Answers

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Answers
Lesson EI.A Fractions
Homework
Lesson EI.B Signed Numbers
Homework
27
5
105
1a. b. 2. 2 2 3 7 3. 18 4. 5. 36
1. 38 2a. –3 b. 13 3a. 35 b. 72 4a. 28 b. –14
10
2
14
1
1
6. 4 7a. b. 8a. b. 9. 5. 21 6. 18 7a. 8 b. 9 8a. 13 b. 65
5
20
5
5
20
10a. b. 11. 12. 13. 9a. –25 b. –23 10. 20 11. 39 12. 10 13a. –84 b. –3
45
18
120
5
21
6
15
9
15
66
14
47
24
14. 12 15. 12
29
14a. 140 b. 12 15. The base is 13, and the exponent is 28.
11
5
16. 17. 3 18. 180 19. 96 20. 21. 5
12
7
21
22. 210 23. 120 24.
7
16. –15 17. 72 18. 128 19. –20 20. 2 21. no 22. 10
14
15
23. 75 24. no
Apply - Practice Problems
Apply - Practice Problems
1. 10 2. 12 3. 30 4. 2 2 2 3 3 5. 3 3 5
1. 4 2. 5 3. –7 4. –6 5. –10 6. –19 7. –20
7
6. 2 3 3 5 7. 6 8. 6 9. 3 10. 5 11. 3 12. 8
4
14. 11 15. 1 16. 8 17. –11 18. –19 19. –53
1
1
13. 14. 15. 3 16. 3 17. 2 18. 2 19. 1
23
20.
3
5
35
21.
1
3
22.
2
5
2
5
2
25
23.
7
7
24. 10 25.
5
4
21
26.
20. –75 21. –27 22. –38 23. –48 24. 11 25. 10
12
77
5
9
27. 7 28. 6 29. 30. 31. 70 32. 72 33. 126
17
23
2
17
34. 180 35. 42 36. 72 37. 1 38. 39. 4
15
36
9
137
40. 5 41. 42. 43. 42 44. 150 45. 252
8
16
120
59
43
115
46. 60 47. 30 48. 120 49. 50. 51. 60
60
8. –28 9. –18 10. –44 11. –32 12. –10 13. –112
13
144
26. 20 27. 15 28. –22 29. –32 30. 54 31. –42
32. –4 33. –3 34. 6 35. –36 36. –15 37. 9
38. 3 3 3 3 = 81 39. 4 4 4 = 64
40. 5 5 5 5 = 625 41. 2 2 2 2 2 2 = 64
42. no 43. no 44. no 45. 18 46. –20 47. 4 48. 24
49. 80 50. –80 51. 32 52. 2 53. 5 54. 10 55. 24
37
13
17
80
17
129
52. 53. 54. or 1 55. 56. 56. –44
Evaluate - Practice Test
Evaluate - Practice Test
48
24
63
63
140
42
4
45
7
9
1. 6 2. 3. 4. 5. 140 6. 60 7. 15
175
8. 13
20
1a. 19 b. –11 c. 15 2. –15 3a. 24 b. –37 c. –27
20
4. 39 5a. 102 b. 84 c. –25 6. 119 7. –28
36
8a. 4 b. 52
LESSON EI.B: ANSWERS
709
Topic EI Cumulative Review Problems
Evaluate - Practice Test
7
16
1
1. 2. 3. –2 4. 5. 112 6. –8 7. 125
1. 3 > –4, –5 > –7, –6 ≤ –6, –1 ≥ –1
56
18
12
1
13. 30
8. 4 9. 261 479 10. 184 11. 1 12. 4
1000
2a. 8 b. 12.18 c. 0.23 d. 15 e. 3.7 3. >, ≥, or ≠
4. (.91) 2 = 0.8281 5. 2 5 6. 43
14. –3 15. 29 16. 2 3 3 3 17. 6 18. 25
13
0
7. –(1.4) 2, –2, , (0.7) 2, and 34
19. 4 13 + 4 7 or 80 20. 9 21. 22. 72
8 a. false b. true c. true d. false
23. The base is 26 and the exponent is 11. 24. 18
Lesson 1.2 Factoring and Fractions
Homework
17
33
25. 26. –9 27. 28. –8 29. 3 30. 18 31. 27
7
7
1. 12 3. 6 5. 108 7. 15 9. 18 11. 1 13. 15. 5
14
35
42
5
1
32. 33. 0 34. 4 35. 1 36. – 3 37. –2
10
4
40. – 3
2
38. 70 39. 56
44.
(–2)6
45.
15
17
46.
41.
16
25
87
13
6
9
8
17.
3
8
19.
14
9
21.
7
30 8
23
23. 5 36
11
25. 21 27. 45
29. 56
42.
8
129
47. 25 48.
43. 80
7
12
Apply - Practice Problems
1. GCF: 2; LCM: 72 3. GCF: 2; LCM: 42
5. GCF: 1; LCM: 450 7. GCF: 16; LCM: 48
5
49. 3 11 11 50. 21
9. GCF: 28; LCM: 168 11. GCF: 12; LCM: 240
Lesson 1.1 The Real Numbers
Homework
13. GCF: 12; LCM: 432 15. GCF: 7; LCM: 490
20
1. 3 < 12, 5 = , 4 ≤ 4, 6 ≠ 7 3. 5 5 5 5 = 625
17. GCF: 21; LCM: 210 19. GCF: 9; LCM: 504
5a. 9 b. 17 c. 2.3 d. 4.8 e. 0.485 7. 8
21. GCF: 19; LCM: 285 23. GCF: 4; LCM: 144
9. 12 3 = 1728 eggs 11. 2 4 7 3
25. GCF: 1; LCM: 70 27. GCF: 8; LCM: 12,768
Apply - Practice Problems
10
1
6
9
3
3
21
29. 31. 33. 35. 37. 39. 41. 4
3
4
19
1. 9 = 9, 7 ≤ 11, 15 ≤ 15 3. 6 ≤ 12, 9 ≥ 9
43.
5a. 0 b. 100 c. 0.001 d. 4.33 e. 2.497
16
55. 7. 64 9. 343 11. 243 13.
78
15.
17a. true b. false c. true d. true
19. 64 21. 1 23. 2000
85
35
27
45. 40
20
35
47. 36
49.
4
87
100
51.
8
26
45
53.
75
Evaluate - Practice Test
1. The prime factorization of 12 is 2 2 3.
The prime factorization of 28 is 2 2 7.
The prime factorization of 40 is 2 2 2 5.
3
2. 4 3. 840 4. 8
710
2
11
33
56
Topic 1 Cumulative Review Problems
5. In the factor trees, the prime factors appear at the
bottom branch.
42
55
7
2 21
5 11 3 21
3 7
3 7
•
11
6
9
13. 240 15. 18 17.
•
•
8
9
19. 8, , 4, 17
•
•
6.
8
5
1. b, c, e 3. 1 5. 7. a, b, c 9. 11. –61
63
7. 6 8. 150 9. 72 10.
8
4
15
1
11. 2 and 7 12. LCM: 210; GCF: 14
3
5
11
22
21. a, c 23. 18 25. 27. – 29. 11
75
1. –284 3. 9 5. –4 7. –190
9. He gets $1.60 change 11. –14
21
13a. 26 b. 24 c. 30 d. or 10 1 e. –19 f. –46
2
75
Lesson 2.1 Algebraic Expressions
Homework
1. 11, –6, –1 3. –19 5. 3x + 2 (in either order)
27
15a. 6 b. 10 c. 0 d. 54 e. –6 f. or 6 3
4
4
Lesson 1.3 Arithmetic of Numbers
Homework
2
2
17
4
7. 11y + 4xy – 7 (in any order) 9. $53
17. true
11. 6 – x + 2y (in any order)
Apply - Practice Problems
1. 48 3. –34 5. –45 7. –60 9. –65 11. 336 13. –6
Apply - Practice Problems
1. 6x 3, 5xy 2, –y, and 25 3. 6y + 4 5. –5x + 38
15. –4 17. 9 19. 7 21. –13 23. 48 25. 19 27. –50
7. 5x – 27 9. 7y +14 11. –5x – 3xy + 20
Evaluate - Practice Test
13. –14x 2 – 30x – 36 15. 3y 2 + 16y + 58
1a. 1 b. –5 c. –6 d. –1 e. –13 f. 10
17. 10x 2 – 15x – 6 19. 3n 2 – 17mn – 32m
2a. 32 b. –32 c. –32 d. 2 e. –2 f. –2
21. 0 23. 5 25. –86 27. 29
3. 32 4a. true b. false c. true d. false
5. Associative Property of Addition;
Commutative Property of Addition;
Associative Property of Addition
Evaluate - Practice Test
6. $7.25
3. 3y + 4y 2 + 3x + 7xy 4. 8
7. Distributive Property
5. –17 6. 6y – 4y 2 + 7
8. –7
7. 63 8. 5x 2 + 7x 2y – 10x
–8
–6
–4
–2
0
2
1. 2, –1, 7, –4, 12 2. 5x + 39
4
6
8
LESSON 2.1: ANSWERS
711
Lesson 2.2 Solving Linear Equations
Homework
7. 8 atoms of carbon, 18 atoms of hydrogen 9. 11
1. x = 22 3. t = 12 5. v = 6 7. y = –12 9. $1.50
13. The legs are 6 inches, 8 inches, and 12 inches.
11. z = –3 13. y = 3 15. no solution 17. z = –3
15. 8” x 17” 17. 10 feet 19. 6’ x 6’ 21. 7”, 7”, and 4”
11. –45 degrees Celsius
C
19. r = 21. x = 17 23. z = 3x – 3 25. x = 1
2
23. 200 + 50
Apply - Practice Problems
27. y = –27 (LCM = 42) 29. z = –3
1. 15 and 27 3. 18 and 27 5. 28 and –12 7. 9 and 47
Apply - Practice Problems
9. 31, 32, and 33 11. 27, 28, 29, and 30
1. no 3. a = 18 5. b = 24 7. z = 19 9. x = 8
13. –82, –80, –78, and –76 15. 6 years old
11. r = 5 13. a = 4 15. p = 4 17. b = –4 19. n = –7
17. 31 years old
21. q = –8 23. c = –5 25. x = –2 27. f = –4
19. Miriam is 48 years old. Edward is 58 years old.
21. Mark is 15 years old. Luke is 5 years old.
29. h = 3 31. t = –2 33. c = –1 35. p = 17
16
37. y = 13 39. c = –16 41. a = 5 43. n = 4
3
23. Boris is 20 years old. Svetlana is 80 years old.
25. Masato is 40 years old. Kim is 20 years old.
45. Any r is a solution. 47. There is no solution.
27. Maria will be 66 years old. Angelica will be 15 years old.
49. There is no solution. 51. Any z is a solution.
29. Each of the other two angles measures 47.5 degrees.
2A
53. z = 3 y + 2 55. x = 9y – 12 57. b = 4
h
3V
59. w = lh
31. 36 degrees, 44 degrees, and 100 degrees
33. 25 degrees, 75 degrees, and 80 degrees
35. 3 cm, 13 cm, 15 cm 37. 6 cm, 10 cm, 10 cm
39. 16 inches, 32 inches, 32 inches
Evaluate - Practice Test
41. The length is 11 inches, and the width is 7 inches.
1. x = –11 2. –2 3. y = –9 4. x = 5
43. The length is 20 cm, and the width is 6 cm.
5. The equation is true for all values of x.
45. The length is 10 inches, and the width is 4 inches.
6. There is no solution. 7. 10x – 2 = 6
47. The length is 11 inches, and the width is 8 inches.
8. z = 1 9. 15x – 10 = 2x + 6
1
5
10. x = 1 11. y = 8x – 5 12. x = y + 8
8
49. The perimeter of the triangle is 120 cm, and the
perimeter of the hexagon is 30 cm.
Lesson 2.3 Problem Solving
Homework
51. 2500 square feet 53. 1350 square feet
1. –31, –30, –29, –28 3. 26, 27, 28
Evaluate - Practice Test
5. K2 is 8611 meters tall,
and Mount Everest is 8848 meters tall.
55. 324 square feet
1. 9 and 12 2. 18 years old and 15 years old
3. 15 years old 4. 11, 13, 15
5. width = 3 yards; length = 9 yards
712
6. 40 degrees, 50 degrees, and 90 degrees
1
11. 6
7. width = 50 yards; length = 90 yards
8. Each side of the triangle is 4 inches, and each side of the
square is 3 inches.
13. y ≥ 5
3
Lesson 2.4 Linear Inequalities
Homework
4
A
21. r =
13.
17
9
27. 29. – 3
–4
0
–2
–2
0
4
–2
4
6
6
8
–2
–0
Lesson 3.1 Introduction to Graphing
Homework
1. (3, 4) 3. Quadrant IV
2
4
–4
–2
–0
2
6
4
–6
–4
9.
5
19. p ≤ –2 21. z > –8 23. –11 ≤ y < 8
25. –1 < z < 39 27. –4
≤ x ≤ – 7
3
Evaluate - Practice Test
1. x < 7 2. z ≤ 4 3. x < 3 4. y > –14
Number of Farms (in thousands)
11. x < 2 13. z > 3 15. a < – 1 17. x > 8
6
4
4
2
2
U (0, 5)
–2
Apply - Practice Problems
1. x ≤ 4 3. a > 12 5. b < 6 7. c ≥ –5 9.
y
6
T (–3, 6)
6
d < – 5
4
7.
y
17.
–6
9 10 11 12 13
7
5.
15.
–4
8
23. 5 meters 25. Any x is a solution.
12
8
x = 7 is not included in the solution of the inequality
x – 2 < 5. This is indicated by the open circle.
–6
7
19. Bjorn is 32 years old, and Ivar is 34 years old.
7
9. x ≤ $24.50 11. x < –2
6
15. z = 3 17. –12
1. x < 9 3. –4 ≤ x ≤ 4 5. x < –3 7. x < 2
–4
5
4
2
x
6
–6
–4
–2
–2
–4
–4
–6
–6
11.
7,000
6,500
6,000
5,500
5,000
4,500
4,000
3,500
3,000
2,500
2,000
1,500
1,000
1,500
4
2
–2
x
6
y
6
4
2
V (–3, 0)
–6
–4
–2
2
4
6
–2
–4
–6
'40 '50 '60 '70 '80 '90
Year
5. x ≤ 7 6. x ≤ 8 7. 0 < z < 5 8. 9 or more hours
13.
y
Topic 2 Cumulative Review Problems
6
P2
4
7
4
1. 8x 2y – 8y + 4x (in any order) 3. – < x < 1
8
5. 9, 25 7. 1 ≤ y < 9. –x 2y 2 – 27x + 4xy – 2
2
3
2
–6
–4
–2
P1
2
4
6
x
–2
–4
–6
LESSON 3.1: ANSWERS
713
x
Answers
Lesson EII.A Real Numbers and Exponents
Homework
2
x
1
6b
55. 2 or 2x –2 56. 8
1. <, ≤, ≠ 2. –5 3. 8 + 17 4. – 5. –4
Evaluate - Practice Test
6. (5 11) 23 7. 9 8. 5
1. 7 2. 15 3. –13, 4. 20
1
2
1
13
1
7
9. additive inverse = –7, multiplicative inverse = 10. >, ≥, ≠ 11. 4 12. –26 13. base: 4; exponent: 3; 64
14. 419 15. 1 16. 712 17. 75 124 18. 40 19. y 6
20. x 12 y 24 21. 8 9 or 72 22. 32y 5z 4 or 9y 5z 4
23. x 5y 3 24. 8x 13
64x11y4
81
5. y 3z 5 6. x 35 y 14 7. 144 8. Lesson EII.B Polynomials
Homework
1. 6 2. 16xz 3. 10y 2 – 7y – 12 4. 10
5. –2x 3 – 2x 2 + 14x – 23 6. 4a 2b 2 – 20abc 2 + 25c 4
Apply - Practice Problems
7. 15 8. 5x 5 – 20x 3 + 40x 2 9. 8y 4 – 4y 2 10. –12
1. 2 ≤ 2, 3 ≥ 0, 2 ≠ 8 2. 4 ≠ 6, 6 ≥ 0, 7 ≤ 7
11. 2x 3 – 15x 2 + 30x – 7 12. 3x + 10 + 3a. 3.5 b. 36 c. 0.005 d. 14.33 e. 36.1
13. 6x 4z 2(2x 3 – 3z 2 – 4xz 4) 14. (x 2 + 6)(x 2 – 6)
4a. 0.26 b. 28 c. 0.13 d. 15.22 e. 2.69
15. (x + 2)(2 + y ) 16. 2xy 2(2x – 3y )(2x + 3y )
7
8
13
x–2
1
3
5. 96 6. 105 7. 42 8. 5.2, –8, 9. 7, – 5
1
1
5
10. –21, 100
, 11. –8, 1 12. –5, 8
17. (3 + a 2)(9 – 3a 2 + a 4) 18. 2b (3 + a )(9 – 3a + a 2 )
19. (x + 7)(x – 3) 20. (2x + 3y )(2x + 3y ) or (2x + 3y )2
2 3
13. – ; 14. π, 7 15. 19
16. 4, 3 17. 1
21. 2x (x – 2)(x – 8) 22. (4y – 3)(7y + 2)
18. 1 19. 1 20. 11 21. 5 22. –1 23. –1 24. 4
23. (2p – q 3)(4p 2 + 2pq 3 + q 6)
25. –2 26. 0 27. 0 28. 0 29. base: 3; exponent: 5; 243
24. (x + y)(x – y) (x 2 + xy + y 2)(x 2 – xy + y 2)
3
5
2
30. base: 2; exponent: 5; 32 31. 1 32. –1 33. m 6n 4
34.
x 4y 3z
35.
a 3b 6c 2
36. 73 37. 24 38. 17
39. 7 5 – 710 40. 88 + 87 41. 57 + 54 42. x 4y 2z 4
43. m 6n 10 44. a 3b 13c 45. a 20b 10 46. x 21y 35
47. x 45y 63z 72 48. a 7b 6 49. x 8y 2 50. b 6c 2
51. 648a 8b 4
32
52. x 6y 5 53. 12a 5b 54. 3a 5
9
Apply - Practice Problems
1. 8 2. 8 3. 12 4. 15 5. 12x 4 + 10x 3 – 8x + 2
6. 3x 3 + 8x 2 – 16x + 5 7. 10x 3 – 4x 2 + 6x + 8
8. 2a 3b – 9a 2b 2 – 9ab 3
9. 5xy 3 – 17x 2y + 8xy + 16x 3y – 7x
10. x 3y 2z – 10x 2y + 14x 2z + 3xy 2 – 25xz 2
LESSON EII.B: ANSWERS
913
11. 8x 2 + 30x + 27 12. 6x 2 – 23x + 20
5. 6x 3z 4(2x 4 – 5z 5 – 7x 2z 2)
13. 12y 2 + 13y – 14 14. a 4 + 4a 2b + 4b 2
6. (3x – 5)(x + 6) 7. (2x – 5y )2 8. 3x (x – 2)(x – 8)
15. 16x 2y 2 – 16x y z 2 + 4z 4
Lesson EII.C Equations and Inequalities
16. 9m 2n 4 – 25n 6 17. 18a 5 + 24a 3 – 30a 2
Homework
18. 5x 7 – 30x 4 + 55x 3
1. x = 5 2. m = 3. x ≥ 9 4. no solution
19. –21x 4y 4 + 30x 3y 3 + 27x 2y 2 20. 43 21. –51
5. x = – + 2 6. x < – 7. x = 1 8. 2 > y > –5
F
a
4x 3
y
5
4y
3
x
22. –4 23. 2x 3 – x + 5 24. + + 2
2
10
17
9. –3 < z ≤ 1 10. x = 3 11. x = 3a 3
5b
25. – 7 – 3
3
b
a
26.
3x 3
+
13x 2
23
5
11
y
1
2
1
2
12. 2 > y ≥ or ≤ y < 2
+ 20x + 12
27. 2x 3 – 11x 2 + 19x – 12 28. x 3 + 8y 3
Apply - Practice Problems
29. (m – 8)(m + 8) 30. (w – 7)(w + 7) 31. (2a + 3)(2a – 3)
1. r = 2. m = 2
32. 7x 2y (5x 3y 2 – 2x y + 3) 33. 8a 4b 2(3b 4 + a )
34. (3a + 4b )(a – 2) 35. (y – 3)(5x + 2)
36. 6a 2(2a – 5)(a + 3) 37. 3x 3(x + 7)(2x – 3)
38. 2w (3w + 1)(w – 4) 39. (a + 7)2 40. (x – 6)2
41. (2m – 5)2 42. (4a – 9)2 43. (3x + 4)2 44. (7m + 5n)2
2Fd
C
2π
v
–3x + 15
3x – 15
3
3. y = or y = or y = x – 3
–5
5
5
y–b
c–b
4. x = 5. m = + 2 6. x < 3 7. x ≥ –20
a
x
8
8
8. y ≥ –6 9. y = – + 5 10. x = 4 – 11. y < 10
x
x
44
12. x < – 13. y ≤ –23 14. y = 1 15. y = –1
5
16. y = 3 17. 2 < x < 7 18. –7 ≤ x ≤ –2 19. 1 ≤ x ≤ 3
45. (a – 4)(a 2 + 4a + 16) 46. (2m + 1)(4m 2 – 2m + 1)
47. (x +
3)(x 2
– 3x + 9) 48.
(x 2
+
3y )(x 4
–
3x 2y
+
9y2)
49. (4p – q 3)(16p 2 + 4p q 3 + q 6 )
50. (5a 3 + 4b 3)(25a 6 – 20a 3b 3 + 16b 6)
51. (5m 2 + 4n)(5m 2 – 4n)
52. (2x – 5y 2)(2x + 4y 2)(4x 2 + 25y 4)
53. (2a – 3b )(2a +
3b )(4a 2
+
9b 2)
17
28
9
7
29
28y + 29
28y
23. x = or x = + 9
9
9
8x
8x – 75
24. y = or y = – 5
15
15
3x + 50
3
68
25. y = or y = x + 5 26. x = – 10
10
5
20. y = 21. x = –9 22. x = – 27. y = –12 28. x = –14
54. (x + 12)(x – 3)
55. (a + 2)(a – 8) 56. (4m – 3)(m + 12)
Evaluate - Practice Test
1. x = 8 2. y = 11 3. z = –2 4. x = –4 5. x = 10
Evaluate - Practice Test
1. 5 2. 8y 2 – 3y 4 + 1 3. –30
4.
2x 3
–
13x 2y
+
20x y 2
z + 5y
3
6. x = 7. y = –1 and y = 1
8. Here is this solution graphed on the number line:
+ 6x – 15y
–10
914
–8
–6
–4
–2
0
2
4
6
8
10
Lesson EII.D Rational Expressions
Homework
7
2
5
7
13
7
1
17
or 1 16
16
1
or 3 49. x = –1
3
1
7
50. a = –1 51. b = 4 52. a = –2 53. x = – or –3 2
2
7
3
4
10
5
17
43. y = 44. x = – 45. y =
11
35
2
2
10
46. x = 47. x = 48. y = 3
7
3
39. y = – 40. x = – 41. a = 42. b = x6
16y 8
6x – 2
1
x+5
1. 5 2. 3. 5 4. 5. 4
2
x
49y
13
23xy
x–3
4y 2
x
10y + 2xy – 3x
15xy
3(x + 3)
2(x – 4)
3x + 9
2x – 8
6. 7. 8. or 10
2(x 3 + 12)
3x
2
5a
6b – 2a – 13
a +a–2
18x – 3
12x + 2
9. 10. 11. 12. 2
2
15
2
1
2
37. 2a2 + 3a – 35 or (2a – 7)(a + 5) 38. x = or 3 15
4
3
2
13. 12 14. x = – 15. y = 16. 24x 8 17. x = 54. z = 2 55. r = –5 56. q = 7
18. no solution 19. 12(a – 2)( a + 2) 20. x = –7
Evaluate - Practice Test
7y 3
x
3c
7a
6x 2 – 3x
12x + 2
8a + 5
2a – 5a – 3
1. 2. 3. 4. 11
2
2
28
21. x = – 22. 2y 2 – y – 3 or (2y – 3)(y + 1)
3
13
23. y = 24. no solution
3
5. 15(a – 3)(a + 4) 6. x =
34
9
7
3
7. The equation has no solution 8. x = Apply - Practice Problems
1
3
1
7
1
y
3
x
8
y
5n 7
m
a5
2b
1. 2. 3. 5 4. 4 5. 7 6. 7. 4
2
10
11
3a 2
x+4
x–4
x+1
x–2
b
x+2
x+3
x+1
x–4
2
2
2
z (z + 3)
x + 5x
y–2
x (x + 5)
13. or 14. 15. x–4
10
x –4
2y
y (y 2 + 2)
2(9b + 1)
18b + 2
16. 17. or 18. 2
9
12b – 1
12b – 1
20a – 1
9x
–(x + 5)
–x – 5
20a – 1
19. or 20. 3 21. or 2(6a + 1)
2y
x–8
x–8
12a + 2
–xy + 3x + 6y
3
y –3
2
22. 3 23. 24. 3 25. 2y
x3
x
6xy
–xz + 9x – 6z
2y – 3x + 15
2y – 3x + 15
26. or 27. x2 + 2x – 35
(x – 5)(x + 7)
6xz
9–a
9–a
28. or 29. 14x 5 30. 6x 3
a2 + 5a – 24
(a + 8)(a – 3)
8. 9. 10. 11. 12. 4
Lesson EII.E Graphing Lines
Homework
Homework
1. P (2, 2), Q (–4, 1), R (–2, –3) 2. 7
3.
y
6
4
2
(2, 0)
–6 –4 –2
4
2
(2, –2) –2 (0, –1)
(4, 1)
6
x
–4
–6
31. 10x 4 32. 6y 2 + 18y or 6y (y + 3)
4. The x-intercept is (9, 0) 5. 6
33. a 2 – 25 or (a + 5)(a – 5)
6.
3
7
y
7. m = 8. 5
6
34. 8x(x – 3)(x + 3) or
8x3
– 72x
4
2
35. 2b2 – b – 10 or (b + 2)(2b – 5)
36.
x3
+
3x 2
– 9x – 27 or (x – 3)(x +
–6 –4
3)2
–2
2
4
6
x
–2
–4
–6
LESSON EII.E: ANSWERS
915
9.
11.
y
–6 –4
y
6
6
4
4
2
2
–2
4
2
6
–6 –4
x
–2
–2
–2
–4
–4
–6
–6
3516 2
4
6
x
2
4
6
x
2
4
6
x
10. The x-intercept is , 0 . The y-intercept is (0, –35).
11. The distance from A to B is 26
, the distance from B to
C is 10
, the distance from A to C is 8 = 22. So
points A and C are closest.
12.
12.
y
6
4
2
–6 –4
y
–2
–2
6
–4
4
–6
2
–6 –4
–2
2
4
6
x
–2
13.
y
–4
6
–6
4
2
13. y – 2 = 5(x – 1) 14. 16x + y = 9 15. y = 12
–6 –4
–2
–2
1
3
1
3
16. y – 3 = – (x + 7) or y – 2 = – (x + 4)
–4
–6
17. –2x + y = 4 18. x = –3 19. y = 18x + 9
1
20. –x + y = 9 21. y = 22. y + 6 = –2(x – 4)
8
1
5
1
23. x + y = 24. y = 8x – 6
6
4
3
2
1
4
14. m = 15. m = – 16. m = 0
17. x-intercept: (5, 0); y -intercept: (0, –10)
18. x-intercept: (–5, 0); y -intercept: (0, 3)
Apply - Practice Problems
1. P (3, –2), Q (–1, 5), R (4, 4)
2. S (5, –5), T (4, 3), U (–5, 0) 3. (–3, 4) 4. (–3, –2)
5. 5 6. 18 7. 9 8. 10 9. 13 10. 5
916
214 19. x-intercept: , 0 ; y -intercept: (0, 7)
20.
27.
y
–6 –4
6
6
4
4
2
2
–2
21.
2
4
6
–2
–2
–4
–4
–6
–6
28.
6
6
4
2
2
2
4
6
x
2
4
6
x
2
4
6
x
y
4
–2
22.
–6 –4
x
–2
y
–6 –4
y
–6 –4
–2
–2
–2
–4
–4
–6
–6
1
4
y
29. y – 5 = 2(x + 3) 30. y + 4 = (x – 2)
6
31. horizontal line: y = 6; vertical line: x = –2
4
2
32. horizontal line: y = 8; vertical line: x = 0
–6 –4
–2
2
4
6
x
–2
33. horizontal line: y = 0; vertical line: x = –3
–4
34. x = 5 35. y = –4 36. y = –5x + 16
–6
1
2
37. y = –4x + 10 38. y = x + 8 39. y = –3x + 7
23. y – 2x = 15 24. 3y + y = 9
1
3
40. y = 2x – 9 41. y = – x + 1 42. (4, 0) 43. (0, 7)
25. 2x + 2y = 14; y = –x + 2
44. (0, 1) 45. x + y = –2 46. –2x + y = 1 or 2x – y = –1
26.
y
1
3
4
–2
2
–2
–4
–6
5
2
2
1
52. y = x + 3 53. y = – x – 1 54. y = 2x – 8
3
4
2
55. y = 3x + 6 56. y = – x – 4
3
49. y = –3x + 13 50. y = x + 1 51. y = –3x – 4
2
–6 –4
1
2
47. x + 3y = 18 or x + y = 6 48. y = – x + 4
6
4
6
x
LESSON EII.E: ANSWERS
917
Evaluate - Practice Test
Apply - Practice Problems
1. To determine in which quadrant each point lies, see the
figure below.
1. y = –128 or y = 128 2. no solution
y
3. x = –250 or x = 250 4. y = –14 or y = 14
5. x = –9 or x = 9 6. x = –11 or x = 11
P
Quadrant II
7. x = –21 or x = 21 8. no solution 9. x = –15 or x = 15
Quadrant I
x
Quadrant III
10. y = –41 or y = 27 11. x = –9 or x = 5
Quadrant IV
12. x = –42 or x = 54 13. y = –4 or y = 9
Q
R
14. x = –4 or x = 6 15. no solution 16. y = 0 or y = 6
2. 15 3. rise = 1 – 3 = –2, run = 5 – 2 = 3 4. 3
5. y + 7 = 9(x – 20) 6. The y-intercept is (0, 2).
17. x = –5 or x = 1 18. x = –6 or x = 1
19. y = –11 or y = 13 20. x = –33 or x = 27
7. x = –11; y = 17 8. –8x + y = 5
21. x = –22 or x = 26 22. x = 4 23. y = 6
Lesson EII.F Absolute Value
Homework
24. y = –11 or y = –1 25. x = 0 or x = 1
26. x = –4 or x = 1 27. y = –5 or y = 7 28. x = –9 or x = 6
1. x = –100 or x = 100 2. x = –17 or x = 17
3. no solution 4. x = 0 5. x = –22 or x = 32
28
14
7
6. x = or x = – 7. x = 1 or x = 3
3
5
16
8. x = – or x = 0
3
9. |x – 457| = 15; highest guess: 472; lowest guess: 442
10. a = 0.1716 or a = 0.1404 11. x = 4
2
12. x = 12 or x = – 13. x ≤ –24 or x ≥ 24
5
14. –8.27 < x < 8.27 15. –1 ≤ x ≤ 1
15
2
15
2
16. x < – or x > 17. –11.5 < x < 25.9
18. –13 ≤ x ≤ 8 19. x ≤ –8 or x ≥ 24
28
3
20. –21.9 ≤ x ≤ 18.3 21. x > or x < –6
22. 7.96 ft ≤ a ≤ 8.04 ft 23. –1.1 < x < –0.1
35
6
49
6
24. x < – or x > 918
29. –7 < y < 7 30. –3 ≤ x ≤ 3 31. –4 < x < 4
32. y ≤ –23 or y ≥ 23 33. x < –1 or x > 1
34. x < –19 or x > 19 35. –9 ≤ y ≤ 9 36. x ≤ –15 or x ≥ 15
37. x < –3 or x > 3 38. |y | – 18 < –18
39. |x | + 9 < 9, |x + 2| < –3, and –|2x + 9| > 0
40. y ≤ –4 or y ≥ 7 41. x < –1 or x > 2 42. x < –1 or x > 5
43. –6 ≤ y ≤ 18 44. –9 ≤ x ≤ 1 45. –5 < x < 1
46. –6 ≤ y ≤ 10 47. –2 < x < 6 48. –2 < x < 6
49. y < 0 or y > 16 50. y ≤ –2 or y ≥ 7 51. x < 2 or x > 4
52. x < –3 53. x ≥ 4 54. x > –3 55. –2 < x < 5
56. –1 ≤ x ≤ 6
Evaluate - Practice Test
36.
–10
1a. x = –4 or x = 14 b. x = –3 or x = 3
–8
–2
0
2
4
6
8
10
2
–6x + 2
–4x – 1
2(–3x + 1)
–4x – 1
40. 5x (9x – 7)(2x + 1) 41. or 4. The equation has no solution.
5. The graph that corresponds to the solution of |x – 5| ≤ 7 is
the first graph:
8b + a + 31
2a + 5a – 3
y
15
10
5
8b + a + 31
(a + 3)(2a – 1)
42. or 43. d = 23
2
44.
0
–4
37. 38. 0 39. 7 12 + 7 33 = 315
2. x = –30 or x = 24 3. x = 2 or x = –4
–5
–6
x2
6
4
2
6. x < –3 or x > 6 7. |x | > 4 8. 3 > x > –5
–6 –4
–2
Topic EII Cumulative Review Problems
4
2
6
x
–2
–4
–6
1. (–3)
5 2. (3x – 1)(x + 7y ) 3.
30x 4y 2
4. x = 61
65
6
45. x = – 46. (4a + b 4)(4a – b 4)
8
9
19
3
5
3
5. –3 < x < – 6. x = or x = – 7. –39
2x 2 + 4y 3
2x 2 + 4 y 3
1
15
8. y = – x – 9. or 3 (x + y )
3x + 3y
4
4
5
10. m = – 11. P (2, 1); Q (–2, –1); R (–3, 4)
7
5
24
47. The vertical line is x = 7. The horizontal line is y = 1.
48. x = 99 or x = –99 49. 18x 2 + 3x – 45
12. no solution 13. x = – 14. –11 < x < 11 15. 9
4096x 17
5
16. y – 2 = 3(x + 1) 17. 18. 8
729
x yz 5
y –b
m
y
m
b
m
1. (3, 4) 3. Quadrant IV
x3 + x2 + 4
32xyz
5.
21. x = or – 22. 2
3
5
Lesson 3.1 Introduction to Graphing
Homework
1
4
19. (y 2 + 7)(y 2 – 7) 20. 4x 6 – x
3(x – 3)
4(x + 2)
y
6
6
4
4
2
2
T (–3, 6)
U (0, 5)
1
6
2y – 5
29. 30. 6a 2 – 4b 2 + 4a 2b + 6ab2 + 2ab + 14
y+8
7.
y
23. x = or x = 24. 4x 4y 2(7x – 3xy 2 + 5y )
3x 5 + 13y11
9
28. x ≤ –2 or x ≥ 6
25. z < – 26. x 2 27. y 2x 2
11
7
5
50. The x -intercept is – , 0 . The y-intercept is (0, 7).
–6
–4
–2
2
4
6
x
–6
–4
–2
2
–2
–2
–4
–4
–6
–6
4
6
3x – 9
4x + 8
31. 3 < z ≤ 10 32. or 12
13
33. (4x + 7)(2x – 3) 34. y = – 35. d = 41
LESSON 3.1: ANSWERS
919
x
Number of Farms (in thousands)
9.
5.
7,000
6,500
6,000
5,500
5,000
4,500
4,000
3,500
3,000
2,500
2,000
1,500
1,000
1,500
7.
y
–6 –4
y
6
6
4
4
2
2
–2
4
2
6
x
–6 –4
–2
4
2
–2
–2
–4
–4
–6
–6
6
x
'40 '50 '60 '70 '80 '90
Year
11.
9.
y
11.
y
y
6
6
6
4
4
4
2
2
2
V (–3, 0)
–6
–4
–2
4
2
–6 –4
x
6
–2
–4
–6
–2
–2
–4
–6
–6
15.
y
6
6
4
4
2
2
P1
–2
–6 –4
4
2
–2
2
4
6
x
6
x
y
y
P2
4
2
6
2
–4
–6 –4
x
–4
4
–6
6
–2
13.
13.
4
2
–2
–6 –4
–2
2
–2
–2
–4
–4
–6
–6
4
6
x
x
6
–2
–4
–6
17. (–2, –3) 19. (–4, 3) 21. (4, –6) 23. (0, –5)
15. rise = 2, run = 3 17. rise = –4, run = –4
25. Quadrant II 27. Quadrant IV 29. rise = 2, run = 8
19. rise = 8, run = 24 21. from 1975–1980
31. rise = 4, run = –9 33. rise = 11, run = 8
23. rise = 126, run = 85 25. c = 13 27. 29
35. rise = 6, run = –3 37. rise = 3, run = 6
29. center: (–5, 7); radius: 2 31. 74
39. rise = –6, run = –8 41. rise = 11, run = 13
33. He ran 20
00
yards;
the distance is approximately 44.7 yards.
43. rise = 7, run = 10 45. rise = 47, run = 28
35. (x + 3)2 + (y – 2)2 = 52 or (x + 3)2 + (y – 2)2 = 25
47. rise = 22, run = 13 49. rise = 26, run = 27
Apply - Practice Problems
1.
–6 –4
920
3.
y
y
6
6
4
4
2
2
–2
2
4
6
x
51. The run from P1 to P2 is greater. 53. (15, 13) 55. (1,
20)
–6 –4
–2
57. c = 20 59. c = 39 61. (x – 2)2 + (y + 3)2 = 16
63. (x + 3)2 + (y – 1)2 = 25 65. (x + 3)2 + (y – 7)2 = 64
2
–2
–2
–4
–4
–6
–6
4
6
x
67. 85
69. 22
6 71. 16
2 73. 5 75. 10 77. 13
79. center: (–5, –2); radius: 3 81. center: (–9, 12);
y
6
radius: 6
4
2
83. center: (–9, 3); radius: 11
–6
–4
–2
2
4
x
6
–2
Evaluate - Practice Test
–4
–6
1. K(3, –4) 2.
y
6
15. (2, 7)
4
P (5, 2.5)
2
–6
16. Several possible answers are shown.
–4 –2
4
2
x
6
y
–2
6
–4
4
–6
2
Average Gas Mileage (mpg)
3. S lies in Quadrant III. 4.
–6
30
–4
–2
2
4
x
6
–2
25
–4
20
–6
15
10
Topic 3 Cumulative Review Problems
05
1970 1975 1980 1985 1990
Year
1
1. 3. x – 3
3
5. rise = 10, run = 6
y
5. rise = 8, run = 3
6
6
4
2
–6
–4
–2
y
Q2 (–1, 5) 6
3 4
P2(7, 5)
10
2
8
4
6
2
x
8
–2
–6
–4
–2
–6
4
2
6
x
–2
–4
P 1(1, –5)
–4
Q1(–4, –3)
–6
6. rise = 12, run = 7 7. rise = 9, run = 36
8. The greatest rise in gas prices was between the years
1975 and 1980.
7. Christine is 28 years old, and Raoul is 35 years old.
9. x < 1
9. c = 15 10. The distance from (–3, 1) to (1, –2) is 5.
11. The distance between (10, 2) and (–2, –7) is 15.
12. The radius is 2, and the center is at (1, –5).
13. Quadrant II
10
11. c =
–8
m
E
–6
–4
–2
0
2
4
6
8
10
13. 0
14. Several possible answers are shown.
TOPIC 3 CUMULATIVE REVIEW: ANSWERS
921
7.
6
6
4
4
2
2
–6 –4
–6
9.
y
y
–4 –2
4
2
4
2
6
x
–2
–4
–4
–6
10
8
6
4
2
–2
x
6
–2
Hours Writing Songs
15. Several possible answers are shown.
2
4
6
8
10
Hours Playing the Guitar
–6
11.
17. 16 (–2) = (–16) 2; 23 52 = 52 23; 6 = 2
9
19.
5
24
21. 2 < x ≤
6
3
4
13
3
2
–6 –4
23. and 25.
13. (5, 5), (3, 5), (0, 5),
(2, 5), (–2, 5), (–4, 5)
y
–2
2
y
6
4
6
x
15. x-intercept = (4, 0),
y-intercept = (0, 1)
–2
–4
R (0, 6)
–6
4
2
17.
–6
–4 –2
2
4
6
–2
–4
P (3, –5)
–6
–6 –4
29. (x – 2)2 + (y – 3)2 = 42 or (x – 2)2 + (y – 3)2 = 16
21.
Lesson 4.1 Graphing Equations
Homework
3.
4
2
2
2
4
6
–6 –4
x
5.
–2
–4
–4
–6
–6
23.
6
40
4
20
2
20
40
60
–6 –4
F
6
6
4
2
2
2
4
6
x
–6 –4
–2
2
4
6
x
2
4
6
x
y
60
–2
–2
–4
–60
y
–2
–2
–60 –40 –20
–20
4
–2
4
–40
y
–6 –4
6
C
1. (1, 4), (–2, 7)
y
6
–2
27. x = 5
3
31. 5 33. no solution 35. center: (–5, 1); radius: 7
19.
y
x
25.
–6
slope = 1
27.
2
4
6
y
6
x
–2
–2
4
–4
–4
2
–6
–6
–6 –4
–2
2
4
6
x
–2
–4
–6
29. undefined 31. slope = – 4
5
33. Answers may vary; some include: (1, 12), (2, 24), etc.
922
35. The line through (2, 5) and (–1, –2).
The line through (4, 5) and (1, –2).
21.
35. A line with slope 2.
The line through (3, 2) and (5, 6).
–6 –4
25.
Apply - Practice Problems
1. (3, 1), (0, –5), and (1, –3) 3. (0, 3), (6, 0), and (–2, 4)
–6 –4
11.
y
–6 –4
y
6
6
4
4
2
2
–2
4
2
6
–6 –4
x
–4
–4
–6
–6
15.
y
6
6
4
17.
4
6
–2
–2
–4
–4
–6
–6
19.
6
6
4
2
2
2
4
6
x
6
–6 –4
x
–2
–4
–4
–6
–6
27.
6
4
4
2
2
4
6
–6 –4
x
4
6
x
2
4
6
x
2
4
6
x
2
4
6
x
2
4
6
x
y
6
2
2
–2
–2
–2
–4
–4
–6
–6
31.
y
6
6
4
4
2
2
2
4
6
–6 –4
x
–2
–2
–2
–4
–4
–6
–6
4
6
35.
y
x
–6 –4
y
6
6
4
4
2
2
–2
2
4
6
–6 –4
x
–2
–2
–2
–4
–4
–6
–6
y
4
–2
4
–2
–2
33.
2
–2
y
–6 –4
–6 –4
x
2
–2
x
2
2
2
y
–6 –4
4
–2
6
2
y
2
–6 –4
4
2
–2
13.
29.
–2
–2
6
4
–2
5. (1, 1), (0, –3), and (2, 5) 7. (–6, 8), (12, 0), and (21, –4)
9.
6
y
4
y
4
–2
35. The line through (9, –1) and (3, –4).
The line through (–1, 1) and (11, 7).
35. The line through (1, 2) and (5, –1).
A line with slope – 3 .
23.
y
–6 –4
–2
37.
2
–2
–2
–4
–4
–6
–6
4
6
39.
y
x
–6 –4
y
6
6
4
4
2
2
–2
2
4
6
x
–6 –4
–2
–2
–2
–4
–4
–6
–6
LESSON 4.1: ANSWERS
923
41.
3.
y
–6 –4
y
6
6
4
4
2
2
–2
4
2
6
–2
–6 –4
x
–2
–4
–4
–6
–6
43. x-intercept: (6, 0); y-intercept: (0, –6)
x
47. x-intercept: (3, 0); y-intercept: (0, 6)
30 –5
–10 15
3
5.
55. x-intercept: (9, 0); y-intercept: (0, 12)
71.
7
2
0
x
y
–3
0
–3
4
y
6
5
2
–3 –4
73. 1 75. – 8 77. – 1 79. – 2 81. –2
9
20
4
57. 3 59. 2 61. –2 63. 1 65. 4 67. – 7 69. 0
3
5
0 10
10
53. x-intercept: (5, 0); y-intercept: 0, – 2
5
4
x
y
10
49. x-intercept: (6, 0); y-intercept: (0, –8)
51. x-intercept: (3, 0); y-intercept: 0,
6
4. The completed table is shown below.
45. x-intercept: (3, 0); y-intercept: (0, 9)
9
4
4
2
–2
–2
–6 –4
2
4
6
x
–2
5
–4
83.
y
–6
6
6. The graph of y = –7 is a horizontal line.
4
2
–6 –4
–2
(5, 1)
•
4
2
•
–2 (0, –1)
6
x
4
8. The x-intercept is (3, 0). The y-intercept is (0, –5).
–4
9. – 7 10. 5
–6
3
Evaluate - Practice Test
1.
7. The x-intercept is 7 , 0. The y-intercept is (0, –7).
4
11. The slope of the perpendicular line is 5.
12.
y
y
6
6
4
4
2
2
–6 –4
–6 –4
–2
2
4
6
x
–2
–4
–6
2. (–5, –2), (3, –4), and (4, 11)
924
–2
2
–2
–4
–6
4
6
x
Lesson 4.2 The Equation of a Line
Homework
Apply - Practice Problems
1. y – 1 = 2(x – 4) 3. 3x + y = 23
5. y – (–2) = 2 (x – 4) or y + 2 = 2 (x – 4)
1. y – 1 = 2(x – 3) 3. y – 7 = –3(x – 2)
3
5. y – 3 = 3(x – 6) or y = 3(x – 5) 7. y – 4 = –1(x – 8)
7. y – (–1) =
9. y = 6x; x = 4.5 hours
9. y – 3 =
11. point-slope form: y + 7 = – 2 x
5
y–3=
2
3
(x +
8
5)
15. 5x + y = 3 17. – 3 x + y = –2 19. 2 x + y = –10
13. slope = 2; y-intercept = (0, 5) 15. x = 4
17. y = x – 6 19. slope =
3
[x – (–5)] or
8
y + 1 = – 1 (x – 3)
11. –3x + y = –13 13. –5x + y = –23
standard form: 2x + 5y = – 35
7
; y-intercept =
4
3
– 1 (x – 3) or
2
0, – 1
2
21. y = 4x +6; In four years the tree will be 22 feet tall.
23. slope-intercept form: y = – 7 x – 3
4
4
5
21. point-slope form: y – 2 = –2(x + 6) or y + 4 = –2(x + 3);
standard form: 2x + y = –10
23. point-slope form: y – 7 = 2(x – 2) or y – 13 = 2(x – 5);
standard form: –2x + y = 3
standard form: 7x + 4y = –12
25.
25. point-slope form: y – 7 = 3(x – 6) or y + 2 = 3(x – 3);
standard form: –3x + y = –11
y
y = 2x + 1
6
y = 3x + 1
4
2
–6 –4
–2
27. point-slope form: y – 4 = – 3 (x + 3) or y + 2 = – 3 (x – 5);
4
y=x+1
2
4
6
x
–2
29. y = 4x – 11 31. y = –2x + 6 33. y = –x – 1
–4
35. y = 2x + 4 37. y = 1 x – 6 39. y = 3x – 3
–6
3
25. As the slope increases, the line comes closer to being
vertical. Since only the slope is changing, each of these
lines has the same y-intercept, (0, 1).
27. With lines drawn through (–2, 3), as a negative slope
becomes more negative, the y-value of the y-intercept
decreases.
29.
5
43. y = –5x – 3
45. slope = 3, y -intercept = (0, 8)
47. slope = 2, y -intercept = (0, –4)
49. slope = 4 , y -intercept = (0, –2)
3
51. x = 7 53. x = 8 55. y = 9
1. y + 5 = –2(x – 2)
6
4
2
–2
41. y = 4x –
1
2
Evaluate - Practice Test
y
–6 –4
4
standard form: 3x + 4y = 7
2
4
6
x
–2
–4
–6
x-intercept: (–2, 0)
2. The slope of the line is m = 4, and a point that lies on the
line is (–2, 1).
3. – 4 x + y = – 1 or –4x + 7y = –1 or 4x – 7y = 1
7
7
4. –3x + y = 10 or 3x – y = –10 5. 3x + y = 2
6. The slope of the line is m = 2, and the y-intercept of the
line is (0, –7).
It is easy to find the slope using the x- and y-intercepts.
7. y = –6
LESSON 4.2: ANSWERS
925
8. Several possible choices for Q are shown.
any point
on this line
6
4
2
–6 –4
–2
2
4
6
x
11.
y
Pounds of Guava Chips
y
9.
y
6
2
4
2
2.50x + 4.00y
1
5.00
–6 –4
4
2
6
x
–2
–4
–2
P(4, –3)
–4
–2
1
2
Pounds of Shredded Coconut
x
–6
–6
Apply - Practice Problems
9. y – 2 = 3(x – 5)
y – 2 = 3 (x – 5)
1.
4
(2, –1) (4, –2) (–5, 2) (3, 8) (–3, 1) (4, 3) (–1, 6)
10. –3x + y –9 or 3x – y 9
11. The slope of line A is greater than the slope of line B.
11. The y-coordinate of the y-intercept of line A is less than
the y-coordinate of the y-intercept of line B.
11. The x-coordinate of the x-intercept of line A is less than
the x-coordinate of the x-intercept of line B.
12. 2x – y = –3
2x – y = 4
x
x –y<1
x –y=1
x –y>1
x
x
x
2x – y < 1
2x – y = 1
2x – y > 1
x
–6 –4
5.
y
–6 –4
6
6
4
2
2
2
4
6
x
6
6
4
2
2
2
4
6
–6 –4
x
–2
2
–2
–2
–4
–4
–6
–6
4
6
x
x
11.
y
–6 –4
–2
–6 –4
2
–2
–2
–4
–4
–6
–6
4
6
x
7. The graph of the inequality x + y ≤ 4 includes the points
on the line x + y = 4, but the graph of the inequality
x + y < 4 does not include these points.
926
y
4
–2
x
y
6
6
4
4
2
2
y
4
–2
x
7.
y
9.
3.
x
x
x
x
y > 2x + 1
x
x
x
y = 2x + 1
x
(–3, 4) (–5, 3) (–1, 4) (3, 5) (3, –8) (5, –1) (– 4, –5)
(1, 7) (4, 2) (2, 5) (0, 0) (–6, 3) (–4, –3) (3, –6)
x
x
3.
1.
y < 2x + 1
x
x
5.
Lesson 4.3 Graphing Inequalities
Homework
x
–2
2
4
6
x
–6 –4
–2
2
–2
–2
–4
–4
–6
–6
4
6
x
13.
15.
y
–6 –4
3.
y
y
6
6
6
4
4
4
2
2
2
–2
4
2
6
–6 –4
x
–2
2
4
6
–6 –4
x
–2
–2
–2
–4
–4
–4
–6
–6
–6
17.
19.
y
6
6
4
2
2
6
x
4. The points (8, –14) and (0, 0) satisfy this inequality.
y
4
4
2
–2
5. 5x + 4y > –20
6.
y
6
–2
–6 –4
4
2
6
–6 –4
x
–2
4
2
–2
–2
–4
–4
–6
–6
6
x
4
2
–6 –4 –2
4
2
x
6
–2
21.
–6 –4
–4
23.
y
y
6
6
4
4
2
2
–2
4
2
6
–6 –4
x
–2
–6
7. (1, 2), (–3, 3), (–5, 6) 8. y ≥ –x + 2
2
–2
–2
–4
–4
–6
–6
4
6
x
Topic 4 Cumulative Review Problems
1.
y
6
25.
27.
y
–6 –4
4
y
2
6
6
4
4
2
2
–2
2
4
6
x
–6 –4
–2
–6 –4
–2
–4
–4
–6
–6
2
4
6
x
–2
–4
2
–2
–2
4
6
x
–6
3. 5x – 4y = 29 5. 120
7.
y
Evaluate - Practice Test
6
4
1.
2
y
6
–6 –4
–6 –4
–2
2
4
–2
2
–4
4
6
x
–6
–2
2
4
6
x
–2
–4
–6
1
9. 2 11. 3
18
2. (0, 0), (–3, –1), (8, –4)
TOPIC 4 CUMULATIVE REVIEW: ANSWERS
927
13.
Lesson 5.1 Solving Linear Systems
Homework
y
6
4
2
–2
–6 –4
1. –x + 2y = 4 and x + y = –1
2
4
6
x
3. –x + 2y = 4 and x + y = 2
–2
–4
5. –x + y = 5 and 3x + y = 9
–6
7. –x + y = 5 and –x + y = 2
15a. Answers may vary. Some possible answers are (0, 2),
(1, 0), (2, 0), and (3, 0).
9. No. It will take him 15 weeks instead of 14 weeks to reach
his goal.
15b. Answers may vary. Some possible answers are (2, 2),
(3, 2), (3, 3), and (3, 4).
190
Weight in Pounds
180
15c. Answers may vary. Some possible answers are (1, 2),
(5, 0), (3, 1), and (–1, 3).
9
17. 4 19. 5 21. – 1 x + y = 4 or –x + 7y = 28
35
2
170
160
150
140
7
71
23. y = 25. Paul is 52 years old, and Rita is 31 years
0
47
old.
2
4 6 8 10 12 14 16
Time on Diet in Weeks
11. One possible solution is shown.
27.
y
y
x = –7
6
6
4
4
2
y = –2x 2
y = –2x + 8
–2
–6 –4
2
4
6
–6 –4
x
–2
2
–2
–2
–4
–4
–6
–6
4
6
x
13. (2, 1) 15. (–1, 4)
29. –2 < x ≤ 7
2
17. Same line—there are an infinite number of solutions.
19. The system has no solution.
–5 –4 –3 –2 –1
0
1
2
3
4
5
6
21. You can drive up to 50 miles before the cost of paying for
mileage is the same as getting unlimited mileage.
31.
y
23. (–3, 7) 25. y = 6x – 8 or y = 3 x + 1
6
2
4
27. (0, 4), (–6, –2) and (6, –8)
2
–2
–6 –4
2
4
6
29. y = x + 3
x + y = –1
x
–2
–4
–6
36
33. y = – 35. slope = 1 37. y + 1 = 4(x – 5) 39. 5 4
7
928
4
9
Apply - Practice Problems
17. There are an infinite number of solutions.
y
1. A and C 3. C and D 5. C and D
7. (2, 0)
6
4
y
2
6
–6 –4
4
–2
4
2
6
x
–2
2
–4
–6 –4
–2
4
2
6
x
–6
–2
–4
19. There are an infinite number of solutions.
–6
y
9. (–3, –1)
6
y
6
4
4
2
2
–6 –4
–2
4
2
6
x
2
4
–2
–6 –4 • –2
2
4
6
x
–2
–4
–4
–6
–6
21. (1, 3)
11. There is no solution.
y
6
y
4
6
2
4
–6 –4
2
–2
6
x
–2
–6 –4
–2
2
4
6
x
–4
–2
–6
–4
–6
13. There is no solution.
23. There are many possible answers. Any line that is parallel to
the given line is a solution. Here is one example.
y
y
6
–6 –4
4
6
2
4
–2
2
–2
4
6
2
x
–6 –4
–2
2
–4
–2
–6
–4
4
6
x
–6
15. (–1, –4)
y
6
4
2
–6 –4
–2
2
4
6
x
–2
•–4
–6
LESSON 5.1: ANSWERS
929
25. There are many possible answers. Any line that is
parallel to the given line is a solution. Here is one
example.
y
6
9. (12, 5) 10. (9, 4) 11. (1, 2) 12. (3, –1)
Lesson 5.2 Problem Solving
Homework
1. 12 and 3 3. 310 adult tickets and 230 student tickets.
4
5. $1150 into his savings account and $250 in his
checking account
2
–2
–6 –4
4
2
6
x
–2
7. 51 quarters 9. 26 and 19
–4
–6
11. 2.1 pounds of almonds and 0.9 pound of walnuts.
27. There are many possible answers. Any line other than the
given line that passes through the point (–4, 3) is a
solution. Here is one example.
y
1. 198 and 169 3. 120 and 15
5. $1275 in the 3% account and $1200 in the 6.5% account
6
4
7. $1788 in the 12% fund and $1712 in the 9.5% fund
•
2
–6 –4
Apply - Practice Problems
–2
4
2
6
9. He owes $3200 on the 9% loan and $4700 on the 7% loan
x
–2
–4
11. 17 quarters and 23 dimes 13. 18 dimes and 47 nickels
–6
29. x = 3, y = 2 31. x = 2, y = –5 33. x = 2, y = –1
12
35. x = , y = 1
39. x =
7
16
–
5
7
9
5
37. x = , y = –
16
16
18
, y = –
5
41. All ordered pairs (x, y ) that satisfy 3x – y = 5 are
solutions; both equations represent the same line.
43. x = 4, y = 1 45. x = 6, y = 4 47. x = 3, y = 2
15. 23 dimes and 115 quarters
17. 160 ml of 75% sulfuric acid and 240 ml of 25% sulfuric
acid
19. 120 ml of 65% boric acid and 180 ml of 15% boric acid
21. 15 ounces
49. x = 6, y = 7 51. x = 2, y = 0
23. 10 pounds of the $6.50 per pound nuts and 15 pounds
of the $4.00 per pound nuts
13
6
53. x = – ,y = 25. 11 pounds of raisins and 9 pounds of peanuts
17
17
55. The system has no solution; the equations represent
parallel lines.
27. 8 pounds
Evaluate - Practice Test
Evaluate - Practice Test
1. (4, 2) 2. (–4, 5)
1. 9 and 16
3. The system has a solution at the point (–2, –5). 4. (5, 0)
2. She has 8 five-dollar bills and 11 ten-dollar bills.
5. The other equation in the system is 3x + 4y = 6.
3. 560
6. x + y = 2 7. (–1, 4)
4. 1.6 pounds of Ethiopian Harrar beans and 1.4 pounds of
Arabian Mocha beans should be used for the blend.
8. The system has only one solution, the point (–2, –3).
5. Deac is now 37 years old and Irina is 15 years old.
930
6. 60
15. (0, 5), (3, 5), (0, 0), (3, 0); Area = 15 square units
y
7. He needs 150 ml of 5% HCl and 50 ml of 9% HCl.
6
8. She invested $1325 at 4% interest and $1050 at 11%
interest.
4
2
–6 –4
–2
Lesson 5.3 Systems of Inequalities
Homework
y
x≤5
–6 –4
6
4
4
–2
4
2
5.
17. Answers may vary; some possible answers are:
(0, 0), (1, 3), (1, 2), (4, 8)
6
6
–6 –4
x
Apply - Practice Problems
2
x + 2y < 3
–2
2
–2
–2
–4
–4
–6
–6
1.
x
3.
y
y
6
6
4
y>x+3
2
4
–6 –4
–2
y<6
4
y>x–2
2
2
4
6
–2
–6 –4
x
–2
y < –x – 2
–4
6
y ≥ –3 x – 1
4
4
4
2
6
x
–2
–4
y < –2x + 3
–6
–6
2
2
–6 –4
6
y
6
y ≥ –3 x + 5
4
4
2x – 3y ≥ 12
7.
y
x
–6
y
2
6
–4
1. (–1, –7), (4, –4), (6, –2), (7, –6) 3.
y > –23 x – 1
4
2
–2
–2
4
2
6
–2
–6 –4
x
4
2
–2
–2
–4
y > – –72
–6
–6
6
x
5.
y ≤ –x + 3
9. x + y ≤ 10
x
≤y
7.
y
–6 –4
y
6
x+y≥4
6
4
4
2
2
–2
2
–2
4
6
–2
–6 –4
x
–4
y
4
2
6
x
–2
y ≤ 3x – 1
–4
x – y < –2
–6
12
–6
10
8
9.
6
11.
y
y
4
6
6
2
4
4
2
2
x+y 6
2
4
8
6
10 12 x
–6 –4
11.
2
–4
6
4
6
x
–6 –4
–2
2
4
6
x
–2
x–y>2
y
–6
4
–4
y ≤ –x – 4
–6
6
2
–2
–2
–2
13. (0, 5), (3, 0), and (0, –5)
y
–6 –4
y < 2x + 5
4
2
4
6
2
x
–2
–4
–6
–6 –4
–2
2
4
6
x
–2
–4
–6
LESSON 5.3: ANSWERS
931
13.
15.
y
y
6
y
y
> 31 x
+5
6
6
4
4
4
y > 23 x + 3 2
2
–2
–6 –4
4
2
–2
y≤
1
2x
6
–6 –4
x
–2
–2
–4
y
– 43 x + 2
–6
17.
19.
y
2
–6 –4
x
–2
–4
–6
–6
y>
+2
2
4
6
–2
–6 –4
x
–2
–4
–4
–6
–6
23.
4
2
3x + 4y –5
4
6
–6 –4
x
2
2
4
6
–6 –4
x
–2
–2
–4
y < – 23 x – 1
2
–6 –4
–1
x
6
y
6
6
4
4
2
2
–2
2
–2
4
5.
y
y x+3
x
6
(5, –1)
(7, –3)
–6
4
2
4
2
–4
y ≤ – 31x – 2
6
y ≥ 2x + 5
2x – 5y < 15
–2
–2
y
6
–6
y
6
2
–2
–2
x
y ≥ 43 x + 1
2
3x + y ≥ 4
4
–6 –4
6
4
y
3x
5
4
3. (5, –1), and (7, –3)
y
4.
21.
y < 32x + 1
2
–4
6
2
x–y<1
6
–2
4
–2
4
2
–2
6
–6 –4
x + y –6
x
4
6
x
y x–4
–6 –4
2y 3 x + 2
–2
4
2
6
x
–2
y –3
–2
–4
–4
–4
–6
–6
x 2
–6
6. (–1, 0), (–3, 1) and (–4, 4)
y
6
25.
27.
y
y
y>x
6
4
y≤3
2
–2
2
6
4
–6 –4
4
2
4
6
–6 –4
–6 –4
x
–2
2
–2
–2
–4
–6
–6
4
6
x
y
6
and (7, –2)
y>3
4
2
–6 –4
–2
2
–2
–4
–6
932
–4
–6
y < 3x – 4
Evaluate - Practice Test
2.
x –6
4
6
x + 2y 4
x
y 0
2
–2
2
y > 3x + 1
–4
1. (–3, –3), (2, –4), (4, 1),
–2
4
6
y – 12 x + 2
x
7. If the direction of the first inequality sign is reversed, the
graph of the new system is:
y
1a. 37 b. 57 c. 77 3a. 76 b. 76
6
b3
x3
5a. x 8 b. a 8 c. 1 d. 7a. b 18 b. y 11 c. 7
4
2x + y > 4
x + 2y > –4 2
–6 –4
Lesson 6.1 Exponents
Homework
–2
4
2
6
a
4
1
1
9. 1 11a. 1 b. c. d. 3
3
4
x
x
–2
–4
y
b
Apply - Practice Problems
–6
1. 78 3. b 15 5. a 11 7. 96 9. n 5
The overlapping region is the solution of the system.
8.
11. 512 13. 1330 15. z 48 17. 81a 4
y
m4
19. 8y 3 21. 23. 1 25. 1 27. 3
6
6
2x – y 6
any point in
this region
4
2
–6 –4
–2
4
2
6
n
Evaluate - Practice Test
x
–2
1a. 114 b. 32 y 5 c. 543 d. x 21y 26 e. 718 b14
–4
y x
–6
33
1
2a. 2 3 b. b 6 c. d. 9
4
x 0
x
Any point that lies in the region shown satisfies the first
two inequalities, but not the third.
Topic 5 Cumulative Review Problems
3
11
1. –7 3. 34 and 19 5. x = , y = – 7. –1
2
2
9.
y
x 6y 2
(5y ) 2
x 7y
5y 2
, and 3. and 4. (31x 8)0 5y, 3 7
4 6
x y
x y
y
5y
5a. b 48 b. 310a 12 c. 299 x 44y 66
54y 40
76 a 6 b 24
6a. b. 4 32
6
3x
5
7a. –1 b. 1 c. –3 d. 1
y
1
8a. a 35 b. 35
6
a
4
y 2x + 3 2
–6 –4
–2
4
2
–2
–4
y
6
Lesson 6.2 Polynomial Operations I
Homework
x
2x – 4
1. 3 1 y 3 + 3y 2 – 5 3a. –4y 5 – 2y 3 + 3y + 2
–6
4
11. x = 4, y = –3 13. slope = – 9 15a. 21 b. 27, 720
4
17. y =
4
5
19. x = –7, y = 8 21. 452 23. B and D
25. A and B 27.
61
10
29. x = – , y = 39
39
1
42
b. 5, 3, 1, 0 c. 5 5. –4v 7 + v 3 + 6v 2 – 5v + 5
7. –7s 3 t 3 + 7st 2 – s 2t + 2st –13t + 9
9. 2x 2y + 10xy 2 + 4y 3 + 3
11. 4w 2yz + 3w 3 – 4wyz 2 + 6wyz – 4wy 2z + 3
31.
13. x 3 y 3 z 3 15. –3t 4u 4v 15 17. 10p 3r 4 + 5p 4r 5
0
2
3
1
3
8
9
1
3xw 5
xy 2
3a 3d
4xy 2
5x 2y 3
19. 21. 23. +
or (4 + 5xy)
5 3
y
2b c
3
3
3
6
33. 93 dimes 35. y = – 37. slope = 6
11
5
LESSON 6.2: ANSWERS
933
Apply - Practice Problems
Lesson 6.3 Polynomial Operations II
Homework
1. 2xy 5xz ; 9y 2 13yz – 8z 2
5. 8 7. 9 9. 7 11. 6 13. 84 15. 6x 2 11x – 8
1. First terms: 2p and p
Outer terms: 2p and –p 2
Inner terms: 3 and p
Last terms: 3 and –p 2
17. 15m 2n 3 2m 2n 2 – 7mn 19. 15a 3b 2 4a 2b – ab 3
3. 2s 3, 5 5. 12x 2 + 24x – 6yx – 12y
21. 20xy 2z 3 – 30x 2yz 2 10x 3y 3z 23. 4x 3 7x – 8
7a. 9x 4 – 4 b. 9x 4 – 12x 2 + 4 c. 9x 4 + 12x 2 + 4
25. y 2 6xy 4y 27. 11a 5b 3 – 4a 4b – 9b 29. 15y 5
9. 169s 2 – 4h 2 11. 91x 4y 4 – 148x 5y 2 + 60x 6
3a.binomial b. binomial c. trinomial d. monomial
3e. trinomial
13. 3x 2 + 4x 2y + 7x + 8xy + 2
31. –45a 9 33. 28x 4y 8 35. –6w 2x 5y 3z 3
15. x 2 + x – y 2 – y or x(x + 1) – y(y + 1) 17. 4x 2 – 8x
37. –6a 7b 7 10a 4b 5 – 12a 4b 2
76 3
19. 48x 5 – 48x 4 – x + 24 x 2 + 7 x + 7
39. 20a 4b 2 10a 4b 3 – 35a 3b 4 – 15a 2b 3
3
–391
20
21. 3x – 7 + 23. 15x 2 – 44x + 132 + 41. 12x 6y 3 – 28x 4y 5 8x 4y 4 – 4x 3y 4
x +3
3n 5p 3
8a 2b 3
3x 3y 2z 5
43. 5a 2b 5 45. 47. 49. 3c
51. 4a 3a 3
53.
7
y
2w
4x 3y
55.
2
x
–
2mq
x 2z 3
2y 2
1.
2.
w 5x 4
– s + 5,
2x 2
m 5n 4 o 3p 2r,
and
3
5
c15 + c 11 –
7
14
is a monomial.
– 36 is a binomial.
1
1
2
x 17 + x 12 – 3
3
3
is a trinomial.
27 is a monomial.
27x 3 – 2x 2y 3 is a binomial.
– 1 27.
a2
x+3
–
b 2,
4x 2
–
9y 2
29. a 2 – 2ab + b 2, 4t 6 – 16u 2t 3 + 16u 4
1. a 2 7a 10 3. x 2 – 15x + 44 5. 5y 2 + 7y – 24
3
7. 8a 2 26ab 15b 2 9. 18y 2 9xy – 5x 2
11. x 2 6x 9 13. 25q 2 30q 9
15. z 2 – 10z 25 17. t 2 – 12t 36
19. 16a 2 – 56ac 49c 2 21. 25m 2 – n 2
23. 4x 2 – y 2 25. 25x 2 – 9 27. 4a 2 – 49b 2
x 2 + 3xy – 2 y 2 is a trinomial.
29. 8a 2 – 34ab 21b 2 31. 18m 2 9mn – 20n 2
8w 8
33. 14xy 21x – 8y – 12
3
3.
25.
9a 2
Apply - Practice Problems
Evaluate - Practice Test
t2
3
+
7w 5
+ 3w 3 – 13w 2 – 2
35. 3m 3n 11m 2n – 4mn – 9mn 2 3n 2
4a. 3x 3y – 8x 2y 2 – 5y 3 + xy + y 2 + 19
b. 7x 3 y – 8x 2y 2 + 3y 3 + 5xy – y 2 + 7
37. 21a 3b 16a 2b 9ab 2 – 16ab 12b 2
5. x 8y 3w 5
39. 10x 3y – 30xy 2 19x 2y – 12y 2 6xy
6. 3n 3p 3 + 2n 5p 5 – 35n 2p 7
41. 20m 5n – 15m 4n 2 40m 3n 3 –
15m 2n 3 12m 3n – 9m 2n 2 24mn 3 – 9n 3
3x 4yz 6
7. 2
43. x 2 3x – 7 45. x 2 7x 2
3t 2u
8. – 1 t 4
2v
934
2
47. x 2 5x – 1 49. 2x 2 – 3x 1
3
51. x 2 2x – 3 remainder 3 or x 2 2x – 3 4x – 1
7a. y + 9 = – 8 (x – 20) b. y = – 8 x + 23 c. 8x + 5y = 115
5
5
3x 2 y 4
2z 6
10
53. x 2 4x 1 remainder –10 or x 2 4x 1 – 9a. 1 b. –1 c. 1 11.
55. 2x 2 – 6x 1
13. slope = 4, y –intercept = (0, –7) 15. –5 < x < –3
Evaluate - Practice Test
2
26
17. = , The GCF of 72 and 108 is 36.
3x 2
6x 5y
1.
–
4x 2
+
9x 4y 2
117
4x 2
– 6xy 2.
– 12xy +
9y 2
9
19.
y
6
3. 4x 2 + 12xy + 9y 2 4. 4x 2 – 9y 2
5.
15x 3+
14x 2
4
2
– 22x + 4
–6 –4
6. 12r 8 – 15p 2r 4 – 18p 4 – 7r 4 + 36p 2 – 10
–2
4x + 2
2
21. 3 , –3 23. y = 3x – 4 25. – 2
10x 7
13
35.
y
7
6
9x - 4y
5x 4
8
35x 4
–15x 5
x
27. no solution for y 29. A and B 31. A and C 33. –261
10. 15y 6 – 5y 5 + 4y 4 + 5y 3 – 5y 2 + 2y
–3x
6
–6
9a. a 4 + a 5 – a 6 – a 7
b. The degree of the resulting polynomial is 7.
2x 3
4
–4
–6
7. 3t + 1 8. 2x 2 – x + 2 + 11.
2
–2
4
2
–6 –4
–2
2
4
6
x
–2
8
16x 3
–24x
56
–4
37. Manuel split his money by putting $984 in his checking
account and $1581 in his savings account.
10x 7 – 15x 5 + 35x 4 + 16x 3 – 24x + 56
12.
9x - 4y < 20
–6
5x 4
–7x 3
7x 2
–8x
x2
5x 6
–7x 5
7x 4
–8x 33
1
5x 4
–7x 3
7x 2
–8x
5x 6 – 7x 5 + 12x 4 – 15x 3 + 7x 2 – 8x
Topic 6 Cumulative Review Problems
1a. 216 b. x 7 c. a 20 b 8
55
3a. y – 7 = – 2 (x – 3) b. y = – 2 x + c. 2x + 7y = 55
7
7
7
39a. binomial b. trinomial c. monomial d. binomial
e. monomial f. trinomial
41. –4a 2b + 10a – 7b
Lesson 7.1 Factoring Polynomials I
Homework
1. x 3yz 2, x 3. 6xy 5. y (x 2 + 6y ) 7. 4ab (a – b )
11. 17x 2y 2z(z + 4x 8y 30 + 9x 7y 2z 11) 13. x 5 + y
15. (xy + yz ) 17. (a 2 + b 2 )(a – b )
19. (x 4y + z )(x + y + z ) 21. (x 2 + y 2)(z + 3)
23. (x + y )(3 + z )
5. The numbers are 14 and 46.
LESSON 7.1: ANSWERS
935
Apply - Practice Problems
27. y (x 2 – 1) or 1 y (x 2 – 1)
2
1. 23 and 8m 3n 3. 4ab 5. 5x y 2 7. 3ac 2
9.
8m (2n 4
1) 11.
7) 13.
2x y (3x 3y 2
2
x 2y
2ab (4a 2b
– 5)
15. 9y 3z 5(4y 4z 3 – 5) 17. 2mn (2 5n 2 – 9m 3)
19.
4ab (2a 2b 3
– 3
5a 2)
21.
8p 5q 3r (4p 2r 3
–
–y
2
2
x2
y
2
–1
5q 2)
y
(x 2
2
23. 3x y 2z 3(3 – 5x 2y 3z 7x 3z 2 )
25. 4a 2bc 2(5ab 4 3a 2bc – 2c )
– 1)
29. GCF = x
27. 3a 2b 2c 2(2ab 3 – 3a 2b 2c 6b – 7a 4c )
B = 52x 2y
A = 2xy 2z
yz
29. (x y )(z 3) 31. (a 9)(3b – 4)
2x
2y
x
13
33. (8m 17)(3n 3 – 4) 35. (7x – 11)(2x 2 3)
C = 13x
37. (m – 3n )(5m 2n ) 39. (x y )(w z )
41. (a – b )(c d ) 43. (2a – 7)(2a 1)
Apply - Practice Problems
45. (6a 5b )(2a 3) 47. (5x 2y )(3x 7)
1. (x 1)(x 4) 3. (x 1)(x 14) 5. (x 3)(x 5)
49. (2z w )(4z – 1) 51. (4a – 5b )(3a 2)
53. (6x – 5y )(3x 2) 55. (3pr – 4s )(4r 5)
7. (x 4)(x 3) 9. (x – 2)(x – 6) 11. (x – 11)(x – 4)
13. (x – 7)(x – 3) 15. (x 3)(x – 10) 17. (x 7)(x – 3)
19. (x 9)(x – 4) 21. (x – 9)(x + 2) 23. (x – 7)(x + 3)
Evaluate - Practice Test
25. (x – 9)(x + 7) 27. (x – 12)(x + 5) 29. (2x 5)(x 1)
1. GCF = x 2. GCF = xyz 3. 3xy (x – y )
31. (3x 2)(x – 7) 33. (2x 7)(x – 4)
4. 3xy 2(y – 2 + x 2y 2) 5. (x 2 + 4)(13 + 6y )
35. (2x – 3)(x 4) 37. (2x 3)(x 5)
6. (3xyz + 4z)(17x 2 – 3yz) 7. (3r – 1)(13s + 3)
39. (3x 2)(x 3) 41. (5x – 2)(2x – 1)
8. 2(3w – 11)(2z + 3)
43. (3x 2)(2x – 5) 45. (2x 1)(4x – 3)
Lesson 7.2 Factoring Polynomials II
Homework
1. (x 4)(x 3) 3. (x 5)(x 7) 5. (x 3)(x – 8)
47. (3x – 5)(3x 4) 49. (4x 1)(9x 1)
51. (5x – y )(x 3y ) 53. (3x y )(x – 2y )
55. (3x – 2y )(3x y ) 57. x 6 or x 2
5
2
59. x 5 or x 8 61. x or x 1
7. (x – 3)(x + 2) 9. (x – 7)(x + 3) 11. (x + 36)(x – 1)
13. (x 5)( 2x 1) 15. (2y + 3)(2y – 7)
Evaluate - Practice Test
17. 15(a – 1)(a – 1) 19. x = 1 or x = – 2
1. (x – 4)(x – 6)
21. (13x + 11)(x + 2) 23. (x + y )(x + y ) 25. xy
2. x 2 + 2x – 1 cannot be factored using integers.
5
5
3. (t + 1)(t – 17) 4. (r + 5t)(r + 5t) 5. (x + 2)(5x – 2)
936
6. (9v – 7)(3v – 4) 7. (x + 12)(4x + 9)
8. x =
12
7
or
x = –1
9. The two true statements are:
• Two factors of C are z and 2.
• The GCF of A, B, and C is 4z.
10. 15u 2 + 20uv and 9uv + 12v 2
11. 7y – 3x
12.
3x
y
2x
6x 2
Evaluate - Practice Test
1. 9x 2 + 12x + 4, 0.25x 2 + 8x + 64, and x 2 – 2x + 1
2a. (x – 5)(x – 5) b. (7y + 2)(7y + 2) c. (4x + 1)(4x – 1)
2d. (3y + 6)(3y – 6)
3. x 2 – 1000 and 9m 2 – 24mn – 16n 2
4. 3x(2x – 5)(2x – 5) 5. x 2 + 8x + 16 and 4x 2 – 12x + 9
6a. 4(x – 3)(x – 3) b. (8z + 1)(8z + 1) c. (2w + 7)(2w – 7)
6d. (3m + n)(3m – n)
7a. (x + 10)(x 2 – 10x + 100) b. (6y – 1)(36y 2 + 6y + 1)
2xy
7c. (7x + 2y )(49x 2 – 14xy + 4y 2 )
–3y
–9xy
8. 3w(3w + 5)(3w + 5)
–3y 2
Topic 7 Cumulative Review Problems
Lesson 7.3 Factoring By Patterns
Homework
1. (x + 7) 2 3. (x + 5)(x 2 – 5x + 25) 5. x(3y – 1)(3y + 1)
7. (x + 4w 2 ) 2 9. (7y – 2x) 2 11. 2x(x + 3) 2
1. a 3 – 2a + 5 3. 7x 2 + 5y + 2
5. Alfredo should use 130 ml of the 15% solution and
120 ml of the 40% solution.
7. (x – 3)2 9. a, d, e
11.
y
Apply - Practice Problems
6
1. (a 9)(a 9) or (a 4
9)2
2
3. (3x 7)(3x 7) or (3x 7)2
5. (2a 5)(2a 5) or (2a 7. (z – 11)(z – 11) or (z –
–6 –4 –2
–2
5)2
13. (a 2 + 2) 2
11. (3x – 2)(3x – 2) or (3x – 2)2
15. 6 ≤ x < 10
21. (3z – 7)(9z 2 21z 49)
23. (c 4)(c 2 – 4c 16) 25. (y 3)(y 2 – 3y 9)
27. 2mn (5m 8n )(5m – 8n )
x
6
–6
9. (4a – 5)(4a – 5) or (4a – 5)2
17. (a – 6)(a 2 6a 36) 19. (x – 5)(x 2 5x 25)
4
–4
11)2
13. (x 6)(x – 6) 15. 25(a 5b )(a – 5b )
2
10
8
6
4
2
0
2
4
6
8 10 12
17a. y – 12 = –2(x + 7) b. y = –2x – 2 c. 2x + y = –2
19. x = 7 or x = –2
17
21a. y + 3 = – 8 (x – 4) b. y = – 8 x + c. 8x + 5y = 17
5
5
5
8
23. 25. no solutions 27. (5x + 7)(x – 1)
33
29. 128 31. a 2 + 2a – 8
TOPIC 7 CUMULATIVE REVIEW: ANSWERS
937
33. Jerome owed $1190 on the credit card that charged
16% interest and $630 on the credit card that charged
14% interest.
35a. y – 3 = 5 (x – 5) b. y = 5 x – 7
6
6
6x
xw
7x
3w + 14
4a. b. 5a. b. 7
7x
6
39.
y
y
1
2x
6
+5 4
4
2
2
x
–6 –4 –2
2 4 6
–2 4x – 3y 6
–4
41. (6b +
5) 2
125
2
4
6
–4
–6
43.
4x 3
+
7xy 2
+ 7 45. (–2, 5)
49. The width of the rectangle is 17 feet, and the length is
51 feet.
Lesson 8.1 Rational Expressions I
Homework
1. x = 14 or x = –2 3.
11.
x(x + 1)
x –1
17.
5
x–7
or
19.
x2 + x
x –1
7
15x
21x
5y
13.
21.
5.
8r 3
3
7.
15.
x4
x2 – 4
23.
1
3
3n
9n
3n p
9.
or
5
9a
x4
(x 2)(x – 2)
23.
25.
4a
2
b
27.
a b c
3m 2np
2bc
x
2q
x2
x (x – 3)
– 3x
or 2(x 7)
2x 14
29.
2b 9
5x – 1
5a
7b
7n
x1
4
3
2
x +5
39. 41. 43. 45. 47. x2
x–3
x3
x–2
xy z
n–1
x+5
x–1
5
n
1
=
–
1. x = –3 or x = 2 2.
938
n(n – 1)
= 1
n
1
The two fractions are 1 and .
4
x +6
7
Apply - Practice Problems
4800
1
1
1
1. 1 3. 5. 81 7. or 4–2 9. or 5–3 11. 8
81
16
3a.
125
89
1
1
b 28 19. a 4d 10 21. m 16
13. 15. 17. 4 6
24 12 4
12
8
20 12
a b
m n p
a
c
n p
4a 25b 5 25. 5.7 x 10–5 27. 4,300,000 29. –1
23. 6
c
x – 7 33. – x – 1 35. – x 1 37. x – 4
31. x–5
9x
7x
x1
5
9z
20
x3
3x (x – 1) 41. –2x (x 5) or 2x (x 5) 43. x 5
39. – Evaluate - Practice Test
x –7
x 6
y–2
n(n – 1)
1
1
49. 3 51. 53. 55. 3
2
8)
1
1
33. –
R1 R2
11 5n
3b 5
2b – 4
7x + 2
31. 33. 35. 37. 2b 1
9x y
11
2x y
y +8
13. –1 15. –x 17. 19.
8
x 1 9
2y – 1
x
2
z +3
21. 23. 25. (x + 5)(x + 5)(x –
(z – 4)(z + 5)
3z
R 1R 2
12
35. R = ;R= ohms
3a
yz
13. 15. 17. 19. 21. 4
3
2
2m
n2
z 10
9. 0.00000001 cm, 0.00000005
cm 11. 8 2
12
n(n – 1)
3w
y2
x –2
7a
s
n–1
=
x5
4b 3
4m 4
14
1. –5 3. 2, –2 5. 7. 9. 11. 3
5
2 2 2
2m 4
m n
n(n – 1)
Apply - Practice Problems
14m 7
x
5
x y
3y 2
7
y– 7
5x + 14y
4z – 3y
1
27. 29. 31. 2 3
2 2
47. 5x 2 + x 2y + 2xy + 25x – 15y
a
2
9b
x– 6
1
1
2
2t 13
1. or 3. 1000 5. 7. 3
3 3
9
–6 –4 –2
–2
–6
z– 8
Lesson 8.2 Rational Expressions II
Homework
y
6
13y
6y + 4
9y – 3
4
6. 7. 8. c. –5x + 6y = –7 or 5x – 6y = 7
37.
15y
b.
8x
2
z
x –5
5–x
x –2
x – 5 47. x 1 49. x 11 51. 3x
5x
45. 53. x3
x –7
3
x7
x –3
(x – 3)(x – 3) or x 2 – 6x 9 57. (x 3)(x 4)(x – 7)
55. 2
5x (x – 7)
5x – 35x
4b 6a 63. 2y x
59. x (x 4)(x – 1)(x – 1) 61. 9ab
3xy
2x – 5
2x x 4 69. 6x 8x – 3
65. 67. 2
(x 10)(x – 5)
2
(x 1)(x – 4)
(x – 3)(x 2)
Evaluate - Practice Test
1. –5 = x; The solution is not extraneous.
2. y = 3; The solution is not extraneous.
3V
3. = h 4. x = 4
2
πr
5. 4 = y; The solution is not extraneous.
2
4n – m 75. 3x – 2yz
2x – x – 29
71. 73. 2 2
2
(x 2)(x 3)(x – 5)
m n
6. x = 5; The solution is not extraneous.
x yz
S
7. – r = h 8. y = 2
–3x – 5
3x 2 – 2x 88 79.
77. (x – 8)(x 3)
2r
(x 5)(x 1)(x – 1)
3x 2
4x 10
81. 83. Lesson 8.4 Problem Solving
Homework
Evaluate - Practice Test
1. 16.8 hr 3. 357 jellybeans
1. 8 2. 7.3901, 10–5 , 208.1, and 0.00009019
105
5. hours (approximately 4.8 hours or 4 hours and
(x 2)(x 3)(x – 1)
x4
22
2(x – 1) 2
b 15
x3
x +3
3. 4. 5. –x – 2 6a. b. 6
8
2
a
7a. –3 b.
64y
x +2
y +4
(y + 6)(y + 1)
8.
x
46 minutes)
7. 4 inches by 12 inches
2(x – 1)
5(x – 3)
77
9. hours (approximately 4.3 hours or 4 hours and
18
17 minutes)
9. LCM = x(x + 5)(x – 5)(x + 7)
7b 17
y
3x
10. 11. 12. (b 1)(b 2)(b 3)
(y 4)(y 5)
11. 5778 fish
5(1 + 3x)
Apply - Practice Problems
Lesson 8.3 Equations With Fractions
Homework
20
1. hours or approximately 2 hours 13 minutes
9
1. x = 3 3. x = 6 or x = 1 5. x = 6 7. y = 3
2
9. 60.8 lbs. 11. x = 3 or x = –1
21
3. 45 minutes 5. hours or 5 hours and 15 minutes
4
7. 30 minutes 9. 24 caramels, 18 nougats
11. 35 puppies, 20 adult dogs 13. 65 units
12. x = 2; The solution is extraneous.
15. Jayme: 30 miles; Terry: 45 miles
Apply - Practice Problems
1. x = 7 3. x = 2 5. x = –9 7. x = –8 9. x = –3
17. Sasha: 2 miles; Leroy: 3 miles
11. x = 4 13. x = 2 15. x = 1 or x = – 4
19. Ranji: 45 miles, Paula: 30 miles
17. x = 2 or x = 3 19. x = 3 or x = –6
21. 68 miles per hour 23. 180 pounds
21. x = 5 or x = –1 23. x = 14 or x = –5
kT
25. 135 square inches 27. V = P
5
2
25. x = 4 or x = 8 27. no solution
LESSON 8.4: ANSWERS
939
Lesson 9.1n Below
Evaluate - Practice Test
1. It will take them
12
7
1
39a. 3 b. 1 c. or a –3b –6c –3
3 6 3
a b c
hours, or about 1 hour and 43
minutes, to wash the dishes working together.
41. radius: 5; center: (2, –6)
46
15a. y + 4 = – 6 (x – 11) b. y = – 6 x + 5
2. Trish lives 4 miles from the park.
5
5
15c. 6x + 5y = 46
3. There are 252 peanuts in the bag of mix.
16
17. 58 19. y = 7 or y = 3 21. 4. The area of the kite is 52 inches 2.
2
5. It will take them 36 minutes working together.
6. The hummingbird can fly at 50 km per hour, and the
eagle can fly at 85 km per hour.
7. The florist received 189 roses.
8. The speed of the wave is 8 feet per second.
Topic 8 Cumulative Review Problems
1. –2 ≤ x < 7 3. (a + b)(a – b) 5. 13 units
5
23. 5w 2x y – 6w 2x + y 25.
5
2
19
29. x = or x = – 2
4
33. x = –1 or x = – 3
3
20
27. x = 6 or x = – 16
47
7
31. 2x 3 –
239
x 2 + 7x
15
35. (5y – 3)(5y – 3) or (5y – 3) 2
37. 11 – 5 = 6
The GCF of 64 and 81 is 1.
If S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then 16 S .
39. 4a 8 – 25b 4
2 ± 3
41. x = 43. –4 ≤ y < 5
4
3
7. y = 3x + 11 9. x = –1
11.
m = – 9 , y-intercept =
5
13. t =
20
13
4 (0, )
x – 5x 6
1
Lesson 9.1 Roots and Radicals
Homework
3a
4c 2
3a 4 – 4c 5
23. –
or 25. A and B
3
3
3 3
a c
27.
43. (7x – 1)(7x – 1) or (7x – 1) 2 45. Any x is a solution.
47. y = – 2 x + 2 49. (x – 3)(x – 1)
19. no solution 21. 61 units
a
3
4x – 11
4x – 11
15. or 17. (x 2 + y 2 )(x + y)(x – y)
2
c
3
11
47. (x 2 + y)(x 2 – y) 49. x = or x = –2
hours ≈ 1 hour and 32 minutes
(x – 2)(x – 3)
45. x-intercept: 5 , 0 , y-intercept: 0, – 5
11
5
y
3
63
3
1a. 27
b. 27 c. 3 d. 3 3. –10 5. 7. 56
5
6
4
9. 38 cm 2 or approximately 119 cm 2 11. 7a 10b3b
2
–6 –4
–2
2
4
6
x
–2
3
13. 3 + 613
+ 3 15. 355
+ 85 17. 73
–4
–6
21. 100 square feet 23. x = 81
19. 910
110
x
29. m = 9 31. 6ab 2(a 2 – 4ab + 4) 33. 2
35. x = –9 37a. y – 6 =
c. – 4x + 3y = 26
940
4
(x + 2)
3
b. y =
x5
Apply - Practice Problems
26
4
x + 3
3
1. –5 3. 10.5 feet 5. 12 cm 7. 5 9. x 2 y x
11. 23 13. –1 + 5 15. 10 17. a 19. 6
3
3
3
3
Evaluate - Practice Test
67. 4x 2x
+ 2x
or (4x + 1)2x
69. 30 – 1445
1a. –1.1 b. 1.21 2. –4 and –3. 3. 7
71. 42y 5 126y
73. 20z – 1444
z2
4. 2u7u
5. 511
– 62 6. –41
75. 10
– 53 – 25 + 56 77. 45z – 6
3
3
1 – 7
6 ) 2
5(–
5x 2 10
2x
79. 50y – 3x 81. 83. x2 – 2
x
–1 + 7
7a. b.
2
–2 or
–6
8. x = –11
Evaluate - Practice Test
Lesson 9.2 Rational Exponents
Homework
64
1. x 10 2. 243 5 3. –12
5 4. 2
3
1. 8 = 2 3. 2
13
20
3
7
3
343x y
3
13
5. 6. 29 7.
15
5. 4 7. not a real number
3
2
9xy z
8. 11z
1
9. 1024 cells 11.
1
7
x
y5
3
13. 3 15. x 17. –3x 2y
5
– 3 10. –19 11. –6 – 122 12. y 6
9. 215x
Topic 9 Cumulative Review Problems
3
19. 2x 3y 2y
z2 21. 2m 23. 2x 2y 3z xy
1. x 3 + 3x 2y 2 + 36xy 2 + 13x 2 + 12x 3. y = 1 or y = –3
4
4
0 –11 4
36
25. 736
0, , 36
0
72
5. Investment at 5% = $1625
Investment at 13% = $12,500
4
3
3
27. –450 29. 163 + 1 2 + 1
4
3
1
3
, 23, 8 3, , 3 3 33. 2π
31. 24
3
3
3
3
27
11. 11 1 minutes
3
35.
98
7
9
13. point-slope form: y – 3 = 5 (x + 7)
Apply - Practice Problems
1.
95
or 9 ; 243 3.
5
3
27
2
or 27
; 9
3
2
5. 81
3 = 81
= 27 7. 6 9. –3 11. –6
4
13. 312
23.
3
4
4
5
16b 8
3
81a
15. 200
25.
5
7
17. y
64
27x 2y 3
11
12
19. x
11
30
21. x
24
3
standard form: 3y – 5x = 44
15. 2a 2b 2 + 5ab + a – b
21. (–4y + 3)(4y – 3) or –(4y – 3)2
5
3
2
4
x
3
23. True: The GCF of 52 and 100 is 4.
The LCM of 30 and 36 is 180.
3
4
75
3
55. 2m 24n
2 57. 5, 1 5, 59. –35
8
3
61. –23 63. 202 – 53
3
65. 6x 2x
2 – 132x
2 or (6x – 13)2x
2
(
25. (x + 13)(x – 10) 27. slope = – , y-intercept = 0, – 9
5
49. 6m 2n 43m
n 51. 4abc 33b
2 53. 2np 25m
2
n 2
p 2
3
44
+
2
27.
7
39. 56 41. –47 43. 45. 6ab 3 47. 8x 2y 3z 5
3
slope intercept form: y =
3
5
x
3
25
17a. b. –27a 6 c. x 24y 16z 4 19. x = 14
11
13
29. 31. 33. – 4 35. – 2 37. 3
8
7. x = –4 or x = –9 9. no solution
2
18x3
29. 31. –12 + 411
33. x 2 + 11x – 8
2
y
35. 7y 2 (x + 1)2 37. 1 ≤ y < 5
39a. 65 b. 6x + 3x 2 c. a 2 – b
41. 9 pins, 19 balls 43. x + y
TOPIC 9 CUMULATIVE REVIEW: ANSWERS
941
)
2. x = 0 or x = 4
4y 6
45. (2x – 1)(4x 2 + 2x +1) 47. a = 2 49. 9x 8
3. 2 = (x – 3)2, x (x + 9) = 4, and x 2 – 9 = 7x + 2
Lesson 10.1 Quadratic Equations I
Homework
6
25
64 5
4. x = – 5 or x = 3 5. (–
8)
2, 4 , and 1. 2x 2 – 3x – 5 = 0 3. y = 0, y = –4
10
6. x = 77 and x = –77 7. 2
5. –11x 2 = 0, 2a(a + 5) = 4, 6x – 9x 2 = 8 7. z = ± 5
and x = 5 – 241
8. x = 5 + 241
2
5
Lesson 10.2 Quadratic Equations II
Homework
9. The dimensions are 2m by 13m by 20m.
11. x = 1, x = – 5 13. a = ± 10 15. x = ± 6
3
4
21. The tree was approximately 34.6 feet tall 203 feet .
23. x =
169
13
1. x 2 + 13x + , x+
17. x = ± 9 19. x = 1 ± 53
9 ± 5
2
2
2
3. x = 2 ± 5 5. x = 18 ± 291
13
–3
7. x = ±
2
2
9. Seana’s speed before lunch was approximately 16.5 mph
and after lunch it was approximately 14.5 mph.
Apply - Practice Problems
1. x = –7 or x = 0 3. x = 4 or x = 0 5. x = –5 or x = 0
17
11. x = 5 ± 13. x = –5 15. x = –1, x = – 1
2
7. x = 6 or x = 0 9. x = 1 or x = 6 11. x = –5 or x = –7
5
15 ± 46
17. –4 ± 13
19. 6
2
6
21. The formulas yield the same child’s dosage at
approximately 1.2 and 9.8 years.
13. x = –3 or x = –6 15. x = –2 or x = 9
17. x = –10 or x = 15 19. x = 5 or x = –2
5 ± 97
23. 25. 3x 2 – 11x – 20 = 0
4
21. x = –12 or x = 10 23. x = –6 or x = 9
27. c = –15, x = –3, and x = 5 29. 18x 2 – 3x – 10 = 0
3
25. x = 6 or x = –5 27. x = –12 or x = 15
Apply - Practice Problems
29. x = –10 or x = 10 31. x = –16 or x = 16
1. x = –3 or x = 9 3. x = –5 or x = 9 5. x = –10 or x = 2
33. x = –43 or x = 43 35. x = –42 or x = 42
or x = –3 + 21
7. x = 1 or x = 7 9. x = –3 – 21
37. x = –9 or x = 9 39. x = –32 or x = 32
11. x = 3 or x = –7 13. x = 9 – 26 or x = 9 + 26
41. x = –23 or x = 23 43. x = –9 or x = 9
–3 ± 73
–7 ± 85
1 ± 57
15. x = 17. x = 19. x = 2
2
2
21. x = –7 or x = 3 23. x = –6 or x = 2
45. x = –12 or x = 2 47. x = –18 or x = 0
49. x = 3 – 13
or x = 3 + 13
51. x = –11 or x = 5
9
5 ± 10
25. x = –8 or x = 18 27. x = 6
53. x = – 9 or x = 5 55. x = 4 – 3 or x = 4 + 3
29. x = 1 or x = 1 31. x = 2 ± 3 33. x = 3 ± 5
Evaluate - Practice Test
–3 ± 89
–3 ± 41
35. x = 37. x = 1 ± 22 39. x = 10
2
5
1. 2x 2 – 17x – 2 = 0
So a = 2, b = –17, and c = –2.
942
5
4
1 ± 5
3 ± 37
41. x = 6 or x = 8 43. x = 45. x = 2
2
5
47. x =
9 ± 33
8
1a. 11 + 8i b. 3 – 4i 2. –8i 2 – 4i 3 3. 5 + 7i
8 – 14i
8
14
4. 2 + 26i 5. 34 6. or –
i
49. The equation has two unequal real solutions.
51. The equation has one real solution.
55. The equation has no real solutions.
2
2
7.
and
2. x = –1 ± 39
5.
y
6
4
4
5.
+ 4x – 7 = 0 6. x =
65
1. (3b + 5)(2x + 1) 3. 5xy 3 – 6x 2y + 14xy – 8
3. x 2 + 8x = –14 4. x = 1 or x = 1
2x 2
65
–i 3
Topic 10 Cumulative Review Problems
Evaluate - Practice Test
81
1. x 2 + 9x + ; x + 9
65
i 37
–3 ± i19
5 ± i11
–1 ± i2
8a. x = b. x = c. x = 2
2
3
53. The equation has one real solution.
4
Evaluate - Practice Test
2
–3 ± 14
5
–6 –4
–2
2
4
6
x
–2
7. x 2 + 4x + 11 = 0, x 2 – x + 1 = 0, and x 2 + 2x + 5 = 0
–4
7 ± 35
8. +36 and –36 9. x = 2
–6
10. 2x 2 – 3x + 6 = 0
7. x = 4 or x = –1 9. y = 2i or y = –2i
49
11. 5x 2 + 14x – 3 = 0 12. c = 11. –12 ≤ x ≤ 2 13a. 27 – 31i b. 40
8
Lesson 10.3 Complex Numbers
Homework
46
15a. y + 4 = – 6 (x – 11) b. y = – 6 x + 5
5
5
15c. 6x + 5y = 46
16
17. 58 19. y = 7 or y = 3 21. 1. –4i + 7; 6 + 1 – 4i; 7 – 3i – i
2
3a. 4i b. 5i c. 9i d. –20 e. 1 f. –i
23.
5a. 17 + 2i b. 3 + 7i c. 12 + 33i
15 136i
136
15
7a. 157 b. or +
i c. x = –2 ± 2i
97
97
97
–3 4i
3
9a. 34 + 8i b. or – + 4 i
5
5
5
–14 29i
29
14
11a. 37 – 50i b. or – + i
17
17
17
11c. x = –1 ± 2i2
5w 2x y
–
6w 2x
3
+ y 25.
5
2
19
29. x = or x = – 2
4
33. x = –1 or x = – 3
31.
20
27. x = 6 or x = – 16
47
2x 3
7
–
239
x 2 + 7x
15
35. (5y – 3)(5y – 3) or (5y – 3) 2
37. 11 – 5 = 6
The GCF of 64 and 81 is 1.
If S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then 16 S .
39. 4a 8 – 25b 4
2 ± 3
41. x = 43. –4 ≤ y < 5
4
3
Apply - Practice Problems
4 1. 13i 3. 4 – 5i 5. i 7. 1 9. –52 11. 19 – 3i
45. x-intercept: 5 , 0 , y-intercept: 0, – 5
13. 13 – 5i 15. 18 – 6i 17. –15 + 23i 19. 32 – 22i
11
47. (x 2 + y)(x 2 – y) 49. x = or x = –2
21. 73 23.
43
53
–
18
i
53
25.
7
25
–
26
i
25
3
3
27. x = –4 ± 2i
TOPIC 10 CUMULATIVE REVIEW: ANSWERS
943
b. domain: all real numbers; range: real numbers ≥ 0
Lesson 11.1 Functions
Homework
c. domain: all real numbers; range; all real numbers
1.
d. domain the interval (–∞, ∞); range: the interval [0, ∞)
x
–5
–4
–3
–2
–1
0
1
2
y
2
3
4
5
6
7
8
9
17a. domain: all real numbers; range: all real numbers
b. domain: the interval (–∞, ∞); range: the interval [5, ∞)
c. domain: all real numbers; range real numbers ≥ 0
19. a: y = |x + 1| + 4; b: y = |x + 1| – 1; c: y = |x + 1| – 3
21. domain: 0 ≤ x ≤ 4; range: 0 ≤ y ≤ 2
23.
y
6
4
3a. domain: all real numbers; range: all real numbers
2
y = –2x – 4
b. domain: all real numbers; range: all real numbers
–6 –4
y = –2x + 5
y = –2x + 1
–2
2
4
6
x
–2
y = –2x
c. domain: all real numbers; range: real numbers ≥ 0
–4
–6
d. domain: the interval (–∞, ∞);
range: the interval [1, ∞)
e. domain: all real numbers except 0;
range: all real numbers except 0
25. y = 4 – 2x + 6x 2; y = 8x 2 + 9x – 1
27a. domain: all real numbers; range: real numbers ≥ 3
b. domain: the interval (–∞, ∞) range: the interval [–5, ∞)
5a. –5 b. 11 c. 44 d. –1 e. 31
c. domain: all real numbers; range real numbers ≥ 0
7a. 9 b. 0 c. 1 d. –26 e. 2
d. domain: all real numbers; range real numbers ≥ 0
9a. 259,200 people b. 1,814,400 people
c. 94,608,000 people
29a. x-intercept: (0, 0); y-intercept: (0, 0)
b. x-intercepts: (–3, 0) and (–1, 0); y-intercept: (0, 3)
c. x-intercept: (–4, 0); y-intercept: (0, 16)
11a. domain: all real numbers except 3.
b. domain: all real numbers except –1 and –2.
c. domain: all real numbers ≥ –2;
range: all real numbers ≥ 0
1
2
1
2
33. domain: 0 ≤ time ≤ 6; range: 0 ≤ height ≤ 40
35.
y
c
6
4
d. domain: all real numbers except –4, 8, and 11.
e. domain: all real numbers greater than or equal to –2 and
less than or equal to 2; range: all real numbers greater
than or equal to 0 and less than or equal to 2.
944
1
2
31. a: y = x 2 + 5; b: y = x 2 + 1; c: y = x 2 – 4
2
y = x2
–6 –4
–2
–2
–4
a
2
4
6
x
b
–6
13. y = 2x + 1; y = 5 – 8x
37. graphs a, b, c, and e 39. Reservoir 1
15a. domain: all real numbers; range: all real numbers
41a. 0 b. 5 c. 3 d. 10 e. 2
Apply - Practice Problems
1
27. domain: all reals except x = – ; range: all reals except
2
3
y= 45 1
3. (1, 4), , 0, and (2, 10)
3
1. (1, 9), – , 0 , and (2, 13)
2
x
3
x
31. f ( x ) = 2x – 1; f ( x ) = 2
1
1
33a. y = – x – 3 b. y = – x + 1
3
3
29. f ( x ) = 3x + 5; f ( x ) = + 1
5. (1, –3), (–1, –9), (2, –3)
7. Tables may vary.
x y
0 –2
1 1
2 4
y
6
35a. y = |x + 2| – 3 b. y = |x + 2| + 4
4
2
–6 –4
–2
2
4
6
x
37.
y
–2
6
6
–4
4
4
–6
2
2
–6 –4
9. Tables may vary.
x y
0 –4
1 –2
2 0
39.
y
–2
y
6
4
2
4
6
–6 –4
x
–2
–2
–2
–4
–4
–6
–6
4
6
x
2
4
6
x
2
–6 –4
–2
2
4
6
41.
43.
y
x
–2
–4
y
6
6
4
4
2
2
–6
–6 –4
11. Tables may vary.
x y
0 4
1 3
2 0
2
–2
y
6
2
4
6
–6 –4
x
–2
–2
–2
–4
–4
–6
–6
4
2
–6 –4
–2
2
4
6
x
45. domain: all real numbers; range: all real numbers
–2
–4
–6
13a. 14 b. 5 c. 0 d. –1 e. 2
47. domain: the interval (–∞, ∞); range: the interval (–∞, ∞)
49. domain: the interval (–∞, ∞); range: the interval (–∞, ∞)
y
51.
15a. –2 b. –3 c. 0 d. 7 e. 18
17a. 2 b. 2 c. 0 d. 22 e. 23
19. domain: all real numbers; range: all real numbers ≥ –16
21. domain: the interval (–∞, ∞); range: the interval [9, ∞)
y
6
–6 –4
y = 2x + 1
53.
y = 2x
6
4
4
2
2
–2
2
4
6
x
–6 –4
–2
2
–2
–2
–4
–4
–6
–6
y=
y=
1
4
4
6
1
4
x
x–5
23. domain: the interval (–∞, ∞); range: the interval [2, ∞)
25. domain: all real numbers; range: all real numbers ≤ 3
LESSON 11.1: ANSWERS
945
x
55.
5a. y = 2x + 3 b. y = 2x – 4
y
6
y = |x – 2|
6. The domain of this function is all real numbers.
The range of this function is y ≥ 0.
4
2
–6 –4
–2
–2
7. The true statements are:
Both functions have the same domain.
the point (0, 3) satisfies both equations.
4
6
2
x
y = |x – 2| + 3
–4
–6
8. The only points that satisfy the equation y = x – 4 are
(5, 1), (2, –2), and (0, –4)
9. The graph crosses the x -axis at the points (–1, 0) and
(5, 0). These are the x -intercepts of the function.
57. y = x 2 – 5, y = –x 2, y = 9 – x 2
59. y = x 2 + 4; y = –5x 2 – 9; y = 3 – 2x – x 2
61a. up b. up c. down d. up e. down
63. domain: the interval (–∞, ∞); range: the interval [–6, ∞)
65. domain: all real numbers; range: real numbers ≥ 9
69a. y = (x + 2)2 – 2 b. y = (x + 2)2 + 4
y
6
4
–2
15a. This is the graph of a function.
b. This is the graph of a function.
2
4
6
x
c. This is not the graph of a function.
–2
–4
14. The true statements are:
The domain of y = 2|x – 1| + 4 is all real numbers
The range of y = 2|x – 1| + 4 is the interval [4, ∞).
For each input value x, there is only one output value, y.
y = x 2 – 3x + 4
2
–6 –4
11. The only functions that are not quadratic are y = 4x + 1
and f (x ) = –3x + 7.
12. (–2, 2) 13a. y = 0 b. y = –2 c. y = –4
67a. y = –x 2 + 5 b. y = –x 2 – 3
71.
10. The true statements are:
Both functions have the same domain.
Both graphs have the same x -intercepts.
y = –x 2 – 3x
d. This is the graph of a function.
–6
16a. the domain is all real numbers.
73. x-intercepts: (–5, 0) and (2, 0); y-intercept: (0, –10)
b. The range is all real numbers ≤ 9.
75. x-intercepts: (–5, 0) and (3, 0); y-intercept: (0, –15)
c. The vertex of the function is the point (–2, 9).
77a. true b. true c. false d. false
79. (3, –5) 81. (4, –1) 83. y =
x2
+ 4x + 6
Lesson 11.2 The Algebra of Functions
Homework
Evaluate - Practice Test
1. (f + g )(x ) = –x + 1 3. (f h)(x ) = 3x + 1
1. (0, 1), (–2, 13), (1, 4)
5. (f – g )(–3) = –14 7. (f g)(–1) = –35
2a. f (0) = 0 b. f (3) = 18 c. f (–2) = –2 d. f (–5) = 10
3. The domain of this function is all x .
The range of this function is y ≥ –2.
4a. f (7) = 23 b. g (7) = –20 c. f (–2) = –13 d. g (–2) = 7
946
961 + F
3
x
+
1
13. f –1(x ) = 6
gf 9. h[g (F )] = 11. (2) = –3
15.
Apply - Practice Problems
2–x
3
y
y = 2 – 3x
f –1(x ) = 6
1. ( g + h)(x ) = x 2 – 4x + 5 3. (f + g)(x ) = 2x 2 – 3x + 7
4
y=
2
2–x
3
–6 –4
–2
4
2
6
5. ( g – h)(x ) = –2x 2 – 2x + 10 7. (f g)(x ) = 40x 2 + 90x
x
–2
9. ( g h)(x ) = 4x 3 + 7x 2 – 20x – 35 11. ( g h)(0) = 0
–4
gf –6
y
17.
6
x–3
4x – 5
21. (f h)(x) = x 2 – 3x + 2 23. (g h)(3) = –3
2
–2
y = x2 – 3
gf 17. (g h)(x) = 6x – 5 19. (f g)(x) =x 2 + 4x + 4
The function is not
one-to-one
4
–6 –4
2x
x+4
13. (x ) = 15. (x ) = 2
2
4
6
25. (g h)(4) – (h g)(4) = 8
x
–2
x
2
x–7
4
27. f (x) = 2x and g(x) = ; f (x) = 4x + 7 and g(x) = –4
–6
x+1
4
1
x–2
2
x–1
10,000 – x
x – 10,000
21. f –1(x ) = or f –1(x ) = – 20
20
3
23. g has an inverse; g –1(x ) = x+1
29. f –1(x) = x – 8 31. f –1(x) = 33. f –1(x) = 25.
39. The function is not one-to-one.
19. g –1(x ) = x
5
11
20
r (x )
20
44
80
c(x )
600
720
900
37. The function is one-to-one.
r (x )
–580
–676
–820
y
27.
2
3(x – 1)
35. f –1(x) = 29.
41. The function is one-to-one. 43. (f –1 f )(x) = x
45. x y = f –1(x)
–4 –1
–3
0
5
2
y = ( f + g)(x) = x 2 + 2x + 1
y
6
4
6
y = |2x 2 – 2 |
4
2
2
–6 –4
–2
2
–2
–4
–6
4
6
x
–6 –4
–2
2
–2
–4
–6
4
6
x
47. x y = f –1(x)
1 –2
2
1
3
6
49. x y = f –1(x)
–3 –3
–1
0
1
3
LESSON 11.2: ANSWERS
947
51.
55.
y
–6 –4
6
6
4
4
2
2
–2
2
4
6
x
Topic 11 Cumulative Review Problems
y
–6 –4
–2
2
–2
–2
–4
–4
–6
–6
4
3
2x – 12
2
5. f –1(x) = or f –1(x) = + 2
x–7
x–7
15i
8
1. 3. x = or x = 1
4
6
x
7. 6 9. 93 + 272 11. (f + g)(x) = –5x + 6
51
8
55. x-intercept: (12, 0); y-intercept: (0, –4)
13. – 15. 2 + 9i and 2 – 9i; 7 + 3i and –3i + 7
Evaluate - Practice Test
17. x = or x = –1
1. (f – h)(–3) = –42
19. x-intercept is (2, 0); y-intercept is (0, –4)
gf 2. (x) – (f g)(x) = 2x – 18x 7 or 2x(1 – 9x 6)
3. The only pair of functions for which (f g)(x) = x is:
f (x ) = 2x
x
g(x ) = 2
4. (f g)(4) = 113
5. Here is the completed table of some of the ordered pairs
that satisfy f –1(x):
f –1(x)
x y
–5 –2
–1 0
3 2
5x – 9
2
6. h –1(x) = 7. (f g)(x) = x
8. (b), (c), and (d)
9. (f g)(5) = 33
10. (f – g)(2) = –9
11. (f g)(2) = –3
12. If f (x ) = 2x + 8, the statements that are true are:
f –1[f (x )] = x
(f f )(x) = 4x + 24
(f f )(x) = (2x + 8)2
948
7
3
x–4
7
21. –54 23. 77/3 25. f –1(x) = 27. No, f does not have an inverse.
–3 ± 35
2
3
2
29. x = – 1 ± 5 or x = 5
2
31. x = 1 or x = – 3
2
33a. x-intercepts – , 0 and (3, 0); y-intercept: (0, –9)
19 b. x-intercepts: (0, 0) and , 0 ; y-intercept: (0, 0)
c. x-intercepts: (2, 0) and (–2, 0); y-intercept: (0, 4)
a 7/2
b
35. or a 7/2b –3 37. (f –1 f )(x) = x 39. a = ±8
3
41a. domain: all real numbers; range: all real numbers
b. domain: all real numbers; range: real numbers ≥ 6
c. domain: all real numbers; range: real numbers ≥ 0
3
4
i 31
4
3 ± i 31
4
43. x = ± or x = 45a. –4 b. –2 c. 4 d. 14 e. –2
7
5
11
5
47. x = or x = – 49. 2313
+ 447
–6
Lesson 12.1 Exponential Functions
Homework
Evaluate - Practice Test
1.
2. Here is the completed table:
x
y
3 8
x
y
2 4
2
1
4
1
1
2
0
1
2
–1
2
4
1
8
–1.5 2.8284
0 1
–1 1
–2 1
–2
3. 0.07
5.
y = f(x)
6
4. e 3 ≈ 20.09, e –1 ≈ 0.37 5. approximately $206.06
4
2
–2
4
3. The only statement that is true is the fourth one. The
function f is one-to-one.
y
y = g(x)
–6 –4
1.5 0.3536
1 2
–3
1
4
1. (1, 2), (0, 1), and –2, 2
4
6
1
8
1
2
6. N0 7. x = 1 8. x = – x
–2
Lesson 12.2 Logs and Their Properties
Homework
–4
–6
1
64
7. The base is 10.
1. log1010000 = 4 3. y = 7x 5. log2 = –6
9. Approximately 82 bacteria will be present after 2 days.
7. log7y = 12
11. The base is 8.
9.
t
6
4
Apply - Practice Problems
2
(1.07, 1)
1. (0, 1), (–1, 4) 3. (0, 1) and (–1, 1.5) 5. e 1.2 ≈ 3.32
1
4
21 1
3
–6 –4
2
4
6
A
–2
3
2
11. f (2) = 13. f = 2 15. b = 17. x = 1
2
19. x = – 21. t = – 23. x = 1 25. x = 2
3
2
1
27. b = 7
–2
–4
–6
11. log 1 16 = –2 13. y 15. log131214
4
17. log23ab – log27cd 19. 1 21. R = log10I – log10 M
1
x
23. logx = –1
25a. is log3x b. is log7x c. is log15x
LESSON 12.2: ANSWERS
949
27. Answers will vary. One answer is shown for each.
P
I
11
7. logw 8. logb17 + 5logbx – 12logb y
xy
4. loge = kt 5. xyz 6. log2919 + log29A + log29B
a. log464 = log432 + log42
b. log464 = log4128 – log42
9.
c. log464 = 2 log48
y
3
y = log b x
2
29. Both graphs include the point (1, 0).
1
(1, 0)
–3
Apply - Practice Problems
–2
–1
y = log a x
1
2
3
x
–1
–2
1. log28 = 3 3. log5625 = 4 5. log3a = x 7. 6 9. 4
–3
11. –3 13. f –1(x) = 12x 15. f –1(x) = 11x 17. f –1(x) = b x
10. Graph c; Graph b 11. This statement is true. 12. 15.6
19. 53 = 125 21. 8x = 512 23. 65 = x
25.
27.
y
–6 –4
6
4
4
2
2
–2
4
2
6
x
Lesson 12.3 Aplication of Logs
Homework
y
6
–6 –4
–2
1. 4 3. log 2x 3 5. 3.43 7. 0.0003
2
–2
–2
–4
–4
–6
–6
29. 4log233 31. log32517 33. logb7x – logb8y
35. log35 + log3x 37. logb21 + logb x + logb y
4
6
x
9. log[2x 3(x + 1)2(x + 2)2 104] 11. 3.731 13. x = 64
15. x = 5 17. x = 1 19. x = 49 21. t ≈ 0.17
23. x ≈ 1.11
Apply - Practice Problems
1. 1 3. –3 5. 7 7. log x 8 9. 5log x 13 or log x 65
a3b5
1
43. log7 45. logx c
2
39. logb12 41. log5 2x6
x5
4x – 1
11. ln (2x 8 + 3x 7) 13. ln 15. 1.39 17. 4.50
47. 1 49. –3 51. –2 53. log5z – 4log5 y
19. 4.01 21. 1.62 23. 133.35 25. 23.71 27. 0.29
55. log3x – log32 – log3 y
29. x = 16 31. x = 243 33. x = 5 35. x = 64
Evaluate - Practice Test
37. x = 6 39. x = 2 41. x = 3 43. x = 3 45. x = 7
1. log18 yz = 12x 2. –3
47. x = 8 49. x = ≈ 1.83
3.
51. x = 2 + ≈ 4.81
y
y=5
ln 19
ln 5
ln 22
ln 3
x
6
ln 6
ln 7
y = log 5 x
2
–6 –4
–2
2
–2
y=x
–4
–6
ln 5 + 1
4
53. x = + 3 ≈ 3.92 55. x = ≈ 0.65
4
4
6
x
Evaluate - Practice Test
1a. ≈ 2.05 b. ≈ 2.19 2. log[10x (x – 2)2]
3. ln 1 = 0; loge 5 = ln 5; 2log x = log x + log x
950
1
9
3
2
21. y = log3 x
4. ≈ 2.12 5. x = 6 6a. x = b. x = y
y = 3x
6
7. x = 13 8. ≈ 1.73
4
y = log 3 x
2
–2
–6 –4
Topic 12 Cumulative Review Problems
4
2
6
x
–2
–4
26 + 57i
2
1. t = – 3. 11
157
–6
1
2
5a. 6log74 b. –3log2x c. x d. log510 e. log1031
7a. y = –2x 2 + 6 b. y = –2x 2 + 3 c. y = –2x 2 – 1
3
23. Yes. y = f –1(x) = x
y
12
9a. 1 b. 0 c. 14
y = x3
8
4
3
11. y = x – 1
4
–12 –8
–4
3
y= x
4
8
12
x
–4
y
–8
6
–12
4
2
–6 –4
–2
2
4
6
x
–2
–4
–6
9
ln 4 + 6
2
25. y = 1 or y = 27. x = or x = 2.27
3
5
29. A = $515.17 31a. 9i b. 5 c. 45i d. –45 e. –i f. –1
13. 613
– 441
+4
33. q = –1 or q = 15a. domain: all real numbers; range: real numbers ≥ –2
35. As x becomes smaller and smaller, y approaches 1.
b. domain: all real numbers; range: all real numbers
1
c. domain: real numbers ≠ or –7; range: all real
2
numbers
d. domain: real numbers ≥ 2 or ≤ –2;
range: real numbers ≥ 0
17. 2 lnx – ln(x + 2) 19. x = 9 or x = –9
7
2
x
y
0
2
y
6
4
–1
1
1
4
–2
1
2
2
8
–3
1
4
2
–6 –4
–2
2
4
6
x
–2
–4
–6
x + 18
33
37. (2x + y )(x – 3) 39. d = –20 41. f –1(x) = TOPIC 12 CUMULATIVE REVIEW: ANSWERS
951
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