3. 3; y 2 1 or -1
2
O
1. the player’s rate of success if she makes x more shots
2. an x-value; the number of free throws she needs to make
3. Answers may vary.
Practice 9-4
y
2
2
(continued)
2
2
22. vertical asymptote at x = -2; hole at x = 2
23. vertical asymptote at x = 1; hole at x = 0 24. vertical
asymptotes at x = 1 and x = -1 25. vertical asymptote at
x = -2 26. no vertical asymptotes or holes 27. vertical
asymptote at x = 3; hole at x = -3 28. vertical asymptote
at x = 4 29. vertical asymptotes at x 5 24 and x = 3
5
30. vertical asymptotes at x = 2 and x = -2
1 3500 , where x = number of pages;
31a. y 5 0.02x x
7 ; x 2 4 or -4 16. x 2 3 ; x 2 -3
15. x 1
4
2
17. 10; a 2 -1, 0 18. -1; x 2 22 , 0, 43
5
19. x2 - 1; x 2 -4, 2 20. x + 3; x 2 -4, -3, -1
2
7y 2 28
21. 6y 1 24 ; y 2 -5, -4 22. 3x 1 3x ; x 2 0, 45
x25
5y 2 1 10y 1 5
; y 2 -2, -1 24. 3x 2 6 ; x 2 -1, 2
36y 1 72
14
y
y
25. y 2 2 ; y 2 2, 49 26. 23 ; y 2 46 27. ; y 2 0, 47
5
2 2 16
x
1
2
x
1
28. x 2 2 ; x 2 2 , 2, 3, 5 29. 2
; x 2 41, 43
x 29
23.
2
30. 1; x 2 -3, 0, 5 31. x2 2 5x 1 6 ; x 2 -3, -2
x 1 5x 1 6
1 ; x 2 0, 46 33. x + 8; x 2 -2, 48 34. 4 ; x, y 2 0
32. x
y
3
2 16
35. 4x 3x
; x 2 0, 1 , 5, 44 36. x ; x, y 2 0
6y
3
37. 3x; x 2 0, -2 38. x
; x 2 -6, -4, 2
3
2
39. x2 2 2x 1 1 ; x 2 -7, -3, 4
x 1 14x 1 49
2
40. x 2 1 2x 1 1 ; x 2 -2, 41
x 1x22
31b. at least 2365 pages 31c. 3571 pages 31d. 7292 pages
31e. x = 0; y = 0.02
Guided Problem Solving 9-4
1. The radius and height are both r. 2. cylinder or
hemisphere 3. V 5 23pr3 4. S.A. 5 3pr2 5. V 5
S.A.
All-In-One Answers
Algebra 2
2r
9
115
Algebra 2: All-In-One Answers
(continued)
V
5 4r 9. The ratio
6. V 5 pr3 7. S.A. 5 4pr2 8. S.A.
for the cylindrical tank is larger. 10. The cylindrical tank has
a larger volume. 11. yes; cylindrical tank holds more than a
hemispherical tank; answers may vary. 12. cylindrical tank
33. no solution 34. 6 35. -5 36. -1 37. about 13 mi/h
tail wind 38. about 14 mi/h head wind
39. about 1.3 days 40. Tom: 125 min, Huck: 500 min
Practice 9-5
1. 700 miles 2. 360 mi/h 3. t 5 ds 4. 35
18 h 5. faster
700
700
6. dt 1 x or 360 1 x 7. 360700
8.
1 x
360 1 360 1 x 5 3.5
35
700
or 18 1 360 1 x 5 3.5 9. 90 mi/h 10. Answers may vary.
11. 50 mi/h
2
2x 2 2 7. 3 8. 2 2 n 9. 2x
6. x 1 12
n24
9
xy3
2
5
3(3y 2 1)
7y 1 5
12y 1 5x
10. 3y
11.
12.
2
y 25
10x2y2
2
2
3 2 2x y
10x 2 26
13.
14.
(x 1 5)(x 2 5)(x 1 1)
8x3y3
9y 1 4x
x 2y
3
15.
16.
17. x 1
2
21x2y2
x2 2 4
(5x 1 1)(x 1 3)
18.
(x 2 3)(x 1 2)(x 1 5)(x 1 1)
2(x 1 2)
7x 1 5
19.
20.
2(3x 2 1)(2x 2 3)(2x 1 3)
x(x 2 3)
2
4x 1 1
36x 1 3
21.
22. 4x 2
x29
(x 1 5)(x 1 1)(x 2 2)
2
2
5x 1 6
23. 3x2 1 14 24. 5x 2 2 25x 1 31 25. 3x
21
x 15
x 2 5x 1 6
2
2
26. 5a 2 1 2a 27. 28c
a 24
2 29. 2
28. gh
6t
t 2 2 25
c 29
2 1 y2
2
x
2y
x12
30. 28r
31. 2
32. 3x 33. 4x
26
r 24
x 1 xy
y
2
2
34. 2 x
35. 4y 36. 15
37. 2x + 3
4
2x 2 3x 2 2
3y(y 2 2)
2y 1 6xy
38. 3x 2 3 39.
40.
x
5x 1 5
(y 2 6) (y 1 2) (y 2 4)
24 ohms 41b. 4 ohms
41a. 17
3
Guided Problem Solving 9-5
1. 1 unit 2. 13 unit 3. 1; 2 4. 1 2
2
2
1 5 1 1 2 5. 3
1
a
b
ab
2
3
4
2
6. 3; 2 7. 5 8. 3 9. 1 1 5 ab ? 1 2 1 5 a2ab
1b
a 1 b
a 1 b
10. Check students’ work. 11. 83
Practice 9-7
1. no 2. yes 3. yes 4. no 5. dependent 6. independent
7. independent 8. dependent 9. 20% 10a. 0.6 10b. 1
10c. 0.7 10d. 0.6 11a. 23 11b. 23 11c. 23 11d. 61
1 15. 0.16 16. 1
12. about 69.6% 13. 12.5% 14. 20
20
17. 11 18. 55% 19. 38%
12
Guided Problem Solving 9-7
1. a multiple-choice test 2. 3 3. 4 4. 1 5. 41 6. no
7. independent 8. 41; 41; 14 9. P(A) P(B) P(C) = 41 41 14
1
10. 64
11. Check students’ work. 12. 18
9A: Graphic Organizer
1. Rational Functions 2. Answers may vary. Sample: inverse
variation, rational functions and their graphs, rational
expressions, solving rational equations 3. Check students’
work.
9B: Reading Comprehension
1. y-axis 2. when it is the ratio of two functions, written as a
fraction 3. The value 2, substituted for the variable x, results
in a value of zero for the denominator, which makes the
(x 2 1)
function undefined. 4. x 2 2 ?
5. When the value 2
x22
1
is substituted for the variable x, the denominator is zero and
the function is undefined. 6. a
9C: Reading/Writing Math Symbols
1. "21 2. <2.718 3. <3.14 4. 7! means 7 factorial,
or 7 3 6 3 5 3 4 3 3 3 2 3 1. 5. 3 : 5 means the ratio of
3 to 5 or 3 . 6. decimal point, read as “and,” separates units
5
and tenths 7. Multiply 7 times 9.
Practice 9-6
4 4. 2 9 5. 9 6. -2 7. -0.2
1. 43 2. 44 3. 211
4
17
9D: Visual Vocabulary Practice/High-Use
Academic Words
8. -0.5 9. 3 10. -2 11. 0 12. -17 13. 12 14. 6
1. notation 2. composition 3. arrange 4. pattern
5. approach 6. equivalent 7. apply 8. exclude 9. solve
3 16. no solution 17. -9 18. 7 19. 11 20. 41
15. 16
21. 5 22. -3 23. 0 24. 219 25. -3 26. 18 27. 60
7
25
14
28. -5 29. no solution 30. 12 31. 4 32. 3
116
Algebra 2
All rights reserved.
3. (2x + 3)2(2x - 3) 4. 10x(x + 3)2(x - 3) 5. 2x
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1. 6x(x + 2)(2x - 3) 2. 6(x - 1)(x - 2)2(x + 10)
Guided Problem Solving 9-6
Algebra 2: All-In-One Answers
(continued)
10.
9E: Vocabulary Check
3
2
1
Branch: A piece of a discontinuous graph.
Inverse variation: An equation of the form y 5 k
x or
xy = k, where k 0.
P(x)
Rational function: f(x) 5
, where P(x) and Q(x) are
Q(x)
polynomial functions and Q(x) 0.
Joint variation: An equation of the form z = kxy,
where k 0.
Point of discontinuity: Occurs at x = a, if a is a real number
for which the denominator of a rational function f is zero.
1
1
2
3
3
11.
3
2
1
All rights reserved.
9F: Vocabulary Review Puzzle
1. simplest form 2. complex 3. extraneous solution
4. discontinuity 5. independent 6. branch 7. rational
8. dependent 9. combined 10. mutually exclusive
O
1
x
hyperbola;
x-axis, y-axis;
{x∆x # -3 or x $ 3},
all real numbers
x
hyperbola;
x-axis, y-axis;
{x∆x # -3 or x $ 3},
all real numbers
x
circle;
all lines through center;
{x∆-3 # x # 3},
{y∆-3 # y # 3}
3
y
O
1 2
Chapter 10
12.
Practice 10-1
1. (0, 0); (43, 0), (0, 43); {x∆-3 # x # 3}, {y∆-3 # y # 3}
2. (0, 0); (43, 0); {x∆x # -3 or x $ 3}, all real numbers
3. (0, 0); (41, 0), (0, 43); {x∆-1 # x # 1}, {y∆-3 # y # 3}
4. (0, 0); (43, 0), (0, 41); {x∆-3 # x # 3}, {y∆-1 # y # 1}
5. (0, 0); (43, 0), (0, 42); {x∆-3 # x # 3}, {y∆-2 # y # 2}
6. (0, 0); (45, 0), (0, 45); {x∆-5 # x # 5}, {y∆-5 # y # 5}
7.
ellipse;
y
3
2
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
21
1
2
3
x
hyperbola;
x-axis, y-axis;
{x∆x # -2 or x $ 2},
all real numbers
y
x
O
32
x-axis, y-axis;
{x∆-2 # x # 2},
{y∆-1 # y # 1}
6
4
2
6
13.
21
1
2
2
3
3
1
32 1
y
x
O
ellipse;
x-axis, y-axis;
{x∆-1 # x # 1},
{y∆-2 # y # 2}
14.
3
2
1
1 2 3
32
y
2
1
3
1
1
2
2
6
O
1 2
y
x
O
2 3
circle;
all lines through center;
{x∆2"2 # x # "2},
{y∆2"2 # y # "2}
2
3
3
9.
O
y
2
1
2 3
8.
2
2
4
6
y
x
O
1
All-In-One Answers
3
ellipse;
x-axis, y-axis;
{x∆-2 # x # 2},
{y∆-3 # y # 3}
15.
3
1
3
1
1
y
x
O
1
3
circle;
all lines through center;
{x∆2"5 # x # "5},
{y∆2"5 # y # "5}
3
Algebra 2
117
3
2
y
x
O
32
ellipse;
x-axis, y-axis;
{x∆2"2 # x # "2},
{y∆-1 # y # 1}
22.
6
4
2
642
2
4
6
2 3
2
3
17.
3
2
1
321
1
2
3
18.
3
2
1
321
1
2
3
19.
3
2
1
321
1
2
3
20.
6
4
2
642
2
4
6
21.
6
4
2
6
118
2
2
4
6
y
x
O
hyperbola;
x-axis, y-axis;
{x∆x # 2"2 or x $ "2},
all real numbers
23.
6
4
2
642
2
4
6
1 2 3
24.
y
x
O
1 2 3
y
x
O
hyperbola;
x-axis, y-axis;
all real numbers,
{y∆y # -1 or y $ 1}
hyperbola;
x-axis, y-axis;
{x∆x # 2"5 or x $ "5},
all real numbers
circle;
all lines through center;
{x∆-5 # x # 5},
{y∆-5 # y # 5}
x
hyperbola;
x-axis, y-axis;
{x∆x # -4 or x $ 4},
all real numbers
2 4 6
y
O
2 4 6
circle;
y
all lines through center;
2
3 2
3
25.
9
6
3
26.
6
2
6
2 4 6
2
2
x
O
2
3
{x∆213 # x # 13 },
{y∆213 # y # 13 }
x
hyperbola;
x-axis, y-axis;
{x∆x # -7 or x $ 7},
all real numbers
x
circle;
all lines through center;
{x∆-4 # x # 4},
{y∆-4 # y # 4}
x
ellipse;
x-axis, y-axis;
{x∆-4 # x # 4},
{y∆-2 # y # 2}
y
963
3
6
9
x
O
O
2
3
1 2 3
y
x
hyperbola;
x-axis, y-axis;
all real numbers,
{y∆y # -3 or y $ 3}
y
3 6 9
y
O
2
6
6
y
x
O
2
Algebra 2
6
ellipse;
x-axis, y-axis;
{x∆-4 # x # 4},
{y∆-3 # y # 3}
27.
6
4
y
O
64
All rights reserved.
16.
(continued)
4 6
4
6
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Algebra 2: All-In-One Answers
Algebra 2: All-In-One Answers
28.
6
4
2
64
x
3
2
1
321
1
2
3
hyperbola;
x-axis, y-axis;
{x∆x # -2 or x $ 2},
all real numbers
642
y
x
O
hyperbola;
x-axis, y-axis;
{x∆x # -1 or x $ 1},
all real numbers
circle;
all lines through center;
{x∆-7 # x # 7},
{y∆-7 # y # 7}
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
642
2
4
6
37.
3
x
hyperbola;
x-axis, y-axis;
{x∆x # -3 or x $ 3},
all real numbers
1
3
2 4 6
y
321
1
2
3
x
hyperbola;
x-axis, y-axis;
all real numbers,
{y∆y # -3 or y $ 3}
x
hyperbola;
x-axis, y-axis;
all real numbers,
{y∆y # -3 or y $ 3}
x
circle;
all lines through center;
{x∆-2 # x # 2},
{y∆-2 # y # 2}
x
circle;
all lines through center;
{x∆-6 # x # 6},
{y∆-6 # y # 6}
x
42
2
4
39.
3
y
x
O
1 2 3
All-In-One Answers
y
O
2 4 6
y
O
2 4 6
y
O
1
3
y
4
2
ellipse;
x-axis, y-axis;
{x∆-1 # x # 1},
{y∆-5 # y # 5}
6
3
2
1
O
3
2 4 6
33.
1
1
38.
O
642
6
4
2
2 4 6 8
y
642
2
4
6
36.
x
O
8
6
6
4
2
642
2
4
6
y
8642
2
4
32.
x
hyperbola;
x-axis, y-axis;
{x∆x # -1 or x $ 1},
all real numbers
y
2 4 6
35.
1 2 3
8
6
4
2
6
4
2
6
4
2
4
6
30.
31.
34.
4 6
2
4
6
29.
All rights reserved.
y
(continued)
ellipse;
x-axis, y-axis;
{x∆-2 # x # 2},
{y∆-1 # y # 1}
1
321
1
2
3
O
2 4
y
x
O
1 2 3
circle;
all lines through center;
{x∆2"3 # x # "3},
{y∆2"3 # y # "3}
Algebra 2
119
Algebra 2: All-In-One Answers
3
1
21
1
y
x
O
ellipse;
x-axis, y-axis;
{x∆-3 # x # 3},
{y∆-2 # y # 2}
1 2
321
1
2
42.
x
O
1 2 3
32
1
2
3
ellipse;
x-axis, y-axis;
{x∆2"2 # x # "2},
{y∆22"3 # y # 22"3}
1 , 0b ; x 5 2 1
1 b; y 5 1
13. a0, 2 12
14. a 20
20
12
1 , 0b ; x 5 1
15. a0, 22 34 b; y 5 23 41 16. a2 12
12
1 , 0b ; x 5 2 1
17. (2, -3); x = -2 18. a 32
32
1 b; y 5 2 1
19. (0, 2); y = -2 20. a0, 32
32
y
2
1
6. left 7. right 8. downward 9. (0, -8); y = 8
3
3
1 , 0b ; x 5 2 1
11. a 4 , 0b ; x 5 2 4 12. a 48
48
y
2
1
1. left 2. downward 3. left 4. upward 5. upward
1 b; y = 1
10. a0, 2 32
32
3
41.
Practice 10-2
x
O
ellipse;
x-axis, y-axis;
{x∆-1 # x # 1},
{y∆-3 # y # 3}
1 2 3
1 x2 23. x 5 2 1 y 2
21. x = 2 81 y 2 22. y = 16
12
1 x2
1 x2
24. y 5 2 16
25. y 5 2 12
26. x 5 1y2
8
All rights reserved.
40.
(continued)
1 y2
27. y 5 1 x2 28. x 5 1 y2 29. x 5 2 24
12
12
1 y2
1 x2 32. y 5 1 x2
30. x 5 2 20
31. y 5 20
28
1 x2 34. x 5 1 y2 35. x 5 1 y2
33. y 5 32
4
24
1. the lamp 2. the very edge of the shadow 3. a plane and a
double cone 4. The wall is like the plane and the lamp shade
is like the double cone. 5. parabola 6. hyperbola 7. circle
8. Hold the lamp at an angle so that the light from the top of
the shade gives a closed, curved oblong area of light on the
wall. 9. Answers may vary. 10. Answers may vary.
1 x2
36. y 5 2 16
37. y 5 41 x2 38. x 5 2 1 y 2
12
1 y2
39. x 5 2 14 y 2 40. x 5 2 40
41. y 5 2 1 x 2
12
1 y2 43. y 5 1 x2 44. x 5 1 y2
42. x 5 20
20
12
1 x2 45b. 12.5 in. 46. y 5 1 x2 47. y = x2
45a. y 5 40
8
48. (3, -1); (3, -2); y = 0
y
O
x
2
4
2
4
6
120
Algebra 2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Guided Problem Solving 10-1
Algebra 2: All-In-One Answers
(continued)
49. (0, 0); a 1 , 0b ; x = - 18
8
Practice 10-3
1. (x + 5)2 + (y + 2)2 = 16 2. (x - 1)2 + (y - 4)2 = 4
y
3. (x + 2)2 + (y - 5)2 = 1 4. (x + 4)2 + (y + 1)2 = 4
2
5. (x + 3)2 + (y + 4)2 = 9 6. (x - 4)2 + (y - 6)2 = 1
x
2
O
7. x2 + y2 = 9 8. x2 + (y - 1)2 = 4 9. (x + 1)2 + y2 = 36
2
10. (x - 2)2 + y2 = 1 11. x2 + (y + 3)2 = 25
2
12. (x - 4)2 + (y + 4)2 = 2.25 13. (x + 2)2 + (y - 6)2 = 16
14. (x - 5)2 + (y + 1)2 = 1.21 15. (x - 1)2 + (y + 5)2 = 6.25
50. (-1, 1); (0, 1); x = -2
All rights reserved.
4
16. (x - 2)2 + (y - 3)2 = 14 17. (x - 4)2 + (y + 2)2 = 9
18. (x + 2)2 + (y - 5)2 = 12 19. (x - 1)2 + (y - 7)2 = 49
y
20. (x - 5)2 + (y - 5)2 = 1 21. x2 + (y - 10)2 = 25
2
22. (x + 8)2 + (y + 6)2 = 36 23. (-1, 8); 1 24. (0, -3); 3
x
2
O
25. (-3, -1); "2 26. (6, 0); "5 27. (6, 9); 2 28. (0, 0); 12
2
2
29.
12
8
4
Guided Problem Solving 10-2
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1. meters 2. speed of the wave, in meters per second
1
3. (0, 0) 4. a = 10
; upward 5. c = 2.5 6. (0, 2.5), y = -2.5
7. Answers may vary. Sample (10, 10), (0, 0), (-10, 10)
8.
d
12
31.
s
8 4
6
8
d
33.
16
12
8
4
4
84
2
16 12 8 4
0
4
8
12
t
16
x
4 8 12
12
8
4
x
4 8 12 16
20 12 4
y
O x
4
8
12
34.
y
8
4
16 8
O
x
4 8 12 16
35.
16 8
8
12
36.
y
8
4
x
O
4 8
y
x
O
4 8
8
12
16
8
12
8
4
All-In-One Answers
O
32.
y
O
y
8
12
16
8
12
16
6
O
1284
8
12
8
4
9. Check students’ work.
10.
8
4
O x
20 12 4 4
6
6 O
30.
y
84
y
O
x
4 8 12 16
8
12
16
Algebra 2
121
(continued)
9. Q 46"2, 0 R ;
1. the center and the radius of the circle 2. no
3. (x2 2 6x) 1 (y2 2 2y) 5 24
4. (x2 2 6x 1 9) 1 y2 2 2y 5 24 1 9
5. (x2 2 6x 1 9) 1 (y2 2 2y 1 1) 5 24 1 9 1 1
2
6. (x 2 3) 2 1 (y 2 1) 2 5 Í 6
7. (x 2 h) 2 1 (y 2 k) 2 5 r2
8. 3; 1; "6 9. The center is (3, 1). 10. The radius is "6.
11. Answers may vary. 12. (2, 3), 4
Practice 10-4
1. Q 0, 43"5 R ;
9
6
3
9 63
x
3 6 9
6
9
9 63
y
x
O
3 6 9
6 42
9
6
3
9 63
y
x
O
2 4 6
12
8
4
1284
2 4 6
y
3
x
O
6 42
y
x
O
2 4 6
4
6
Algebra 2
6
4
2
6 42
x
O
2 4 6
O
x
3
17. Q 4"65, 0 R ;
63
x
O
2 4 6
6
9
3 21
y
x
O
1 2 3
1O
21
1 2
1
x
16. Q 0, 4"11 R ;
y
y
4
2O
x
642
2 4 6
2
4
18. Q 0, 42"6 R ;
y
O
3 6
y
3
2
3
y
3
2
1
3
O
1 2
9
6
x
4 8 12
14. Q 4"5, 0 R ;
y
3
2
x
4 8 12
O
2
3
15. Q 4"15, 0 R ;
8. Q 0, 4"21 R ;
6
4
2
y
2
1O
1
1
1
2
21
1284
y
12. Q 4"5, 0 R ;
3 6 9
y
12
8
4
8
12
13. Q 0, 4"5 R ;
8
12
7. (44, 0);
3 6 9
4
6
x
6. Q 0, 44"5 R ;
4
6
122
6 42
y
6
9
5. Q 0, 4 72 "3 R ;
6 42
6
4
2
O
x
O
11. Q 0, 44"3 R ;
4. (46, 0);
6
9
6
4
2
6
4
2
y
6
9
4
6
3. Q 0, 4"91 R ;
9
6
3
9 63
2. Q 0, 4"35 R ;
y
O
9
6
3
10. Q 43"13, 0 R ;
All rights reserved.
Guided Problem Solving 10-3
6
y
x
x
642
2 4 6
6
4
6
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Algebra 2: All-In-One Answers
Algebra 2: All-In-One Answers
19. Q 4"2, 0 R ;
20. Q 4"2, 0 R ;
y
3
2
3
2
3
y
2
x
2 3
4. Q 0, "19 R , Q 0, – "19 R
y
3
2
O
32
(continued)
x
O
1
1
3
2
3
All rights reserved.
3
2
y2
2
y2
5
5
3
y2
2
y2
2
y2
2
2
y2
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
2
y2
y2
51
5 1 33. x 1
49
100
25
y2
y2
2
x 1
5 1 35. x 1
51
34. 100
100
196
196
2
y2
y2
5 1 37. x 1
51
36
625
20.25
2
2
y2
x2 1 y 5 1 40. x2 1 y 5 1
38. x 2 1 4 5 1 39. 16
4
32
16
2
x 1
36. 400
2
y2
2
y2
2
1. Q 42"2, 0 R ;
6
4
2
y2
2
y2
2
y2
x 1
x 1
5 1 46. x 1
5 1 45.
51
44. 20
9
18
26
16
25
2
2
y2
y2
5 1 49. x 1 y 2 5 1
5 1 48. x 1
49
25
4
5
2
2
y2
y2
51
50. x
1
5 1 or x 1
2500
10,000
10,000
2500
47. x 2 1
Guided Problem Solving 10-4
1. eccentricity = ac 2. 10; 9 3. 0.9
All-In-One Answers
64 2
4
6
2. Q 0, 4"34 R ;
y
x
O
2 4 6
3. Q 4"85, 0 R ;
6
4
2
64 2
4
6
2 4 6
8
x
O
8
x
O
8
8
8
8
8
5. Q 4"10, 0 R ;
64 2
4
6
x
O
y
8
6
4
2
y
4. Q 0, 42"10 R ;
y
y2
x 1
51
5 1 43. x 1
5 1 42. x 1
41. 20
4
81
121
100
36
2
x
5
Practice 10-5
29. x4 1 y2 5 1 30. x 1 4 5 1 31. x9 1 18 5 1
5
2
O
7. The shape is close to a circle; the shape is close to a line
segment. 8. No; since c2 5 a2 2 b2, c a, so ac , 1.
9. Check students’ work.
2
2
x2 1 y 5 1 28. x2 1 y 5 1
27. 16
25
0.25
2.25
2
x
x
x 1
24. 29
5 1 25. x2 1
5 1 26. x 1 y2 5 1
4
10
5
x 1
32. 36
8
y
x 1
22. 81
5 1 23. x 1
51
4
16
16
2
4
5. 10; "99 9.95; 1; 0.1
6.
21. Q 0, 42"2 R ;
2
1O
1
1
1
2
8 4 O
6. Q 42"17, 0 R ;
y
x
O
2 4 6
6
4
2
64 2
4
6
y
x
O
2 4 6
Algebra 2
123
64 2
4
6
y
x
O
2 4 6
5" 5
9. a0, 4 2 b ;
6
4
2
64 2
4
6
1284
4
y
x
O
2 4 6
64 2
4
6
64
x
2 4 6
10
4 8 12
x
10
x
2 4 6
42
y
x
O
2 4
4
6
15. Q 4"26, 0 R ;
8
x
O
8
8
Algebra 2
x
6
x
x
O
6
6
6
y
9
6
3O
63
3 6
3
6
9
24. Q 0, 44"2 R ;
6
x
y
2O
x
642
2 4 6
2
6
2 4 6
y
4 6
2
4
6
6
y
6
4
2O
42
2 4
2
4
6
x
642
22. Q 4"37, 0 R ;
y
6
4
2O
25. Q 0, 42"5 R ;
16. Q 4"29, 0 R ;
y
64
y
4
6
23. Q 44"5, 0 R ;
14. Q 0, 45"2 R ;
6
4
2
6
4
4
6
10
y
y
x
O
2 4 6
642
y
6
4
2O
x
642
2 4 6
2
4
6
20. Q 4"17, 0 R ;
21. Q 42"5, 0 R ;
O
x
O
x
6
4
O
y
2
4
6
y
18. Q 0, 4"41 R ;
4 6
19. Q 0, 4"13 R ;
10
4
6
124
2 4 6
6
4
2
y
O
8
6
4
2
y
13. Q 0, 4"29 R ;
642
x
O
12. Q 0, 42"26 R ;
8
12
6
4
64 2
4
6
y
10. (0, 45);
11. Q 4"73, 0 R ;
12
8
4
6
4
2
17. Q 0, 4"10 R ;
All rights reserved.
8. Q 4"13, 0 R ;
7. (0, 45);
6
4
2
(continued)
y
2O
x
642
2 4 6
2
6
26. Q 45"2, 0 R ;
y
6
4
2O
x
642
2 4 6
2
4
6
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Algebra 2: All-In-One Answers
Algebra 2: All-In-One Answers
27. Q 4"29, 0 R ;
64
x
6
x
O
2 4 6
642
y
x
O
2 4 6
4
6
x
O
8
8
64
8
33. a0, 4 25
b;
4
x
y
6
4
2O
6
All-In-One Answers
2O
x
642
2 4 6
2
6
x
64
y
6
y
2O
x
642
2 4 6
2
6
45. Q 42"17, 0 R ;
6
4
2O
2
4
6
y
6
4
2O
x
642
2 4 6
2
4
6
44. Q 0, 42"5 R ;
4
2O
x
642
2 4 6
2
4
y
6
x
6
36. Q 4"13, 0 R ;
y
6
4
2O
2
2
2
4
6
6
y
y
6
4
2O
x
642
2 4 6
2
4
6
42. Q 43"5, 0 R ;
y
2
4
6
43. Q 0, 4"29 R ;
4
6
4
2O
x
642
2 4 6
2
4
6
6
4
2
x
4 6
2
4
6
y
4
6
41. Q 0, 4"17 R ;
y
6
4
2O
x
642
2 4 6
2
4
6
40. Q 4"41, 0 R ;
x
O
2 4 6
642
34. a0, 4 25 b ;
y
35. Q 4"13, 0 R ;
6
4
32. Q 42"5, 0 R ;
8
y
2O
x
642
2 4 6
2
39. Q 0, 42"5 R ;
y
6
4
2O
2
2
2
4
6
y
38. (45, 0);
6
30. Q 4"10, 0 R ;
31. Q 4"26, 0 R ;
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
y
4
6
6
4
All rights reserved.
6
4
4 6
2
4
6
29. Q 0, 4"13 R ;
6
37. Q 0, 4"10 R ;
28. (0, 45);
y
6
4
2O
642
(continued)
x
4 6
64
y
6
4
2O
2
4
6
x
4 6
Algebra 2
125
(continued)
y
x2
2
51
11
1.869 3 10
3.752 3 1012
y2
x2
2
51
10
3.112 3 10
3.907 3 1012
2
y2
x2 2 y 5 1 49.
x2
48. 49
2
51
32
8.582 3 1010
4.812 3 1010
2
y2
y2
x2
50. x 2
2
51
5 1 51.
25
200
5.858 3 107
1.667 3 107
2
2
2
x2 2 y 5 1 53. x 2 y
51
52. 4489
5625
26,775
3975
2
2
2
x2 2 y 5 1 55. x2 2 y 5 1 56. x2 2 y 5 1
54. 64
336
36
36
64
45
2
2
2
x2 2 y 5 1 58. x2 2 y 5 1 59. x2 2 y 5 1
57. 36
9
28
80
40
2
2
2
2
x 2 y 5 1 61. x 2 y 5 1
60. 64
36
63
81
47.
Practice 10-6
1. ellipse; (-1, 2);
2"30
a21 4
5
6
4
2
64
3.
2
Q 4"10, 2 R ;
, 2b ;
y
x
O
2 4 6
3. ellipse; (-4, 0);
Q 24 4 4"3, 0 R ;
x
O
12 6
6
6
9
4
x
4
2
2
(x 2 1) 2
– (y 1 1) 2 5 1
4. subtract 5. add 6.
4
7.
1
42
3
y
O
x
2 4 6
8. Answers may vary.
9.
(x 1 1) 2
(y 2 2) 2
2
5 1;
4
9
4
y
2
4
2
y
x
O
1 2 3 4 5
4
2
2
4
y
x
O
2 4 6 8 10
8. circle; (0, 0); "7;
(8, 2), (-2, 2);
8
6
4
2
1
8
7. hyperbola; (3, 2);
3
3
2
1
6. hyperbola;(5,3); Q 5 4 "5, 3 R;
x
1
2 4 6
2
3
4
6
8
y
O
x
O
4. circle; (4, 2); 1;
y
9
6
y
O
642
y
4
6
5. circle; (0, -3); 6;
4
6
4
2
4
6
Guided Problem Solving 10-5
2
1. down 1 unit 2. x4 2 y2 5 1
2. hyperbola; (0, 2);
y
3
2
1
x
O
2 4 6 8 10
3 1
y
x
O
1 2 3
2
3
x
4
2 O
2
2
126
Algebra 2
All rights reserved.
2
46.
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Algebra 2: All-In-One Answers
Algebra 2: All-In-One Answers
9. circle; (-1, -7); 9;
10. hyperbola; (-1, -1);
Q 21 4 "34, 21 R ;
y
O
3
63
4
2
x
3
(continued)
9
86
6
9
12
15
2
17. circle; (-4, -1); 4;
y
x
O
4
All rights reserved.
2
1
1
x
O
2 3
1
5
13. circle; (5, -2); 6;
4
2
9
6
3
9 3
x
2 4 6
22.
y
x
O
4
2
4 6 8 10
42
x
O
4 6 8
(y 2 5) 2
(x 1 4) 2
51
2
4
5
(x 2 50) 2
y2
5 1 24. x = 1 (y + 2)2 + 1
2
2304
2
196
2
2
2
(y
2
2)
(y 1 5) 2
(x
1
4)
25. x9 1
5 1 26.
1
51
4
9
4
x
O
6 9
27. (x + 1)2 + (y - 2)2 = 36 28. y = -(x + 1)2 + 5
(x 2 2) 2
(y 2 2) 2
2
51
4
5
y
30.
(x 2 2) 2
(y 1 5) 2
51
1
16
25
31.
(x 2 125) 2
y2
2
51
36
15,589
8
6
O
y
29.
8
642
4 6
20. parabola; (2, -1);
16. parabola; (-3, -2);
y
4
2
x
O
23.
x
15. parabola; (1, 2);
y
21. (x + 4)2 + (y - 5)2 = 36
14. circle; (-1, 5); 8;
6
8
64 2
4
6
y
2
4
6
1 2 3 4 5
3
4
2 4 6 8 10
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
x
O
15
O
6
4
2
y
y
x
2
19. parabola; (2, -1);
Q 2 4 "6, 21 R ;
2
1
6
4
2
6
12. ellipse; (2, -1);
y
y
O
10 642
4
6
8
11. circle; (2, 2); 3;
5
4
6
4
18. hyperbola; (0, 0);
Q 42"2, 0 R ;
x
O
86
2 4
2
(y 1 2) 2
32. x 1
51
2.25
6.25
4
Guided Problem Solving 10-6
1. hyperbola 2. (3, -2) 3. (-3, -2) 4. 6 5. (10.2, -2)
6. 7.2 7. b2 = (7.2)2 - 62 = 15.84 8. horizontal
9.
(x 2 h) 2
a
2
2
(y 2 k) 2
b
2
5 1 10.
11. Answers may vary. 12. (y –
(x 2 3) 2
(y 1 2) 2
2 15.84
36
2) 2 2 (x 2 3) 2 5
51
1
10A: Graphic Organizer
1. Quadratic Relations 2. Answers may vary. Sample:
parabolas, circles, ellipses, hyperbolas 3. Reading for Problem
Solving 4. Choosing Cannot Be Determined 5. Answers may
vary. Sample: design, solar energy, machinery, architecture
6. Check students’ work.
All-In-One Answers
Algebra 2
127
(continued)
10B: Reading Comprehension
1. y-axis 2. x-axis 3. upward; to the right 4. downward; to
the left 5. b
10C: Reading/Writing Math Symbols
1. the set of all x such that x is a real number 2. the set of all
x such that x is greater than zero 3. the set of all y such that y
is less than negative 1 4. the set of all x such that x is between
5 and 9 or the set of all x such that x is greater than 5 and less
than 9 5. the set of all x and y such that x is equal to y
6. the set of all x and y such that y is equal to 3 times x
10D: Visual Vocabulary Practice
1. vertices of a hyperbola 2. ellipse 3. foci of an ellipse
4. parabola 5. vertices of an ellipse 6. hyperbola 7. radius
8. circle 9. foci of a hyperbola
10E: Vocabulary Check
Radius: The distance between the center of a circle and any
point on the circumference.
Conic section: A curve formed by the intersection of a plane
6. a n 5 a n 2 1 1 1 where a1 = 2 ; 2 1
3
3
3
7. an = an-1 + 3 where a1 = 36; 51
8. an = an-1 - 6 where a1 = 36; 6
9. a n 5 1 a n 2 1 where a1 = 9.6; 0.3 10. an = 7n; 140
2
11. an = 6n - 4; 116 12. an = n + 4; 24
13. an = n - 2; 18 14. an = 2n + 1; 41
15. an = 0.8n; 16 16. a n 5 n ; 5 17. a n 5 1 ; 1
4
2n 40
2
1
18. a n 5 n 2 ; 19 19. multiply by 2; 32, 64, 128
3
3
20. subtract 5; 19, 14, 9 21. add 0.1; 1.2, 1.3, 1.4
22. add 7; 39, 46, 53 23. multiply by 2; 40, 80, 160
24. subtract 3; -21, -24, -27 25. explicit; 1 , 2 , 1, 4 , 5
3 3
3 3
26. explicit; -5, -2, 3, 10, 19 27. recursive; 5, 8, 17, 44, 125
28. explicit; 0, 1 , 1, 1 1 , 2 29. recursive; 5, -2, 5, -2, 5
2
2
30. recursive; -4, -8, -16, -32, -64 31a. 1, 6, 36, 216
31b. a n 5 6a n 2 1 where a1 = 1 32a. 60° 32b. a n 5 360
n
32c. No polygon has one or two angles.
All rights reserved.
Algebra 2: All-In-One Answers
Guided Problem Solving 11-1
of the parabola is the same distance from the focus and this
line.
Circle: The set of all points in a plane at a distance r from a
given point.
Center: The point that is the same distance from every point
on the circle.
1. 2 2. 7 3. 15 4. an = an - 1 + [2n + (n - 1)] 5. 26 6. 40
7.
10F: Vocabulary Review Puzzle
E
C
L
I
L
H
Y
P
E
R
A
B
O
I
P
R
B
O
L
A
C
A
S
A
E
L
I
C
T
R
I
X
F
O
C
U
S
U
S
3
4
5
Cards Needed
2
7
15
26
40
8. Yes, the numbers of cards per level is correct.
9.
Levels
1
2
3
4
5
Blocks Needed
1
3
6
10
15
1. 96 2. -406.9 3. 36.3 4. -99 5. 464 6. -231 7. 5.5
8. -10.5 9. 171 10. no 11. yes; -3 12. yes; -0.4
13. yes; 5 14. yes; -29 15. yes; 0.3 16. yes; 6 17. yes; 0.2
18. yes; 13 19. 36 20. 21 21. 31 22. 14.5 23. -42
24. -3.5 25. 0 26. -2 27. 21.5 28. -28.5 29. 227
30. 189.5 31. 4.5 32. 14.5 33. 9 34. 3 35. -1 36. -6.5
A
E
2
Practice 11-2
E
R
1
A
D
D
Levels
I
5
Chapter 11
Practice 11-1
1. an = an-1 + 6 where a1 = -14; 16
2. an = an-1 - 0.3 where a1 = 6; 4.5
3. an = -2an-1 where a1 = 1; -32
4. an = 3an-1 where a1 = 1; 81
37a. a n 5 a n 2 1 1 5 where a1 = 32 37b. 32, 37, 42, 47, 52
37c. a n 5 32 1 5(n 2 1) 37d. 127 people
Guided Problem Solving 11-2
1. 403, 417, 431 2. 403; 14 3. an 5 403 1 (n 2 1)(14)
4. an = 495 5. n = 8 6. 501 7. 6 min 8. 3:20 P.M. = 920;
1 min 9. 403, 417, 431, 445, 459, 473, 487, 501, …;
501 - 495 = 6 min 10. 69
5. a n 5 1 a n 2 1 where a1 = 1; 1
32
2
128
Algebra 2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
and a double cone.
Directrix: The fixed line used to define a parabola. Each point
Algebra 2: All-In-One Answers
(continued)
Practice 11-3
Guided Problem Solving 11-4
1. 8 2. 12 3. 4 4. 6 5. 10 6. 4.8 7. yes; 3; 243, 729
8. yes; 2; 64, 128 9. no 10. yes; -2; 64, -128
11. yes; 0.5; 0.0625, 0.03125 12. yes; 0.3; 0.81, 0.243
13. no 14. yes; -0.5; 4, -2 15. no
16. geometric; 1 , 1 17. neither; -9, -14
1. 20 2. Front row of middle section has 10 seats; each of the
two side sections has 4 seats 3. Last row of middle section
has 29 seats; each of the two side sections has 23 seats
4. Total seats in middle section is 390; each of the two side
All rights reserved.
9 27
18. geometric; 2, -2 19. arithmetic; 17, 22
20. arithmetic; -11, -14 21. neither; 5, -6
22. an = 3(-2)n-1; 3, -6, 12, -24, 48
23. an = 5(3)n-1; 5, 15, 45, 135, 405
24. an = -1(4)n-1; -1, -4, -16, -64, -256
25. an = -2(-3)n-1; -2, 6, -18, 54, -162
26. an = 32(-0.5)n-1; 32, -16, 8, -4, 2
27. an = 2187 a 13 b
n21
; 2187, 729, 243, 81, 27
n-1
28. an = 9(2) ; 9, 18, 36, 72, 144
29. an = -4(4)n-1; -4, -16, -64, -256, -1024
30. an = 0.1(-2)n-1; 0.1, -0.2, 0.4, -0.8, 1.6
31a. about 19.2 in. 31b. 9 mm 32a. an = 2537(1.025)n-1
32b. about 2732 33a. an = 1(1.5)n-1 33b. 1.5 in.
33c. 2.25 in. 33d. about 86.5 in.
Guided Problem Solving 11-3
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1. geometric mean = !product of the two numbers
2. an 5 a1 ? rn21 3–6. Answers may vary: A sample is
given 3. 3 and 12; 6 4. 3, 6, 12; 2 5. 768 6. 48 7. 5th term
8. The answers check. 9. Answers may vary. The answer to
20
sections has 270 5. 930 seats 6. middle section: a (n 1 9) ;
n51
20
side section: a (n 1 3) 7. $46,950 8. The answers are
n51
reasonable. 9. n = 24; d = 6
Practice 11-5
1. converges; yes 2. converges; yes 3. converges; yes
4. diverges; no 5. converges; yes 6. diverges; no 7. 15
8. no sum 9. 23 10. no sum 11. 16 12. 1.5 13. 600
255
14. 4000 15. arithmetic; 126 16. geometric; 1024
17. geometric; 1023 18. arithmetic; 240 19. 79.921875
20. 28,697,812 21. about 74.99 22. 40.5 23. 0.22222222
24. 6300 25. $8553.71 26. $40,928.80 27. 5000 cm
28. about 177.78 mm 29. $2,319,367.05; $4,950,000
Guided Problem Solving 11-5
1. 4 2. 4
3.
step 7 is the same since halfway from the 1st term to the 9th
term is the 5th term.
Practice 11-4
1. 4; 0; 3; 6 2. 5; 3; 11; 35 3. 6; 28; 33; 183 4. 4; 13; 28; 82
5. 4; 2.5; 8.5; 22 6. 6; 2; -3; -3 7. 6; 5; 10; 45
8. 4; -4; -7; -22 9. 4; 11; 20; 62
10. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15; 64
11. 5 + 8 + 11 + 14 + 17 + 20 + 23 + 26; 124
12. 4 + 9 + 14 + 19 + 24 + 29 + 34 + 39 + 44; 216
13. 10 + 25 + 40 + 55 + 70 + 85; 285
14. 17 + 25 + 33 + 41 + 49 + 57 + 65; 287
15. 125 + 126 + 127 + 128 + 129 + 130 + 131; 896
7
5
n51
4
n51
16. a (2n 2 1) 17. a (0.3n 1 2)
6
18. a 4n 19. a (23n 1 13)
n51
8
n51
7
20. a (4n 2 1) 21. a (10n 1 5)
n51
n51
22. sequence; finite 23. series; infinite 24. sequence; infinite
25. series; finite 26. sequence; infinite 27. series; finite
28. -9 29. 39 30. -72 31. -51 32. 4.5 33. 60
34. 1025 stitches 35. 19 musicians; 84 musicians
All-In-One Answers
Stage 1
4
Stage 2
16
Stage 3
64
4. 4, 16, 64 5. 4 6. 4 + 16 + 64 + 256 + 1024 + 4096
7. 5460 8. formula gives 5460 also 9a. $10, $20, $40
9b. $10 + $20 + $40 + $80 + $160 9c. $310
Practice 11-6
For Exercises 1–19, answers are in units2.
1a. 0.5(3.75) + 0.5(3) + 0.5(1.75) + 0.5(0); 4.25
1b. 0.5(4) + 0.5(3.75) + 0.5(3) + 0.5(1.75); 6.25
2a. 0.5(15.5) + 0.5(14) + 0.5(11.5) + 0.5(8); 24.5
2b. 0.5(16) + 0.5(15.5) + 0.5(14) + 0.5(11.5); 28.5
3a. 0.5(1.875) + 0.5(1.5) + 0.5(0.875) + 0.5(0); 2.125
3b. 0.5(2) + 0.5(1.875) + 0.5(1.5) + 0.5(0.875); 3.125
4a. 0.5(4) + 0.5(4.25) + 0.5(5) + 0.5(6.25); 9.75
4b. 0.5(4.25) + 0.5(5) + 0.5(6.25) + 0.5(8); 11.75
Algebra 2
129
Algebra 2: All-In-One Answers
(continued)
5a. 0.5(6) + 0.5(6.5) + 0.5(8) + 0.5(10.5); 15.5
5b. 0.5(6.5) + 0.5(8) + 0.5(10.5) + 0.5(14); 19.5
6a. 0.5(2) + 0.5(2.125) + 0.5(2.5) + 0.5(3.125); 4.875
6b. 0.5(2.125) + 0.5(2.5) + 0.5(3.125) + 0.5(4); 5.875
7a. 0.5(14.25) + 0.5(12) + 0.5(8.25) + 0.5(3); 18.75
7b. 0.5(15) + 0.5(14.25) + 0.5(12) + 0.5(8.25); 24.75
8a. 0.5(2) + 0.5(2.75) + 0.5(5) + 0.5(8.75); 9.25
8b. 0.5(2.75) + 0.5(5) + 0.5(8.75) + 0.5(14); 15.25
9a. 0.5(9.75) + 0.5(9) + 0.5(7.75) + 0.5(6); 16.25
9b. 0.5(10) + 0.5(9.75) + 0.5(9) + 0.5(7.75); 18.25
10a.
y
12
8
5. 3 units2
6.
y
8
4
2
12
4
x
units2
7. 7.5 units2 8. The mean best approximates the area because
it is between the other measures known to be larger and smaller
than the actual value. 9. 75 , 147 ; 111
16 16 16
10a–b.
4
y
All rights reserved.
8
x
O
6
4
10b. 5.5 10c. 9.5 10d. 7.5; the mean
11. 6.75 12. 16.5 13. 9 14. 12 15. 2.25 16. 18 17. 9
18. 6 19. 4.6 20. total feet 21. total number of computers
22. total miles 23. total gallons 24. total molecules
25. total price
26.
; 3.25 units2
y
4
2
x
1
2
3
4
area = 7 units2
4
10c.
y
2
8
x
O
2
27.
12
4
6
; 4.25 units2
y
4
2
8
x
4
1
x
4
O
4
Guided Problem Solving 11-6
1. less 2. greater
3–4.
y
8
3
4
area = 15 units2
10d. mean area = 11 units2; The mean best approximates the
area because it is between the other measures known to
be larger and smaller than the actual value.
11A: Graphic Organizer
1. Sequences and Series 2. Answers may vary. Sample:
arithmetic sequences, geometric sequences, arithmetic series,
geometric series 3. Answers may vary. Sample: geometry,
fund raising, design, crafts 4. Check students’ work.
4
2
130
2
4
Algebra 2
x
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
4
Algebra 2: All-In-One Answers
(continued)
11B: Reading Comprehension
2a.
Rolling Two Number Cubes
1. terms in a geometric sequence 2. The recursive formula is
Sum
based on knowing the previous term. The explicit formula is
based on knowing the ratio. 3. In an-1, n - 1 is a subscript
that tells which term you are finding. In r n-1, n - 1 is the
exponent that tells you how many times to use the base, r, as a
factor. 4. the recursive formula 5. the explicit formula 6. a
5 or less
Greater than 5
Frequency
10
26
Probability
10
36
26
36
2b.
Rolling Two Number Cubes
Sum
11C: Reading/Writing Math Symbols
means “negative” and is describing a kind of number, so it is
an adjective. In 7 - 5, the symbol means “subtract” or
“minus” and names a binary operation, so it is a verb that
describes an action. 6. Answers may vary. Sample: The letter
m alone represents “line m.” The letter m in front of an angle
represents “the measure of” angle A.
11D: Visual Vocabulary Practice
1. arithmetic sequence 2. circumscribed rectangles
3. arithmetic mean 4. geometric mean 5. geometric series
6. geometric sequence 7. arithmetic series 8. inscribed
rectangles 9. explicit formula
Composite
Frequency
15
21
Probability
15
36
21
36
2c.
Only 1
Cube
shows 2
Both cubes
show same
number
Cubes show
different
numbers,
neither is 2
Frequency
10
6
20
Probability
10
36
6
36
20
36
Numbers
showing
3a. Student Pizza Preferences
11E: Vocabulary Check
Sequence: An ordered list of numbers.
Term: Each number in a sequence.
Common ratio: The ratio of consecutive terms of a
Sausage
56
Cheese
43
Pepperoni
39
Supreme
28
Other pizza
31
No pizza
19
geometric sequence.
3b. sausage: 25.9%, cheese: 19.9%, pepperoni: 18.1%,
Series: The sum of the terms of a sequence.
Limit: The least and greatest integer values of n in summation
supreme: 13.0%, other pizza: 14.4%, no pizza: 8.8%; 100.1%;
There is a rounding error of 0.1%.
notation.
3c.
Chapter 12
Pizza
No pizza
80%
11F: Vocabulary Review
1. Answers may vary. Sample: A sequence is an ordered list of
numbers; a series is the sum of the terms of a sequence.
2. Answers may vary. Sample: In calculating the area under part
of a curve, circumscribed rectangles are partially above the
curve while inscribed rectangles are completely under the curve.
3. Answers may vary. Sample: The common difference is the
difference between consecutive terms in an arithmetic
sequence. The common ratio is the ratio between consecutive
terms in a geometric sequence.
4. Answers may vary. Sample: An arithmetic sequence is an
ordered list of numbers in which the difference between
consecutive terms is constant. A geometric sequence is an
ordered list of numbers in which the ratio between
consecutive terms is constant.
100%
Probability
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Rolling Two Number Cubes
60%
40%
20%
0%
3d.
Outcomes
100%
Cheese
80%
Probability
All rights reserved.
1. line AB 2. line segment CD 3. angle A 4. triangle
XYZ 5. Answers may vary. Sample: In -5, the symbol
Prime
40%
Sausage or
pepperoni
Supreme
or other
20%
No pizza
60%
0%
Outcomes
Practice 12-1
1a. about 0.66 1b. about 81 persons 1c. about 0.05
1d. about 0.15 1e. about 0.37
All-In-One Answers
Algebra 2
131
Algebra 2: All-In-One Answers
(continued)
3e. The sum of the probabilities of pizza categories in part d
equals the probability of pizza in part c. The overall total in
4a. 45% 4b. 6%
5. M = male, F = female, C = attend concert,
both is 100.1% (0.1% rounding error).
4a. Check student’s work. 4b. Check student’s work.
N = not attend concert
C
0.45
M
Guided Problem Solving 12-1
1. the ratio of the number of times the event occurs to the
number of times the event does not occur 2. A 1:4, B 2:3,
C 1:3, D 1:7 3. the probability of each event 4. find the sum
0.55
0.51
0.49
of the number of times it occurred and did not occur
0.49
5. P(A) = 0.2, P(B) = 0.4, P(C) = 0.25, P(D) = 0.125
6.
0.4
0.51
F
5a. about 47% 5b. about 25%
0.2
Guided Problem Solving 12-2
0.1
A
B
C
Event
W
X Y
Event
P(A and B)
5. 0.6 6. P(A) is equal to
P(B)
P(A|B). 7. The fact that P(A) = P(A|B) illustrates that the
probability of A is the same, regardless of the occurrence of B.
1 9b. 1
8. Yes, the conclusions are the same. 9a. 26
13
9c. They are not equal. The events are dependent.
4. P(A|B) 5
Probability
7. Yes, the answers are reasonable.
8.
0.10 y
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
D
1. The occurrence of B has no effect on the probability of A.
2. P(A) = 0.60; P(B) = 0.25 3. 0.15
Practice 12-3
x
Z
1. 23 2. 78 3. 3 4. 110 5. about 93.3; 97; 97 6. about 47.6;
48; 41, 49 7. about 2.6; 2.45; 2.4 8. about 15.7; 15.6; no mode
9. about 418.8; 423; no mode 10. about 1021.9; 1023; 1023
11. about 0.019; 0.019; 0.018, 0.019 12. about 26.4; 27; 29
13. about 44.8; 45; 42, 45, 49 14. about 48.1; 50.5; no mode
15. 18; 16.5; 15 16. about 1.5; 1.5; 1.3, 1.5 17. about 9.2; 9;
no mode 18. about 116.2; 116; 114 19. about 4.29; 4.26; 4.25
20. about 32.4; 34; no mode
21.
Practice 12-2
1a. 8.9% 1b. 24.6% 1c. 0.2% 1d. 1.1% 1e. 6.3%
1f. 4.0% 2a. 11.7% 2b. 36.8% 2c. 21.0% 2d. 47.2%
2e. 14.4% 2f. 16.0% 2g. 48.9% 2h. 51.1% 3. about
58.2% 4. D = drizzle, F = fog without drizzle,
0
5
10 15 20 25 30 35
22.
C = cancelled game, P = played game
0.8
C
D
0.3
0.7
P
C
0.3
F
1125
1250
1375
1500
40
42
44
46
48
50
52
24.
0.7
P
132
1000
23.
0.2
Algebra 2
All rights reserved.
N
0.3
10
20
30
40
50
60
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Probability
N
C
Algebra 2: All-In-One Answers
(continued)
25. 174; 188 26. 346; 368 27. 94; 98 28. 22; 86
29a. about 47.4 29b. 47.9 29c. 50.8
29d. 44.1, 47.9, 50.8;
Q2 Q3
Q1
38 40 42 44 46 48 50 52 54
Guided Problem Solving 12-3
1. 16 2. 1, 2, 4, 6, 7, 7, 8, 8, 9, 12, 13, 15, 16, 20, 22, 38
3. Q1 = 6.5, Q2 = median = 8.5, Q3 = 15.5, minimum = 1,
maximum = 38
All rights reserved.
4.
0
10
20
30
40
5. 38 6. Q1 = 6, Q2 = median = 8, Q3 = 15,
minimum = 1, maximum = 22
7.
0
10
20
random classrooms would be more accurate. 3. The pizza
restaurant sells to many different groups of people. The class
might not like the same kinds of pizza as the population as a
whole. The poll should be of class members. 4. The people
eating in the restaurant probably are not indicative of the
population as a whole, either geographically or economically.
The poll should be a random sample of the residents, possibly
a random sample from each phone exchange to include people
from all the different areas of the county. 5. This excludes the
people who are working during the day. Contacting randomly
selected people, either from the phone book or voter
registration lists, would be more accurate. 6. This is fairly
accurate usually. 7. about 44 8. about 2500 9. about 12,346
10. about 27,778 11. 53%; 416%; 37% to 69%
12. 72%; 44%; 68% to 76% 13. 62%; 48%; 54% to 70%
14. 30%; 46%; 24% to 36% 15. 42%; 43%; 39% to 45%
Guided Problem Solving 12-5
x 4. 63%
1. 408 2. 258 3. sample proportion = n
5. margin of error = 4 1 6. 5% 7. 58% to 68%
"n
8. 63%; sample proportion; yes 9a. 17.2% 9b. 12.5%
9c. 4.7% to 29.7%
30
8. The main effect of removing the outlier is a shortening of
the long whisker. 9. The median decreases from 8.5 to 8.
10. Yes, the answers are correct.
Practice 12-6
1.
M 0.125
0.5
F 0.125
0.5
M 0.125
0.5
F 0.125
0.5
M 0.125
0.5
F 0.125
0.5
M 0.125
F 0.5
F 0.125
0.5
M
0.5
0.5
69
71
73
75
F
77
Practice 12-4
1. 295.7; 47.4 2. 30.3; 3.2 3. 2.4; 0.1 4. 74.3; 3.9
5. 66.8; 33.1 6. 8; 9.5; 4 7. 189; about 109.6; 114.5
8. 15; about 531.4; 6.5 9. 1.7; 2.3; 1.05 10. 4; 46.7; 2
11. 8; 100.5; 2.5 12. 5 13. 3 14a. about 3.49
14b. about 0.55 14c. 1.7 14d. 2; 1 15a. 33 15b. 18.5
15c. about 88.2 15d. about 10.5 15e. 3 15f. 2 16. +0.375
17. +2.75
Guided Problem Solving 12-4
(x 2 x) 2
1. s2 5 a n
2. s 5
2
a (x 2 x) 3. 5.5
n
Å
4. 6.5, -2.5, -3.5, -1.5, -0.5, 1.5 5. 42.25, 6.25, 12.25,
2.25, 0.25, 2.25 6. 6 7. 10.9 8. 3.3 9. The values match.
10. s2 = 41,000; s = 202.5
Practice 12-5
M
0.5
0.5
F
0.5
1a. 87.5% 1b. 50% 1c. 37.5% 2. the weather outcome on
a given day, acceptable weather; Check students’ work.
3. asking a person chosen at random; favoring an early curfew;
Check students’ work. 4. selecting a part; part is defective;
Check students’ work. 5. about 1% 6. about 0.002%
7. about 25% 8. about 38%
9.
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5
Number of Successes
Probability
67
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
0.5
M
11.
1. It is most likely that Sample C was largest since it has the
smallest standard deviation, implying less variation than
Samples A and B. 2. This sample is likely to contain a
disproportionate number of readers. Selecting students in
All-In-One Answers
Algebra 2
133
Algebra 2: All-In-One Answers
8.
8.2 13.4 18.6 23.8 29 34.2 39.4
0 1 2 3
Number of Successes
Probability
11.
9.
496 556 616 676 736 796 856
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Probability
0.5
0.4
0.3
0.2
0.1
0
x
10.
17.3 29.6 41.9 54.2 66.5 78.8 91.1
x
11. about 34% 12. about 13.5% 13. about 2.5%
14. about 68% 15. about 16% 16. about 50%
17a. about 6 students 17b. about 37 students
17c. about 156 students 18a. about 3 nails
18b. about 82 nails 18c. about 19 nails 19a. about 10%
19b. about 5 bags 19c. about 40 bags
0 1 2 3
Number of Successes
12.
x
Guided Problem Solving 12-7
1. 63 min 2. 4 min 3. 2.5% 4. 13.5% 5. 16% 6. yes
7. 59 min 8. Yes, the z-score is less than -1. 9. 81.5%
0 1 2 3 4
Number of Successes
13a. 68% 13b. 99% 13c. 97% 13d. 84% 14a. 18%
14b. 6% 14c. 56%
Guided Problem Solving 12-6
1. 99% or 0.99 2. 1% or 0.01 3. nCxpxqn2x 4. n = 10,
x = 9 5. 0.0914 or 9.14% 6. n = 10, x = 7 7. 0.0001
or 0.01% 8. There is a malfunction in the machinery that
must be corrected. 9. 0.0042 or 0.42%; Yes, it is between
9.14% and 0.01% 10. 0.25 or 25%
12A: Graphic Organizer
1. Probability and Statistics 2. Answers may vary. Sample:
probability distributions, analyzing data, standard deviation,
working with samples 3. Answers may vary. Sample: social
science, genetics, market research, recycling 4. Check
students’ work.
12B: Reading Comprehension
1. how probability is affected by a small number of cases
2. probability of getting heads when tossing a coin
Practice 12-7
3. 12 4. experimental probability
1. 53.3 2. 69.9 3. 36.7 4. 28.4
5.
5. 12 6. b
12C: Reading/Writing Math Symbols
59 71 83 95 107 119 131
1. Answers may vary. Sample: -8, 3 2. no 3. yes
4. Answers may vary. Sample: -8, 4 5. yes 6. no
7. the probability of event R, given event Q 8. Answers may
x
6.
vary. Sample: given that the event that follows takes place
55 70 85 100 115 130 145
7.
x
12D: Visual Vocabulary Practice
1. box-and-whisker plot 2. quartiles 3. mean
4. conditional probability 5. frequency table 6. probability
distribution 7. z-score 8. interquartile range 9. standard
deviation
42 48 54 60 66 72 78
134
All rights reserved.
Probability
0.5
0.4
0.3
0.2
0.1
0
Algebra 2
x
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
10.
(continued)
Algebra 2: All-In-One Answers
(continued)
3.
12E: Vocabulary Check
Median: The middle value in a data set.
Outlier: An item of data with a substantially different value
from the rest of the items in the data set.
Sample: Information gathered from only part of a
population.
x , where x is the number of times an
Sample proportion: n
event occurs in a sample of size n.
Margin of error: An estimate of error of a sample
proportion.
135°
x
x
O
O
5.
6.
y
210°
y
270°
x
x
1. mean 2. outlier 3. quartiles 4. median 5. random
sample 6. mode
All rights reserved.
y
100°
12F: Vocabulary Review Puzzle
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
4.
y
O
O
Chapter 13
7.
Practice 13-1
1. not periodic 2. periodic; 2 3. periodic; 3 1 4. any two
4
points on the graph whose distance between them is one period;
sample: (0, 2) and (3 1 , 2); 3 1 5. any two points on the graph
3
3
whose distance between them is one period; sample: (0, 0) and
(4 1 , 0); 4 1 6. any two points on the graph whose distance
4
4
between them is one period; sample: (0, 2) and (4, 2); 4 7. 2 1 ; 1
8
3
3
1
2
8. 3; 2 9. 2; 3 10. 6; 2 8 11. 6; 1 12. 1 ; 1 13. 4; 2
4
3 4
5
2
1
1
14. 5; 1 8 15. 1 ; 2 16. 4; 2 17. 5; 1 18. 2 12 , 1 58
3
2
2
8.
y
y
330°
x
x
9.
30°
O
O
10.
y
y
x
x
O
O
90°
Guided Problem Solving 13-1
190°
1. 0.2 s 2. 0.5 mV 3. Yes; the y-values repeat in a regular
pattern. 4. 5 cycles 5. 5 units 6. 1 sec 7. 1 sec 8. 6 units
9. 3 mV 10. 1.5 mV 11. Check students’ work. 12. The
11.
period is 0.5 s and the amplitude is 1.5 mV.
12.
y
y
Practice 13-2
1.
2.
y
x
x
y
O
O
330°
150°
30°
O
x
60°
x
O
13.
14.
y
y
315°
x
x
O
All-In-One Answers
45°
O
Algebra 2
135
Algebra 2: All-In-One Answers
16.
y
"2 "2
66. (0, 1); (0, 1) 67. a 2 2 , 2 b ; (-0.71, 0.71)
y
120°
x
x
O
O
180°
Guided Problem Solving 13-2
1. Quadrant I 2. negative 3. positive 4. (cos θ, sin θ)
5. cos θ = -, sin θ = + 6. -; -; +; - 7. II and III
8. II 9. If the terminal side of an angle is in Quadrants I or
18.
y
y
145°
x
x
O
O
120°
19.
II, then the sine of the angle is positive; otherwise it is not.
If the terminal side of an angle is in Quadrants I or IV, then
the cosine of the angle is positive; otherwise it is not.
10. Check students’ work. 11. positive
Practice 13-3
20.
y
p
5p
4p
p
3p
p
1. 4 2. 2 3. 6 4. 6 5. p 6. 3 7. 2
10p
5p
11. 4p
12. 11p
13. 8p
14. 9
8. 3 9. 2p 10. 2p
9
9
9
18
11p
15. 9 16. 180° 17. 360° 18. 150° 19. 135° 20. 270°
y
x
21. 30° 22. 210° 23. 330° 24. 60° 25. 240° 26. 225°
O
O
145°
x
355°
21. 260° 22. 300° 23. 135° 24. 215° 25. 12° 26. 345°
27. 122° 28. 124° 29. 340° 30. 61° 31. 49° 32. 322°
33. 16° 34. 150° 35. 27° 36. 30° 37. 300° 38. 80°
39. 190° 40. 10° 41. 20° 42. 98° 43. 120° 44. 46°
45. 240° 46. 100° 47. 138° 48. 30° 49. 233° 50. 17°
"2 "2
51. a 2 , 2 b ; (0.71, 0.71)
"2
"2
52. a 2 2 , 2 2 b ; (-0.71, -0.71)
"3
27. 315° 28. 120° 29. 20° 30. 40° 31. 2 ; 12
"2
"2
"2 "2
"3
32. 12 ; 2 33. 2 2 ; 2 2 34. 2 2 2
"3 1
"3
"3
35. 2 2 ; 12 36. 2 21; 2 2 37. 2 ; 2 2
1 "3
38. 2 2 ; 2 39. 11.0 in. 40. 39.8 cm 41. 10.5 cm
42. 92.2 cm 43. 2.1 ft 44. 15.7 m 45. about 17.8 in.
46. 1.2 m
"2 "2
53. a 2 2 , 2 b ; (-0.71, 0.71)
Guided Problem Solving 13-3
"3
"3
55. a 2 , 2 12 b ; (0.87, -0.5) 56. a 2 , 21 b ; (0.87, 0.5)
p 5 330p < 1036.7 mi 8. p radians
7. 3960 ? 12
12
395p
p
9. 1580 ? 12 5 3 < 413.6 mi 10. C = 2π (3960) "2
54. a 2 , 2 "2 b ; (0.71, -0.71)
2
"3
57. a 2 2 , 12 b ; (-0.87, 0.5)
"3
58. a 2 2 , 2 12 b ; (-0.87, -0.5)
"3
"3
59. a 12 , 2 2 b ; (0.5, -0.87) 60. a 12 , 2 b ; (0.5, 0.87)
"3
"3
61. a 2 12 , 2 2 b ; (-0.5, -0.87) 62. a212 , 2 b ; (-0.5, 0.87)
63. (0, -1); (0, -1) 64. (1, 0); (1, 0) 65. (1, 0); (1, 0)
136
Algebra 2
All rights reserved.
17.
"3
68. a212 , 2 b ; (-0.5, 0.87) 69. -60° 70. 120° 71. 315°
+
+
1. 24 2. 360º 3. 360
5 30 5 15 + 4. 2π radians
24
2
2p
p
p
5. 24 5 12 radians 6. 12 radians
24,881
24,881 mi;
1036.7 mi 11. C = 2π (1580) 9927 mi;
24
9927 413.6 mi 12. more; Check students’ work. 13. 8 o’clock
24
Practice 13-4
1. 4; 2p; y = 4 sin u 2. 1.5; p
; y = 1.5 sin 4u
2
3. 2; 3p; y = -2 sin 32 u 4. 1; 6p; y = sin 13 u
5. 2.5; p; y = -2.5 sin 2u 6. 4; p; y = -4 sin 2u
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
15.
(continued)
Algebra 2: All-In-One Answers
7.
; y = 2 sin 2u
y
2
(continued)
14.
2
y
u
u
O
p
2
2
8.
p
O
3p
2
2
; y = 3 sin u
y
2
p
2
15.
2
p
3p
2
p
3p
2
y
u
u
O
p
2p
O
3p
2
2
9.
; y = 2 sin 4u
y
2
All rights reserved.
p
2
16.
4
y
u
u
O
p
4
2
10.
2
p
2
O
3p
4
p
2p
3p
p
2
p
3p
2
p
3
2p
3
p
p
2
p
3p
2
p
5
2p
5
3p
5
4
; y = 2 sin 8u
y
17.
2
y
u
u
O
p
8
2
11.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
2
p
4
O
3p
8
2
; y = 1.5 sin 6u
y
18.
4
y
u
u
O
p
6
2
12.
2
p
3
O
p
8
4
; y = 2.5 sin u
y
19.
4
y
u
O
p
2p
u
O
3p
2
13.
2
4
y
20.
4
y
u
O
p
2p
2
All-In-One Answers
3p
u
O
4
Algebra 2
137
Algebra 2: All-In-One Answers
21.
4
(continued)
6.
y
y
2
u
O
2p
p
O
u
3p
2
4
6
p
2p
3p
p
2
p
3p
2
2
4
22. about -0.1 23. about 0.2 24. about 0.2 25. 0.3
26. about 0.1 27. about 0.2 28. -0.3 29. about -0.2
7.
y
2
u
Guided Problem Solving 13-4
2
8.
u
Practice 13-5
2
O
y
4
u
O
p
2p
9.
3p
y
2
2
u
O
2.
2
y
3p
2
u
O
2p
p
2
4
10.
4
6
y
2
u
O
3.
4
y
4
u
O
p
2p
11.
4
3p
p
2
p
3p
2
2
4
6
y
4
u
O
4.
2
y
4
u
O
p
2p
12.
2
3p
4
O
p
2p
4
6
3p
13.
2
p
2
p
3p
2
y
u
4
O
2
138
2
2
y
u
O
y
u
2
5.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1.
y
4
All rights reserved.
1. the sound wave for the note A above middle C
2. 0.001; 880π 3. the amplitude 4. the number of cycles in
0 to 2π 5. period = 2p 6. 0.001 7. 2p 8. 1 9. 880π
880p
440
b
10. Answers may vary. 11. 480; 1
O
Algebra 2
All-In-One Answers
Algebra 2: All-In-One Answers
14.
4
(continued)
12.
y
4
y
u
O
2
4
O
6
4
4
15.
4
13.
y
4
p
2
p
3p
2
u
p
2
p
3p
2
u
p
4
p
2
3p
4
u
p
2
p
3p
2
p
4
p
2
3p
4
y
u
O
2
4
6
O
All rights reserved.
4
4
14.
16. y = 6 cos 2p t 17. y = -5 cos u
4
5
y
18. y = 4 cos 2u 19. y = 3 cos 4u 20. 2p; 1; p; 0, 2p; p , 3p
21. p; 4; 0, p, 2p; p , 3p ; p , 3p , 5p , 7p
2 2
4
4
4
2 2
O
4
4
22. 2p; 5; p; 0, 2p; p , 3p 23. 0.24, 1.85, 2.34, 3.95, 4.43, 6.04
2
2
24. 2.36 25. 1.00, 3.00, 5.00 26. 1.34 27. 0.84, 5.44 28. 0
15.
4
y
29. 2.67, 5.33 30. 4.19 31. 3.14 32. y = 2p cos 2pu
u
33. y = 21 cos 2u
O
4
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Guided Problem Solving 13-5
1. 7 ft 2. 5.5 ft 3. 1.5 ft 4. 12 h 22 min 5. 742 min
2p
6. y 5 1.5 cos 742
t 7. less 8. y = -0.5 9. 225.632,
516.368, 967.632, 1258.368 10. 12:17 A.M.- 7:49 A.M.,
12:39 P.M.- 8:11 P.M. 11. Answers may vary.
2p
12. y 5 2 cos 720
t
Practice 13-6
1. p; p
, 3p 2. 2p; p 3. 4p; 2p 4. p ; p , 3p , 5p , 7p
2 2
16.
4
O
4
17.
4
2 4 4 4 4
p p 3p 5p 7p
9
3
5
7
1
11
5. 2; 1, 3, 5 6. 1; 2 , 2 , 2 , 2 , 2 , 2 7. 2 ; 4 , 4 , 4 , 4
8. p; p , 3p 9. 1; 1 , 3 , 5 , 7 , 9 , 11
2 2
2 2 2 2 2 2
10.
4
y
y
y
u
O
1
2
18.
p
6
p
3
p
4
p
2
y
u
p
2
4
11.
4
p
u
3p
2
O
4
y
3
4
4
O
19.
4
y
u
O
4
p
2
p
All-In-One Answers
3p
2
u
u
O
4
3p
4
Algebra 2
139
Algebra 2: All-In-One Answers
20.
4
(continued)
28. p
29. p 30. 2p 31. undefined 32. 1 33. -1
4
y
34. undefined
O
1
2
3
u
1
4
1
2
3
4
u
35.
; 200, undefined, -2200
4
y
O
4
Xmin=0
Ymin=–300
Xmax=470 Ymax=300
Xscl=50
Yscl=100
36.
22.
4
y
p
8
O
4
23.
4
; -14.9, -31.1, -50.1
p
4
3p
8
u
Xmin=0
Ymin=–300
Xmax=470 Ymax=300
Xscl=50
Yscl=100
y
37.
p
6
O
4
24.
4
1
8
4
4
u
1
4
3
8
Xmin=0
Ymin=–300
Xmax=470 Ymax=300
Xscl=50
Yscl=100
u
1. θ is the measure of one of the base angles of the isosceles
triangular tiles 2. 140.4 ft2
y
3.
p
2
4
4
p
2
Guided Problem Solving 13-6
O
26.
p
3
; -50, undefined, 50
y
O
25.
p
3p
2
y
4
u
O
y
u
O
4
3
2
3
9
2
4
4. about 1.732 in. 5. about 5.196 in.2 6. about 15.588 in.2
7. 20,217.6 in.2 8. 3891; 1297 9. 27.714; 3891; fewer.
10. 3216
Practice 13-7
1.
4
140
y
y
x
O
u
O
60
30
2
27.
All rights reserved.
4
p
8
Algebra 2
p
4
3p
8
2
p
2
p
3p
2
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
21.
Algebra 2: All-In-One Answers
2.
4
(continued)
9.
y
y
2
x
O
p
2
4
3.
2
p
x
O
3p
2
p
2
2
10.
y
4
p
3p
2
y
x
O
p
2
2
4.
All rights reserved.
2
p
x
O
3p
2
4
11.
y
2
p
2
p
3p
2
p
2
p
3p
2
p
2
p
3p
2
p
2
p
3p
2
p
3p
2
p
3p
2
y
x
x
O
p
2
2
5.
2
p
O
3p
2
2
12.
y
2
y
x
x
O
p
2
2
6.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
2
p
O
3p
2
2
13.
y
4
y
x
O
p
2
2
7.
4
p
O
3p
2
4
14.
y
2
y
x
x
O
p
2
4
8.
2
p
O
3p
2
p
2
2
15.
y
2
y
x
x
O
2
p
2
p
3p
2
x
O
2
p
2
16. y = sin x - 2 17. y = cos (x + p) 18. y = cos x + p
4
19. y = sin (x - 3.2) 20. 3; 2p; none; 2 units up
21. 2; 2p; p
units left; none 22. 1; p; none; 1 unit up
2
23. 1; 2p; p
units right; none 24. 1 ; 2p; none; 3 units down
2
3
All-In-One Answers
Algebra 2
141
Algebra 2: All-In-One Answers
(continued)
25. 1; 4p; none; 2 units down
Practice 13-8
26.
1. 0.86 2. 2 3. -1.10 4. -1 5. undefined 6. -1.07
7. 0.58 8. 14.14 9. -1.00 10. undefined 11. -1.01
2" 3
12. 1.41 13. "2; 1.41 14. undefined 15. 3 ; 1.15
y
x
O
2
16. 2 17. undefined 18. - "2 ; -1.41 19. undefined 20. 1
4
2" 3
2" 3
; 1.15 23. ; -1.15 24. 2
3
3
25. 23 26. 25 27. 10
28. - 32
7
4
2
y
2
29.
4
2
x
O
u
2
28.
4
2
O
2
y
x
O
2
4
29
2
30.
2
p
3p
2
p
2
p
3p
2
p
3p
2
p
3p
2
p
3p
2
p
3p
2
y
u
O
2
2
p
2
4
y
2
y
31.
4
y
2
x
O
u
2
O
30.
2
x
2
32.
4
u
O
p
2
2
y
x
O
y
2
4
2
31.
p
2
2
y
O
2
All rights reserved.
27.
21. undefined 22.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
4
33.
2
y
4
u
4
32. -2; 2 units to the left 33. 1; 1 unit to the right
34. -1.5; 1.5 units to the left 35. 1; 1 unit to the right
36. p2 , p2 units to the right 37. -p; p units to the left
O
p
2
2
34.
4
y
u
Guided Problem Solving 13-7
1. cosine graph and sine graph 2. horizontal 3. p2 units
4. right 5. positive; p2 6. sin x 5 cos (x 2 p2 ) 7. left
8. negative; -p2 9. cos x 5 sin (x 1 p2 ) 10. Answers may
p
vary. 11. p2 12. T 5 65 sin (12
x 1 p2 ) 1 6
142
Algebra 2
O
4
p
2
All-In-One Answers
Algebra 2: All-In-One Answers
35.
(continued)
13A: Graphic Organizer
y
2
1. Periodic Functions and Trigonometry 2. Answers may
vary. Sample: exploring periodic data, angles and the unit
circle, radian measure, sine function, cosine function, tangent
function 3. Check students’ work.
u
O
p
2
2
36.
2
p
3p
2
13B: Reading Comprehension
y
1. converting between two units of angle measure:
degrees and radians 2. the meaning of a radian: 2p radians a complete circle, or 360° 3. 30° and 60° 4. 1 5. p 6. a
2
2
u
O
p
2
2
All rights reserved.
37.
2
p
3p
2
13C: Reading/Writing Math Symbols
1. p 2. pi 3. S 4. sigma 5. p 6. u 7. theta
y
13D: Visual Vocabulary Practice
1. sine function 2. secant 3. phase shift 4. cosecant
5. coterminal angles 6. cosine function 7. periodic function
8. cotangent 9. unit circle
u
O
p
2
2
p
3p
2
13E: Vocabulary Check
38. 1.73 39. undefined 40. 0.36 41. -5.76
42. 1.56 43. 1.02 44. 2.75 45. -2
46a.
y
10
t
O
1
2
Cosine θ : The x-coordinate of the point at which the terminal
side of the angle θ intersects the unit circle.
Central angle: An angle whose vertex is at the center of a
circle.
Intercepted arc: The portion of a circle whose endpoints are
46b. about 14.14 ft 46c. 10 ft
on the sides of a central angle of the circle and whose
remaining points lie in the interior angle.
Radian: The measure of a central angle of a circle that
intercepts an arc of equal length to a radius of the circle.
Guided Problem Solving 13-8
13F: Vocabulary Review Puzzle
1. cotangent and tangent
2.
y
2
1. amplitude 2. clockwise 3. cosine 4. cycle 5. period
6. sine 7. tangent
10
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
3
2
1
Periodic function: Repeats a pattern of y-values at regular
intervals.
π
2π
π
x
3. Domain is all real numbers except odd multiples of p2 ; range
is all real numbers; asymptotes occur every π units at x = . . .
p p 3p
-3p
2 , - 2 , 2 , 2 , . . . 4. Domain is all real numbers except
multiples of p; range is all real numbers; asymptotes occur every
π units at x = . . ., -π, 0, π, 2π, 3π... 5. The graphs have the
same period and range. 6. Their asymptotes are shifted by p2 .
C
L
O
C
K
W
I
S
E
T
N
E
G
N
A
T
D
T
C
R
N
R
I
C
U
P
I
N
Y
D
E
O
T
W
E
N
E
I
C
S
I
Y
N
R
U
T
D
I
L
Z
E
R
I
O
W
N
P
O
E
I
E
O
O
E
M
T
R
W
S
R
D
Y
A
M
I
E
P
S
U
E
I
p
5p
7. x = p4 ; x = 5p
4 8. Check students’ work. 9. x = 2 ; x = 2
All-In-One Answers
Algebra 2
143
Algebra 2: All-In-One Answers
(continued)
16. d = 5.1; &F = 11.3°; &E = 78.7°
17. 771.7 ft 18. 270.9 ft 19a. 3.8° 19b. 4.8° 19c. 2.4°
3"13
19d. 5.1° 19e. 7.2° 19f. 11.2° 20a. 13 ; 0.8
1.–18. Answers will vary 19. -tan2 u 20. csc u 21. sec u
22. cos u 23. 1 24. cos2 u 25. 1 26. csc u 27. sin u
28. 1 29. sec2 u 30. csc u 31. 1 32. 1 33. -1 34. cos u
Guided Problem Solving 14-1
1. To verify an identity, you should transform one side of the
equation until it is the same as the other side.
2
sin u ; cotu 5 cos u 3. a sinu b or sin u
2. tan u 5 cos
u
cos u
sin u
cos 2u
4. (1 2 cos 2u) a
2
b 5. sin 2u 2 sin 2u cos 2u
cos 2u
6. sin 2u; sin2u cos 2u 7. tan 2u 2 sin 2u 8. Yes, it verifies.
9. sin2ucsc2u 2 sin2u 5 sin2u(csc2u 2 1) 5 sin2u(cot2u)
2
5 sin 2ua cos 2 u b 5 cos 2u
sin u
sin 2u
Practice 14-2
5p 7p
p 4p
p 5p
3p 7p
1. 4 , 4 2. 3 , 3 3. 6 , 6 4. 3 , 3 5. 0.85, 2.29
5p 7p 2p 4p
p 2p
6. 3.99, 5.44 7. 6 , 6 , 3 , 3 8. 0, 3 , 3 , p
p 5p
p 3p 2p 4p
9. 2 , 2 , 3 , 3 10. 0.93, 5.36 11. 0, 3 , 3 , p
p 5p
3p
7p
5p
p
12. 0, 4 , p, 4 13. 0, 3 , 3 14. 0, 4 , p, 4
15a. 15.7° 15b. 11.5° 16. 1.19 + 2pn, 4.33 + 2pn
17. 0.85 + 2pn, 2.29 + 2pn 18. 1.81 + 2pn, 4.47 + 2pn
19. 1.10 + 2pn, 5.18 + 2pn
20. 45° + n ? 360°, 135° + n ? 360°
21. 45° + n ? 360°, 225° + n ? 360°
22. 45° + n ? 360°, 315° + n ? 360° 23. 90° + n ? 360°
24. p 25. p , 3p
2 2
20b. 32 ; 1.5 20c.
2"13
; 0.6 20d. 2 ; 0.7
3
13
"13
"13
; 1.2 20f.
; 1.2 21. 45° 22. 60° 23. 60°
3
3
24. 18.9° 25. 36.9° 26. 45° 27. 66.4° 28. 73.0° 29. 48.6°
30. 26.6° 31. 85.2° 32. 6.0°
20e.
Guided Problem Solving 14-3
1. 90 ft 2. 60.5 ft 3. x2 5 902 1 902 4. x 127.28 ft
6 8. θ 3.4°
5. about 67 ft 6. 6 ft 7. tan u 5 100
9. Yes, the answers are reasonable. 10. 100.6 ft
Practice 14-4
1. 14.9° 2. 15.9 3. 15.0 4. 43.9° 5. 136.6 6. 32.6°
7. 27.8° 8. 14.8 9. 11.5 10. 38.2° 11. 12.8° 12. 90.4
13. 32.0° 14. 30.0 15. 69.8 in2 16. 33.3 ft2 17. 1.7 cm2
18. 164.4 in.2 19. 1025.5 ft 20. 2542.4 yd and 1866.4 yd
Guided Problem Solving 14-4
1. triangle with two equal sides 2. 180°
3. x° 1 x° 1 85.9° 5 180° 4. x = 47.05; 47.05°
47.05° 5 sin 85.9°
5. sin 150
6. c = 204; 204 ft 7. Yes, the
c
answers check. 8. 31.1 yd
Practice 14-5
1. 5.3 2. 3.1 3. 43.0° 4. 12.5 5. 21.8° 6. 35.9° 7. 18.5
8. 32.5° 9. 439.3 10. 72.5° 11. 5.8 12. 3.2 13. 14.5
14. 15.2 15. 77.9 16. 18.2° 17. 66.7° 18. 102.4° 19. 28.7°
20. 73.4° 21. 70.3° 22. 28.7 mi
Guided Problem Solving 14-2
Guided Problem Solving 14-5
1. I = the current in amps 2. t = seconds
I ; sin21 I ; 1 sin21 I 4. t = 0.0028 5. 0.0028 sec
3. 40
40 60p
40
1. 85 mi 2. 20 mi 3. 65 mi 4. 20 mi
5. d2 5 652 1 202 2 2(65)(20)cos10° 6. d 45.4;
1 1 0.0028 < 0.019 sec 8. Yes, check
6. t = -0.0028 7. 60
the answers. 9. 0.0045 sec; 0.0212 sec
Practice 14-3
1. 4 2. 3 3. 3 4. 43 5. 3 6. 5 7. 53 8. 4
5
5
5
4
4
4
9. d = 17; &F = 28.1°; &E = 61.9°
10. e = 1.7; &F = 30°; &E = 60°
11. d = 2.2; &F = 26.6°; &E = 63.4°
12. d = 2.2; &F = 63.4°; &E = 26.6°
13. f = 500; &F = 0.1°; &E = 89.9°
14. f = 19.4; &F = 67.6°; &E = 22.4°
15. f = 10.4; &F = 60°; &E = 30°
144
Algebra 2
All rights reserved.
Practice 14-1
about 45.4 mi 7. sin10° 5 sinx° ; x 14.4° or x 45.4
65
180° -14.4° = 165.6° 8. Turn 14.4° left. 9. 4.4° 10. Yes,
the answers are reasonable. 11. 8.7 mi
Practice 14-6
2"6 2 "2
"3
"6 1 "2
1. 2 2 2. "3 3.
4.
4
4
"6 2 "2
"2
"2
5.
6. 2 7. 2 2 8. 1 9. "3
4
"3
"3
10. 2 11. 2 12. 22 2 "3
13.–16. Answers may vary 17. cot A 18. sin A
All-In-One Answers
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Chapter 14
Algebra 2: All-In-One Answers
(continued)
7p 11p
p 5p
p 5p
19. 6 , 6 20. p 21. 4 , 4 22. 0, p, 6 , 6
, 7p 24. 0 25. No solution 26. 0, 2p , p, 4p
23. p
6 6
3
3
p , 3p
p
5p
"
27. 3 , 3 28. 2 2 29. 1 30. -1 31. 0 32. 2
2
All rights reserved.
Guided Problem Solving 14-6
1. 10cos(u 1 60°) 2. 10sin(u 1 60°)
3. cos(A 1 B) 5 cosAcosB 2 sinAsinB
4. 10cos(u 1 60°) =10(cosucos60° 2 sinusin60°)
5. 5cosu 2 5"3sinu
6. sin(A 1 B) 5 sinAcosB 1 cosAsinB
7. 10sin(u 1 60°) =10(sinucos60° 1 cosusin60°)
8. 5sinu 1 5"3cosu
9. (5cosu 2 5"3sinu, 5sinu 1 5"3cosu)
10. Yes, the coordinates are the same.
11. sin 3θ
Practice 14-7
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
5"2
5"34
"2
7"2
1. 10 2. 10 3. 7 4. 5"2 5. 7 6. 71 7. 34
"34
"34
3"34
8. 2 34
9. 2 3 10. 2 53 11.
12. 2 3
5
5
"3
"3
13.–20. Answers may vary. 21. 2 22. "3 23. 2 2
"3
24. 12 25. Undefined 26. 0 27. 2"3 28. 2 2
#2 1 "2 1 !3
29. 2"3 30. "2 1 !3 31.
2
2
#2 2 "2 1 !3
2 2 "2 1 !3
33.
2
Å 2 1 "2 1 !3
#2 1 "2
"2
2 2 "2
34. 2 35.
36.
37. 1 38. 0
2
Å 2 1 "2
32.
Guided Problem Solving 14-7
1. sin2u 5 2sinucosu 2. cos2u 5 cos2u 2 sin2u or
cos2u 5 2cos2u 2 1 or cos2u 5 1 2 2sin2u 3. 2sinucosu
4. 8sinucosu 5. 8sinu 2 3 6. 8sinu 2 3
, 3p , 0.384, 2.758 8. Yes, the answers check.
7. u 5 p
2 2
9. 2cos2u 2 cosu 2 1 5 0; u 5 0, 2p
, 4p
3 3
Using Inverses: evaluate inverses of trigonometric functions
and solve trigonometric equations; Right Triangles and
Trigonometric Ratios: find lengths of sides, and the measures
of angles of right triangles; Area and the Law of Sines: find the
area of any triangle and use the Law of Sines; Law of Cosines:
use the Law of Cosines in finding the area of a triangle; Angle
Identities: verify angle identities, and sum and difference
identities; Double-Angle and Half-Angle Identities: verify
double- and half-angle identities
14B: Reading Comprehension
1. early history of trigonometry
2. 150 A.D. 3. 1600 B.C. 4. Hipparchus, Ptolemy, Menelaus,
Copernicus 5. astronomy 6. b
14C: Reading/Writing Math Symbols
1. 25 2. -25 3. 12 4. 14 5. 14 6. x + 5
1 2pn and 5p 1 2pn
7. p
6
6
14D: Visual Vocabulary Practice
1. cosine 2. secant 3. cotangent 4. trigonometric identity
5. Law of Sines 6. Transitive Property of Equality 7. Law
of Cosines 8. cosecant 9. sine function
14E: Vocabulary Check
Trigonometric identity: A trigonometric equation that is
true for all values except those for which an expression on
either side of the equal sign is undefined.
Radian: The measure of a central angle of a circle that
intercepts an arc equal in length to a radius of the circle.
Function: A relation in which each element of the domain is
paired with exactly one element of the range.
Tangent function: A function that matches the measure θ of
an angle in standard position with the y-coordinate of the point
at which the line containing the terminal side of a central angle
of the unit circle intersects the tangent line x = 1.
Trigonometric ratios for a right triangle: The six
different ratios of the sides of a right triangle.
14F: Vocabulary Review
1. h, i 2. e 3. c, g 4. d, f 5. b 6. a 7. m 8. k 9. j 10. l
14A: Graphic Organizer
1. Trigonometric Identities and Equations 2. Answers may
vary. Sample: trigonometric identities, solving trigonometric
equations using inverses, right triangles and trigonometric
ratios, area and the laws of sines, the law of cosines
3. Answers may vary. Sample: physics, construction, surveying,
sailing 4. Check students’ work. Chapter: Trigonometric
Identities and Equations; Trigonometric Identities: verify
trigonometric identities; Solving Trigonometric Equations
All-In-One Answers
Algebra 2
145