■ Lesson 1.1
1. Add 4 to the preceding number; 18, 22, 26
2. Subtract 11 from the preceding number; 55, 44,
33
3. Divide the preceding number by 5; 25, 5, 1
4. Multiply the preceding number by 5; 1250,
6250, 31250
5. Multiply the preceding fraction by 2;
32 64 128
3, 3, 3
6. Add 32 to the preceding number; 9, 21
2 , 12
7. Add 1 to each preceding numerator and
6 7 8
denominator: 5 , 6 , 7
8. Multiply each preceding number by n 1 2
starting with n 5 0; 600, 3600,
25200
9. The pattern is every fourth letter of the
alphabet; P, T, X
19. The numbers represent the speed in miles per
hour that you are traveling. The larger the
number, the faster you are traveling. Therefore,
you and your family will arrive at the beach
much sooner than your friend and her family,
since your family was traveling 320 mph faster
20. The numbers represent the points scored for a
particular team. Because Dallas scored more
than Buffalo, Dallas won the game.
■ Lesson 1.2
1. The quotient of 21 and 3 is 7.
2. The sum of 14 and 5 is 19.
3. The product of 42 and 3 is 126.
4. The difference of 133 and 17 is 116.
5. 178
6. 56
9. 94.4
7. 995
10. 0.245
10. The pattern is every third letter of the alphabet;
L, O, R
13.
11. The pattern is every other letter of the alphabet
starting with Z and working in reverse; T, R, P
17. 112
18. 56
21. 2.5
22. 14.4
7
8
7
15
14.
6
8
5
3
4
16.
20. 6
23. 14,074
26. 1445
13. 60, 54, 48, 42, 36, 30
30. 10 2 4 5 6
14. 2, 4, 6, 10, 16, 26
32. 5 1 10 1 5 5 20
15.
34. 6,174,100
56
12. 5.71
1
7
19. 352.6
25. 114.375
28.
11. 4.07
15.
12. The pattern is every other letter starting with B;
J, L, N
42
7
8. 42.6
24. 80.25
27. 145
29. 3 1 3 1 3 5 9
31. 18 2 12 5 6
33. 239,500
35. \$761,800
1. 3 raised to the 4th power is 81.
2. The square root of 1.69 is 1.3.
16.
3. 10.52; 110.25
4. 75; 16,807
5. 1.23; 1.728
7.
17. The larger the number, the warmer the temperature. The smaller the number, the colder the
temperature with 328F representing the freezing temperature of water. Therefore it was 708
warmer in Tempe than in Duluth.
18. The larger the number, the better the score with
a score of 100 being a perfect score. So, your
score is better than your friendÕs by 2 points.
118
64
s 25 d6; 15,625
9. 25
13. 2.74
6. 8.24; 4521.2176
8.
1
s 19 d4; 6561
10. 26
14. 2.06
17. 5.8
18. 3.5
21. 5
22. >
11. 15.6
15. 9
19. 144
23. <
12. 24.41
16. 5
20. 729
24. >
25. The perimeter of the kitchen is 80 ft. The
perimeter of the bathroom is 32 ft. The area of
the living room is 784 sq ft. The total area is
1248 sq ft.
Passport to Algebra and Geometry
■ Lesson 1.3
26. a. 512 cubic inches
b. 384 square inches
c. Yes, if neither the length, width, nor height
of the “smaller box” is greater than 8 in.
11. No, the graph only shows the average monthly
snowfall is very small, perhaps not measureable. But it does not state that it never snows
during those months.
■ Lesson 1.4
■ Lesson 1.7
1. 7
2. 15
3. 28
4. 0
7. 6
8. 6
9. 120
6. 41
11. 1
12. 30
15. 42.25
13. 57
16. 57
20. 192
10. 16
14. 17
17. 4
21. 34
5. 8
18. 8
22. 129
19. 42
23. True
3. Hexagon
2. Decagon
4. Octagon
5. It is not a polygon because not all its sides are
straight.
6. It is a pentagon.
7. It is not a polygon because it has one more side
than number of vertices.
24. False, s18 2 6d 4 2 5 6
25. False, 6 ? s3 2 2d ? 3 5 18
8. It is an octagon.
26. False, s24 2 3d 4 7 1 2 5 5
27. False, s5 1 22d 4 3 5 3
28. True
29. False, 24 4 s4 1 2d 2 22 5 0
30. True
31. 36 4 s9 1 3d 5 3
32. 6 1 s42 4 21d 5 8
33. 42 4 s14 4 2d 5 6
34. 12 2 s4
11. An equilateral octagon
? 2d 5 4
35. Total cost 5 4s5.25d 1 4s1.25d 1 4s1.15d 1
3.75 1 3.00 The total cost is \$37.35. The
amount of money remaining is \$2.65.
For Exercises 12–18, see the following table.
■ Lesson 1.5
1. 4
2. 21
3. 6
4. 16
5. 14
6. 48
7. 4
8. 0
9. 16
10. 25
Type of
Polygon
No. of
Sides
No. of
Vertices
Total No.
Diagonals
11. 4
12. 25
13. 3
14. 20
15. 16
12. Triangle
3
3
0
16. 19
17. 49
18. 64
19. 54
20. 55
13. Octagon
8
8
20
21. 23
22. 5
23. 3
24. 9
14. Nonagon
9
9
27
26. 13
27. 9
28. 49
4
4
2
16. Hexagon
6
6
9
35. a. 8a 1 6c; b. \$112.00
17. Pentagon
5
5
5
36. a. 5 miles; b. 150 minutes
18. Decagon
10
10
35
31. a
32. b
33. 2
29. c
25. 3
30. d
34. 3
37. a. 255 yds; b. 765 ft; c. 114,750 sq ft
19. Yes
20. No, no vertices, no straight edges
■ Lesson 1.6
21. Yes
22. No, curved edges.
1. Pocahontas
2. \$75.7 million
3. \$333.2 million
4. University of Iowa
5. Yes, five more.
6. Yes, Iowa has dominated.
8. March
9. < 10.8 in.
■ Lesson 1.8
1.
n
0
1
2
3
4
5
6
55n
0
55
110
165
220
275
330
10. < 49.8 in.
Passport to Algebra and Geometry
720
n
3. 3x 1 3
1
2
3
4
5
6
720
360
240
180
144
120
n
4. 20x 1 10
x
x
1
1
3.
1
n
1
2
3
4
5
6
7
8
9
n
5
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
5. 6 1 10 or 16
7. 3x 1 6
4.
x
x
x
6. 48 1 84 or 132
8. 15y 1 60
10. 16 1 8p
9. 4z 1 12
11. xy 1 3x
12. ac 1 4a
n
1
2
3
4
5
6
7
8
9
13. 2x 1 2y 1 2z
14. az 1 4z 1 bz
4
n
4.0
2.0
1.3
1.0
0.8
0.6
0.571428
0.5
0.4
15. fg 1 3f 1 fh
16. 20 1 10y 1 10z
17. 30.8
5.
n
1
2
3
4
5
6
7
n 1 1
n
2
1.5
1.3
1.25
1.2
1.16
1.142857
18. 159.12
19. 20,251.5
Total summer
earnings
20. a.
1
5 16
6.
Weekly
earnings
job 1
Weekly
1 earnings
job 2
n
0
1
2
3
4
nsn 1 1d
2
b. \$1256 5 16s56 1 22.50d
0
1
3
6
10
monthly payment
21. a. Total 5 12
for bike
7. 6, 12, 18, 24, 30, 36, 42. Possible explanation:
The sequence is the product of the first 7
natural numbers and 6, 6n.
8. 102, 204, 306, 408, 510, 612, 714. Possible
explanation: The three digit numbers can be
determined by combining the first term as the
first digit and twice the first term as the second
and third digits.
9. 2 1 9 5 5 5 , 38, 47, 56, 65
1
monthly payment
for CD player
monthly payment
1 for in-line skates
■ Lesson 2.2
1. 4x
3. 8z 1 10
2. 9y
4. 9a 1 5b
5. 9z 1 9
7. 11s 1 2t 1 4
6. 21z 1 5
8. 12x 1 9y 1 4
11. 6 3 5 5 5 5 , 3750, 18750, 93750,
468750
12. 2x3 1 2x2
13. 9y 1 6
15. 10st 1 12
16. 3x 1 7z 1 8
12. 6144 4 4 5 5 5 , 24, 6, 1.5, 0.375
17. 4x 1 3y 1 26
13. 2500
19. 9x 1 2y, 35
16. 25,010,001
■ Lesson 2.1
1. 2 units by x 1 3 units, 2sx 1 3d, 2x 1 6
2. 3 units by 2x 1 4 units, 3s2x 1 4d, 6x 1 12
2
b. \$783.00 5 12s26.50 1 21.25 1 17.50d
9. 10x 1 11
15. 63,001
2
1
10. 4 3 3 5 5 5 , 324, 972, 2916, 8748
14. 250,000
1 1
1
1
1
1
1
1
10. 2a2 1 10a
11. 6z2 1 7z
14. 10z 1 16
18. 4ab 1 2a 1 4
20. 3y 1 4, 16
21. 7x 1 5y, 41
22. x2 1 xy 1 3y, 33
23. 2x2 1 xy, 30
24. 5x 1 5y, 35
25. Perimeter 5 8x
x
1
2
3
4
5
Perimeter
8
16
24
32
40
The perimeter increases by 8 each time x
increases by 1.
120
Passport to Algebra and Geometry
2.
26. Perimeter 5 12x
5. 23
6. 54
10. 14.9
x
1
2
3
4
5
9. 77
Perimeter
12
24
36
48
60
13. 4.49
The perimeter increases by 12 each time x
increases by 1.
d. 3sa 1 1d 1 5sb 1 2d 5 3a 1 5b 1 13
■ Lesson 2.3
2. c
3. d
20. x 2 7 5 28; 35
3. 5
26. 19,251
11. Yes
12. No, x 5 4
13. Yes, 4 5 4
14. No, 4 Þ 20
15. 5
16. 13
18. 51
20. Identity; true for all values of x.
21. 6.4 million
22. 5.4 million
23. 6.3 million
■ Lesson 2.4
x 1 21 5 65
x 1 21 2 21 5 65 2 21
x 5 44
58 5 y 2 32
58 1 32 5 y 2 32 1 32
90 5 y
z 2 28 5 101
z 2 28 1 28 5 101 1 28
z 5 129
312 5 w 1 217
312 2 217 5 w 1 217 2 217
95 5 w
Passport to Algebra and Geometry
5. 9
9. 21
9. No, x 5 4
10. Yes
25. 1553 yds
4. 10
8. 20
26. 1411 yds
6. 5
10. 60
14. 33.75
17. 51.2
18. 48
22. 6
23. 5748
15. 15.6
19. 4
20. 3
21. 9
25. 3857
28. 6
Yards per
carry
Total
12. 2.6
16. 45
24. 4840
27. 4
33. a. yards 5
7. 72
11. 22
31. 5m 5 45, 9
30. 14
29. 17
32. 8c 5 56, 7
?
Number of
carries
b. x 5 s4.368ds3838d; x 5 16,764.384 yards
(NOTE: Actual total yards 16,726.)
19. Conditional equation; true for x 5 12.
21. y 1 2.7 5 8.3; 5.6
1. The product of 5 and a number is 10; x 5 2.
13. 45
4.
19. 5418.08
■ Lesson 2.5
6. 5 subtracted from what number is 3?; 8
x
7. 5 1 x 5 19; 14
8. 5 7; 56
8
3.
16. 10.229
2. The quotient of a number and 2 is 11; z 5 22.
4. a
5. What number can be multiplied by 3 to obtain
36?; 12
2.
15. 522.35
18. 97.02
24. 1538 yds
c. 3x 1 5y
1.
12. 8.7
23. a 2 5.01 5 22.7; 27.71
b. 2x 1 3y
17. 24
11. 3.44
14. 62
17. 10.93
8. 618
22. z 1 3.1 5 15.2; 12.1
27. a. x 1 2y
1. b
7. 66
■ Lesson 2.6
1. a
2. c
3. b
4. d
5. 16 1 n
n
n
6.
7.
8. 8n
9. n 2 12
12
11
10. 6n 1 14
13. 6sn 1 4d
11. 8 2 5n
n
14.
m14
16. a 1 5
17. a 1 5
20. a 2 6
21.
12. 3n 1 17
15. 3n 2 6m
18.
a 1
or a
3 3
n
4
19. 5c
22. 4a
23. a 1 14
24. a. C 5 38.70 1 5.75m;
b. \$211.20
■ Lesson 2.7
1. d
2. b
3. a
5. n 2 5 5 13, 18
7.
b
5 9, 63
7
4. c
6. 225.75 5 3x, 75.25
8. 32 5 18 1 y, 14
12. 5 days per week 3 2 trips per day 3 16 miles
per trip 5 160 miles per week
9. The difference of a and 6 is 13.
10. 45 is the product of 5 and c.
13. 3 miles per day 3 7 days per week 3 21 miles
per week
11. The quotient of e and 5 is 40.
12. 15 is 3 more than f.
■ Lesson 2.9
Number
13. Verbal Model:
6
5 21
Missing number 5 x
Labels:
Algebraic Model:
14. Verbal Model:
x
5 21
6
x 5 126
8. y ≥ 12
7. x < 5
5 Number 3 11
165
Labels:
Missing number 5 x
Algebraic Model:
165 5 x ? 11
9. z < 5
10. a > 22
11. b < 10
13. p < 15
14. q > 48.8
17. 110.5 ≥ y
16. 294 > c
22. 69 > 3a, 23 > a
23. The difference of e and 4 is greater than 6.
Cost of item
5
Total
cost
24. The sum of 5 and f is less than or equal to 10.
Labels:
Cost of items for you 5 2.50 1 6.50 1 13.50
25. 28 is less than the product of 7 and r.
Cost of item for your sister 5 x
27. No
Algebraic Model:
2.50 1 6.50 1 13.50 1 x 5 39.00
31. first five
Length
1 Width
25
33. x ≥ 92
Perimeter
4. w 5 22
5. Width is 22 ft and length is 70 feet.
7.
34. Yes, any test score greater than or equal to 92
would guarantee a point total greater than or
equal to 540.
1.
−3
−1
?
Monthly
sales
5
Sales
commission
3. <
Monthly sales 5 2600
13. 10, 10
Sales commission 5 x
16. 257
122
? 2600 5 x
10. x 5 104
11. \$404
0
4. <
9. 23, 3
1
8. Sales commission rate 5 25 ;
1
25
−2
−1
0
1
2.
? 5 5 \$920
Sales commission
rate
Point total for
course to
earn an A
≥
1 sixth exam
■ Lesson 3.1
? sw 1 48 1 wd 5 184
6. 184
Scores on
30. No
32. 85 1 92 1 88 1 96 1 87 1 x ≥ 540
2. Width 5 w
Length 5 w 1 48
Perimeter 5 184
3. 2
29 No
1
5. >
10. 2, 2
2
3
6. >
19. 26, 24, 2, 3, 5
5
7. <
11. 25, 5
14. 100, 100
17. 15
4
8. >
12. 6, 6
15. 700
18. 20
20. 210, 27, 0, 6, 8
Passport to Algebra and Geometry
?1
28. Yes
exams
■ Lesson 2.8
1. 2
26. The product of 17 and r is less than 102.
Scores on
x 5 16.50
9.
18. 2.8 < z
19. d 2 5 ≤ 4.25, d ≤ 9.25
21. 40x < 120, x < 3
15. Verbal Model:
1
15. x < 9.7
20. y 1 7 > 10, y > 3
15 5 x
Cost of items
for you
12. 27 > c
21. 23, 22, 1, 2, 4
23. 3 days
22. 23, 21, 0, 1, 2
24. 9 days
25. 7 days
26. 3 days
27.
Tampa
San Diego
−20 −10 0 10 20 30 40 50 60 70
29. 658
2. 26 1 s23d 5 29
1. 3 1 12 5 15
3. 212 1 s212d 5 224
6. 12 1 s218d 5 26
5. 25 1 5 5 0
8. 26 1 s226d 5 0
7. 219 1 12 5 27
9. 4 1 0 5 4
4. 6 1 16 5 22
10. 0 1 s211d 5 211
11. 15 1 s22d 5 13
12. 212 1 0 5 212
25. 5x 1 11, 26
26. >
27. >
28. <
31. >
32. \$5yshare
3. 6 2 s28d 5 14
19. x 5 29
20. z 5 2
7. 14 2 s23d 5 17
8. 16 2 s216d 5 32
9. 216 2 16 5 232
23. a, x 5 70, \$70 in the account
27. a, c
17. 10x 1 s212d 1 s25d; 10x, 212, 25
18. 26x 2 7
19. 9m 1 2
21. 258x
25. 209
30. Asia
North America
Africa
Europe
30,340 ft
20,602 ft
19,852 ft
18,602 ft
32. 830 ft
2. 8s10d 5 80
4. 215 ? 3 5 245
5. 10 ? s23d 5 230
4. 216 1 15 1 s23d 5 24
7. s23ds27d 5 21
5. 210 1 11 1 s22d 5 21
9. s4ds0d 5 0
6. 210 1 6 1 s28d 5 212
12. 11w
13. 212
8. 6 1 s25d 1 s24d 5 23
16. 212
17. 60
9. 10 1 s22d 1 13 5 21
20. 30
13. 247
24. 3978
6. 7
21. 36
25. 240
? s24d 5 228
8. s0ds230d 5 0
11. 210a
10. 8y
7. 210 1 s26d 1 s215d 5 231
Passport to Algebra and Geometry
27. 26
26. 6
3. 23 ? s22d 5 6
3. 6 1 s27d 1 s28d 5 29
12. 2342
20. 29y 2 3
23. 6 2 m or 2m 1 6
22. 12z
1. 6 ? 5 5 30
2. 26 1 s22d 1 10 5 2
11. 155
14. 0, 0
■ Lesson 3.5
1. 6 1 s22d 1 s28d 5 24
10. 265
13. 4, 8
16. 4x 1 s22xd 1 8; 4x, 22x, 8
31. 21030 ft
■ Lesson 3.3
10. 21, 25
12. 0, 24
22. b, x 5 270, 70 feet below sea level
4. 10 2 s22d 5 12
6. 12 2 s28d 5 20
24. 24
21. m 5 13
33. 50th floor
5. 223 2 2 5 225
15. 4, 24
30. <
2. 24 2 s23d 5 21
1. 3 2 7 5 24
14. 0, 21, 22, 23, 24
The numbers decrease by 1.
29. <
■ Lesson 3.4
11. 1, 5
23. 6x 1 8, 26
22. x, 3
24. 19x 1 4, 61
13. 2, 3, 4, 5, 6 The numbers increase by 1.
15. 24, 22, 0, 2, 4 The numbers increase by 2.
18. 2x, 6
20. 5x 1 7, 22
21. 8x 1 6, 30
°F
■ Lesson 3.2
26. b, c
17. 11x 1 4, 37
19. 9x 1 10, 37
St. Paul
| |
|
15. Positive, |115| > |238 1 s242d|
16. 2x, 6
Anchorage
28. 708
|
14. Negative, 2321 > 215 1 43
14. 236
15. 4
18. 230
22. 351
19. 24
23. 24242
26. 299
27. 1806
28. 29
29. 25
30. 210
32. 212
33. 5
36. 216
37. 418F, 148F
34. 28
31. 3
35. 24
21. \$10,000
■ Lesson 4.1
3. 232
2. 45
5. 218
20. \$17,500
22. V 5 25000 2 2500t
■ Lesson 3.6
1. 32
19. 12 2 2 5 10; Answers vary.
6. 0
7. 0
1. 9
4. 26
9. 242
8. 48
6. 225
2. 3
3. 21
7. 36
8. 2
9. 3
10.
10. 218, 217, 216, 215, 214
The numbers increase by 1.
5. 215
4. 8
=
11. 2, 3, 4, 5, 6; The numbers increase by 1.
13. 4
16. 20
17. 218
20. 230
15. 216
14. 6
18. 222
=
19. 230
22. 26
21. 15
=
23. 55.576 seconds
24. Less than result in Exercise 23. If trend of
faster times continues, then the average of the
next six Olympic games will be faster.
12. 6x 1 11 5 65; 9
11. 2x 1 3 5 13; 5
x
x
13. 1 2 5 27; 227
14. 2 6 5 1; 28
3
4
15. 2x 1 17 5 43; 13
16. 4x 1 34 5 94; 15
■ Lesson 3.7
1. Yes
2. No, y 5 24
3. Yes
4. No, m 5 248
6. 23
5. 3
9. 210
10. 28
13. 33
8. 29
7. 17
11. 23
15. 23
14. 2
12. 16
16. 216
17. x 1 3 5 26, x 5 29
The sum of 29 and 3 is 26.
20. 4080
22. 21334
23. 2528
■ Lesson 4.2
24. 253
26. a
27. b
29. f
30. e
31. 72 5 32t
1. No; x 5 2
28. d
32. t 5 2.25 hours (2 hours 15 minutes)
■ Lesson 3.8
1. S, 3
2. Q, 1
5. U, 2
6. T, 3
10. 2
11. 2
15. 3 units2; 8 units
3. R, 4
4. P, 2
4. Yes
5. 24
8. 11
9. 213
12. 13
13. 26
2. No; y 5 22
6. 12
10. 2
3. Yes
7. 216
11. 29
14. 2x 1 5x 1 s23xd 1 s23d 5 9; 3
8. 1
9. 3
15. 7y 1 2y 2 11 5 238; 23
13. 3
14. 4
16. 10x 2 10 1 4x 1 8 5 180; x 5 13; 1208, 608
7. 4
12. 1
b. Length 5 78 feet
Width 5 w
d. The width is 36 feet.
21. 36
25. c
17. a. Length 5 2 ? Width 1 Six feet
c. 78 5 2w 1 6
w 5 36
18. 23z 5 227, z 5 9
The product of 9 and 23 is 227.
19. 22556
=
16. 36 units2; 26 units
17. 2 1 s212d 5 210; Answers vary.
17. 22x 2 2 1 15x 1 18x 1 2 1 5x 5 360;
x 5 6; 1308, 908, 1108, 308
18. 9 2 3 5 6; Answers vary.
124
Passport to Algebra and Geometry
12. 12
18. a.
s8 1 7 1 7 1 4 1 7 1 10 1 10dx 5 323.30
b. x 5 6.10; \$6.10 per hour
■ Lesson 4.3
■ Lesson 4.5
1. c
2. a
5. 1
6. 24
9. 28
4. 26
3. b
10.
7. 26
5
23
13. 3x 1 14 5 x 1 20; x 5 3
2. Divide both sides of the equation by 23 or
1
multiply both sides by 2 3 .
15. 4x 2 2 5 3x 1 2; x 5 4
4. 215
5. 20
4
7. 4
8. 2 3
11. 7
12. 10
9. 2
6. 18
14. 28
16. 4sx 1 3d 5 2x 1 8; x 5 22
18. x 5 6; the length of each side is 20 units.
19. x 1 18 1 10 5 2sx 1 10d; x 5 8
The second culture is 8 days old. The first
culture is 26 days old.
15. 4n 1 16 5 100; n 5 21
16. 3n 2 23 5 34; n 5 19
17. 12 n 1 27 5 40; n 5 26
■ Lesson 4.6
18. 13 5 15 n 2 8; n 5 105
20. a.
14. 5x 1 38 5 2x 1 47; x 5 3
17. x 5 4; the perimeter is 36 units.
10. 10
13. 29
12. 22
11. 2
1. Divide both sides of the equation by 4 or
1
multiply both sides by 4 .
3. 10
8. 231
19. 75 cm
1. StudentsÕ tables and graphs may vary slightly.
2w + 6
Minutes
w
b. Width 5 11 inches
Length 5 28 inches
1
2
3
4
5
Company 1
2.00
2.15
2.30
2.45
2.60
Company 2
2.50
2.60
2.70
2.80
2.90
6
7
8
9
10
Company 1
2.75
2.90
3.05
3.20
3.35
Company 2
3.00
3.10
3.20
3.30
3.40
11
12
13
14
15
Company 1
3.50
3.65
3.80
3.95
4.10
Company 2
3.50
3.60
3.70
3.80
3.90
Minutes
21. ArkansasÕ governor salary 5 \$60,000
New YorkÕs governor salary 5 \$130,000
■ Lesson 4.4
Minutes
2. The second line should be 4x 2 8 1 6 5 16;
9
x 5 2 or 4.5
3. 2
4. 4
8. 3
9. 230
6. 22
5. 5
10. 234
7. 2
11. 28
12. a. 220
13. a. 23
b. 220
b. 23
Cost (in dollars)
1. The second line should be 23x 1 2 5 8;
x 5 22
14. 6sx 1 5d 5 42; x 5 2
15. s3x 2 2d 1 s2x 2 1d 1 s7x 1 3d 5 180;
x 5 15; 438, 298, 1088
16. 7sxd 1 3s9d 5 5s9 1 xd; x 5 9; 9 pounds of
cashews
Company 2
3.50
(11, 3.50)
3.00
2.50
Company 1
2.00
2
2.
Cost 1 minute
Company 1
5
Passport to Algebra and Geometry
4.00
4
6
8 10 12
Number of minutes
1
Cost 1 minute
Company 2
Cost per
minute
after first
1
3
Cost per
minute
after first
14
t
Number of
minutes
after first
3
Number of
minutes
after first
3. Cost first minute Company 1 5 \$2.00
Cost per minute after first 5 \$0.15
Number of minutes after first 5 t 2 1
Cost first minute Company 2 5 \$2.50
Cost per minute after first 5 \$0.10
Number of minutes after first 5 t 2 1
4. 2 1 0.15st 2 1d 5 2.50 1 0.10st 2 1d
6. 11 minutes
7. \$3.50
8. 2500 1 12x 5 52x; x 5 62.5; so you need to
sell at least 63 helmets to break even.
■ Lesson 4.7
2. The second line should be
0.8575x 2 2.037 5 12.64; x < 17.12
7. 1.58
4. 1.08
15. 1.39
6. 1.67
9. 221.58
8. 1.22
11. 25.27
5. 1.12
12. 7.96
16. 0.72
10. 2.62
13. 5.67
14. 12.24
17. \$25.65
18. \$5.65
19. 29 wings (total bill \$4.98)
8. Periodic table of elements introduced.
9. BoyleÕs Law formulated.
■ Lesson 5.2
1. A simple bar graph, one bar could be used for
each type of blood.
2. A double bar graph or stacked bar graph
3. 1901Ð10
5. Yes, it appears that during the twentieth
century, the number of immigrants was at the
highest from 1901Ð1910. Then the number
decreased, reaching its lowest from 1931Ð1940.
Since then it appears the number of immigrants
6. If the trend continues there should be more than
8000 immigrants from 1991Ð2000.
7. See studentsÕ graphs. Time intervals may vary.
One possible graph:
20. < 56.78 miles or 57 miles
1. 8; each side is 6 units.
2. 4; width is 22 units; length is 10 units.
3. x 5 3; each side is 13 units.
4. x 5 25; m/1 5 708, m/2 5 1108
5. x 5 14; m/1 5 458, m/2 5 508, m/3 5 858
7. 52 square inches
8. 12,636 square feet
9. 53,125 square miles; area of rectangle 1 area
of triangle
■ Lesson 5.1
10
Number of Students
■ Lesson 4.8
6. 1836 square feet
7. < 1803
6. 25 years
4. 1921 to 1930 and 1931 to 1940
1. The second line should be
5.5x 1 11.25 5 22.5; x < 2.05
3. 23.5
5. There would be half as many TVÕs in each row.
8
6
4
2
0
4.5-4.9 5.0-5.4 5.5-5.9 6.0-6.4 6.5-6.9 7.0-7.4
Time in Seconds
■ Lesson 5.3
1. The units of the horizontal axis are years
starting with 1980 increasing in increments of
one year. The units of the vertical axis are
number of tornadoes starting with 0 increasing
in increments of 100.
1.
2. < 1050
Korean Desert
Mexican War Civil War
French and
War
Storm
Indian War War of 1812
W.W. I
3. 1981, 1983, 1984, 1985, and 1987
1650
1700
1900 1950 2000
W.W. II
Vietnam
Revolutionary
War
Spanish American
War
War
2. 5 seasons
126
1750
1800
1850
3. 33 seasons
4. Many possible theories:
1. greenhouse effect causing more severe
weather
2. better reporting of data
Passport to Algebra and Geometry
5. t 5 11
4. 8 seasons (as of 1996)
Width
2
2
2
2
2
Length
2
3
4
5
6
Perimeter
8
10
12
14
16
18
16
14
12
10
8
6
4
2
0
1. The consumption of poultry appears to be 3
times as much as that of eggs.
2. The consumption of poultry is only about 2
times as much as that of eggs.
3. Yes, because the vertical scale starts at 15
4.
1
2
3
4
5
Length (in inches)
6
7
1000
800
120
105
90
75
60
45
30
15
0
Red
Meat
600
Food
200
5. JulyÕs bill appears to be twice JuneÕs bill.
1970
1980
Year
1990
6. JulyÕs bill is \$85 and JuneÕs \$65. JulyÕs is only
\$20 more than JuneÕs.
7. The vertical scale is misleading because the
units start at \$50.
■ Lesson 5.4
1. A pictograph or bar graph would be best for
simple data. Possible graph:
Show
8.
Number of Performances
A Chorus Line
Oh Calcutta
Cats
Les Miserables
Phantom of
the Opera
= 1 thousand shows
2. a. About 1000 thousand or 1,000,000
90
80
70
60
50
40
30
20
10
0
J F M A M J J A S O N D
Month
■ Lesson 5.6
1. Yes. Explanations vary.
b. In the category of living with their spouses
2. Yes. Explanations vary.
3.
d. Possibly a stacked bar graph if you want
to compare the total of each living
arrangement.
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
2
3
4
3. A time line is the best way to present the data.
Cobb
1910
Eggs
Poultry
400
1960
Consumption (in pounds)
7.
Amount (in \$ billions)
Perimeter (in inches)
6.
■ Lesson 5.5
Electric bill (in dollars)
5.
Klein and Foxx
Medwick
Hornsby
1920
Zimmerman
1930
1940
Gehrig
Robinson
Mantle
1950
Williams
Passport to Algebra and Geometry
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
5
6
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
7
8
9
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
10 11 12
1960
Yastrzemski
4. a. 1 hit per game;
b. 0.250 batting average
■ Lesson 5.7
5. Yes: 2, 3, 6, and 9; No: 4, 5, 7, and 10
6. Yes: 3, 5, 7, and 9; No: 2, 4, 6, 8, and 10
7. 8
9. 1, 4, or 7
8. 1, 3, 5, 7, or 9
10. 0 or 6
4. Positive correlation. As the number of study
hours increases, test scores should increase.
11. 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
5. No correlation. The number of pets you own
and your age have no pattern.
14. Let a 5 4x and b 5 4y, and let x and y be
integers. Then
12. 315
6. Negative correlation. As the number of hours
you watch TV increase, test scores should
decrease.
a. a 1 b 5 4x 1 4y 5 4sx 1 yd
b. sa 2 bd 5 4x 2 4y 5 4sx 2 yd
c. ab 5 s4xds4yd
1125
1100
1075
1050
1025
1000
975
950
a 4x x
5
5
b 4y y
In a, b, and c, x and y can still be integers so
that the expressions are always divisible by 4.
x
In d, may be a fraction or an integer not
y
divisible by 4.
d.
0
5 10 15 20 25 30 35
Altitude (in thousands of feet)
15. 1, 2, 3, 4, 6, 8, 12, 24
8. Negative correlation
16. 1, 2, 3, 6, 9, 18, 27, 54
17. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
18. 1, 3, 5, 7, 15, 21, 35, 105
19. 1 mi-by-80 mi, 2 mi-by-40 mi, 4 mi-by-20 mi,
8 mi-by-10 mi, 16 mi-by-5 mi
12. Positive correlation. As the years go by, the
average salary increases.
13. Answers will vary slightly. In 1998, the
average salary should be about \$55,000.
■ Lesson 5.8
1.
6.
1
6
1
3
2.
7.
1
2
1
13
1
3
3.
8.
4.
3
13
2
3
9.
5.
3
26
■ Lesson 6.2
1. Composite, 39 5 13
?3
2. Prime, 41 5 41 ? 1 only
1
2
10.
20. 20 yd-by-20 yd
2
13
3. Composite, 57 5 19
?3
24
33
1. Yes: 2, 3, 4, 6, and 8; No: 5, 7, 9, and 10
5.
6. 2 ? 33
?3
7. 2 ? 3 ? 7
8. 26
9. 22 ? 3 ? 7
10. 24 ? 32
11. 23 ? 52
12. 22 ? 32 ? 5
13. s21d ? 2 ? 2 ? 3 ? 3; s21d ? 23 ? 32
14. s21d ? 3 ? 3 ? 5; s21d ? 32 ? 5
15. 2 ? 2 ? 2 ? 3 ? x ? x; 23 ? 3 ? x2
16. 2 ? 2 ? 2 ? 2 ? a ? a ? a ? b ? b; 24 ? a3 ? b 2
2. Yes: 3, 5, 7, and 9; No: 2, 4, 6, and 10
17. 90
18. 336
3. Yes: 2, 3, 4, 5, 6, 8, 9, and 10; No: 7
20. 1, 2, 4, 8, 16
4. Yes: 2, 3, 4, 6, 8, and 9; No: 5, 7, and 10
22. 1, 2, 3, 6, 9, 18, 27, 54
11. 5 blue socks, 10 white socks, 4 black socks and
1 argyle sock
379
2528
349
b. 2528
905
2528 <
12. a.
13.
< 0.15
< 0.14
0.36
14.
1623
2528
< 0.64
■ Lesson 6.1
128
4.
19. 2540
21. 1, 2, 3, 4, 6, 8, 12, 24
Passport to Algebra and Geometry
Speed of Sound
(in feet per second)
7.
13. 24
23. 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97
5 5 4 1 1, 13 5 9 1 4, 17 5 16 1 1,
29 5 25 1 4, 37 5 36 1 1, 41 5 25 1 16,
53 5 49 1 4, 61 5 36 1 25, 73 5 64 1 9,
89 5 64 1 25, 97 5 81 1 16
6. 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,
60, 65, . . .
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, . . .
12, 24, 36, 48, 60, 72, . . .
LCM 5 60.
24. No other pairs exist because for a pair of
numbers to be consecutive one must be even
and therefore composite.
7. 36 5 2 ? 2 ? 3 ? 3, 54 5 2 ? 3 ? 3
LCM 5 2 ? 2 ? 3 ? 3 ? 3 5 108
■ Lesson 6.3
1. 6
6. 165
2. 6
3. 10
7. 2xy
10. 9x 2y 3
4. 18
8. 2xy 2
5. 240
9. 5r 2p
11. 10 and 15, 20 and 25, . . .
12. 3 and 6, 9 and 12, . . .
13. 12 and 24, 36 and 48, . . .
14. Yes
15. No, GCF 5 3
16. Yes
8. 15 5 3 ? 5, 35 5 5 ? 7
LCM 5 3 ? 5 ? 7 5 105
9. 145 5 5 ? 29, 275 5 5 ? 5 ? 11
LCM 5 5 ? 5 ? 11 ? 29 5 7975
10. 81 5 3 ? 3 ? 3 ? 3, 216 5 2 ? 2 ? 2 ? 3 ? 3
LCM 5 2 ? 2 ? 2 ? 3 ? 3 ? 3 ? 3 5 648
12. 3x2 5 3 ? x ? x, 5y 2 5 5 ? y ? y
LCM 5 3 ? 5 ? x ? x ? y ? y 5 15x 2 y 2
18. A 5 108, P 5 42
They are not relatively prime, GCF 5 6.
13. 3 and 13
20. GCF 5 2
21. GCF 5 3
22. 7 children; A can of soda costs \$0.48 and one
candy bar costs \$0.35.
■ Lesson 6.4
1. 5, 10, 15, 20, 25, 30, 35, 40, . . .
7, 14, 21, 28, 35, 42, 49, . . .
LCM 5 35.
2. 3, 6, 9, 12, 15, 18, 21, 24, 27, . . .
8, 16, 24, 32, . . .
LCM 5 24.
3. 9, 18, 27, 36, 45, . . .
12, 24, 36, 48, . . .
LCM 5 36.
4. 12, 24, 36, 48, 60, 72, 84, 96, . . .
14, 28, 42, 56, 70, 84, 98, . . .
LCM 5 84.
5. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, . . .
5, 10, 15, 20, 25, 30, 35, . . .
6, 12, 18, 24, 30, 36, . . .
LCM 5 30.
Passport to Algebra and Geometry
?3
11. 13xy 2 5 13 ? x ? y ? y,
26x 2y 3 5 2 ? 13 ? x ? x ? y ? y ? y
LCM 5 2 ? 13 ? x ? x ? y ? y ? y 5 26x 2y 3
17. A 5 28, P 5 22
They are not relatively prime, GCF 5 2.
19. A 5 77, P 5 36
They are relatively prime.
?3
14. Possible answers: 4 and 9, 4 and 18, 12 and 18
15. 4 and 25
16. Possible answers: 8 and 18 or 18 and 24
17. 75 bottles, 4 packs
18. 352 miles; AngelÕs car used 11 gallons. MoÕs
car used 16 gallons.
19. 84 minutes later at 2:24 A.M.
■ Lesson 6.5
3
1. 4, 7
5. 2,
9.
13.
2
19
1
3z3
9
16
2
2. 4, 9
6. 12,
10.
14.
1
3. 9, 5
7
9
24. >
b
4a
2x
12. 2
5y
8.
9 15
64 , 20
16
8 12
10 , 15 , and 20
28
14 21
16 , 24 , and 32
3
1 2
3 , 6 , and 9
15.
20. >
1
3y
3x 2
11. 4
5y
7.
8yz
9
7 4
12 , 49
2
4. 11, 7
21. 5
22. <
25. 5
1
11
26.
16.
25
64
23. 5
27.
2
11
24
28. Mr. MorganÕs class did better because 36 >
21
35 .
■ Lesson 6.6
4.
20. 1.95 3 106; 1,950,000
11
2. 20
17
5. 2 5
3.
6.
9
25
67
4
21. 3.744 3 1029; 0.000000003744
22. 2.185 3 1023; 0.002185
7. Rational, 0.36, repeating
23. 1 3 106 > 6 3 105 because
1,000,000 > 600,000
8. Rational, 0.625, terminating
24. 1 3 1024 < 4 3 1023 because
0.0001 < 0.004.
9. Rational, 4, terminating
10. Irrational, 5.6568542 . . . , non-repeating
25. Approximately 4.4688 3 1014 mi
11. Rational, 0.5625, terminating
26. 0.006, 6.0 3 1023 gal; 1.994 gal
12. Rational, 0.32, terminating
13.
18.
7
10
38
9
13
25
15.
19. b
20. a
14.
19
20
16.
11
50
21. d
17.
94
99
22. c
23. 0.1, 0.2, 0.3, 0.4, 0.5, 0.6
Each number is a repeating decimal. The digit
which is repeating is increasing by one.
24.
25.
2
14
3 in., 43 in., 4.6 in.
4
1 in., 4 in., 4.0 in.
■ Lesson 6.9
1.
2.
n
1
2
3
4
5
6
n2 2 n
0
2
6
12
20
30
n
1
2
3
4
5
6
n2 1 2
3
6
11
18
27
38
26. 0.2, 0.16, 0.12, 0.22, 0.1, 0.15, 0.05;
Jose, Ken, Vicki, Doug, Cindy, Brenda, JiLynn
the preceding fraction; 15 , 16 , 17
■ Lesson 6.7
4. Possible answer: The denominators increase
1 1 1
by consecutive odd integers; 37
, 50 , 65
1.
1
16
1
2. 2 27
5.
3
x2
6.
3. 1
1
16x2
7. s23d22 5
1
8. 1421 5 14
15. 1024
18. 214
19. 7
22. 825 ? 87
23.
27.
55
and
16. 4
20. 9
21. 3
7. 25 and 41;
56
524
sq yd
17. 0
24. >
25. >
28. \$4081.47
6. 1.05 3 1025
8. 0.000635
11. 0.00000827
1022
16. Yes
17. No, 7.64 3 1021
18. Yes
19. 1.28 3
130
9. 0.0043
12. 325,000
14. No, 3.5 3 105
108;
1
3
5
7
7
9
7
5
3
1
4. 2.05 3 1022
5. 6.2153 3 107
15. No, 2.65 3
and
1
2. 6.2 3 10 4
3. 3.75 3 1024
13. Yes
1
3
1. 3.5 3 103
10. 97,500
3
5
5
■ Lesson 6.8
7. 320,000
6. 9 and 11;
13. 14539.336
14. 7396
26. >
5. Each term is the sum of the two previous terms
plus one; 41, 67, 109
1
9
10. 37 5 2187
9. x 5
12. x3
11. 8
4. 9
8. Possible answers: 11 and 29, 3 and 37
9. Possible answers: 11 and 19, 7 and 23
10. The midsegment of each side is replaced by 2
new segments.
11. 3 in star 1, 6 in star 2, 18 in star 3
128,000,000
Passport to Algebra and Geometry
1.
2 31
32
3
12. The factors of 48 except for 1 and 48 are 2, 3,
4, 6, 8, 12, 16, and 24.
The factors of 75 except for 1 and 75 are 3, 5,
15, and 25.
75 5 2 1 3 1 4 1 6 1 8 1 12 1 16 1 24
and 48 5 3 1 5 1 15 1 25
■ Lesson 7.1
1.
5
7
2.
23
6.
3
4
10. 2
x
1
3. 2 3
1
4
3x
7.
4
6
11.
z
z
8. 2
7
18. 21
9
13. 2
4
5
16. 22
17. 2 3
20. 20.45
19. 0.67
21. 20.88
5 7
2
22. 63 , 6 , 6 ; every fraction after the first is 6 greater
than the preceding fraction. The next three
9 11 13
numbers are 6 , 6 , 6 .
23.
24.
11
3,
2 93 , 73 ; the numerators are odd numbers
decreasing in order with every other term being
negative and the denominators are three.
5 3
1
The next three numbers are 2 3 , 3 , 2 3 .
3
8
1 48 5 78
25.
5
6
2 36 5 26
■ Lesson 7.2
2.
5. 2 13
18
17
24
4.
7a
15 1 6y
8. 2
9.
12
5y
5b 2 2a
21 1 2n
11.
12.
ab
3mn
14. 0.71
15. 0.60
5 1219
24
19.
17.
311
24
5 1223
24
1
5
1
b. 6 ;
20. a. Hank;
d.
9
3. 2 16
5x
7.
8
9
14t
13. 20.06
18.
14. < 2 2 s0.702 1 0.842 1 0.24d < 0.22
15. < 5x 2 s0.571x 1 0.545xd < 3.88x
16. < 5.25 1 3.222 2 2.545 < 5.93
18.
20.
90
100
41
100
19.
or 0.9
10
100
or 0.1
or 0.41
21. a, to avoid a round-off error, you should begin
by rounding the numbers to 3-decimal placesÑ
one place more than is required in the final
result.
■ Lesson 7.4
1.
5.
1
9
33
7
9. 2
13.
1.
1
14
10. 2
307
24
1
8
13. < 0.806m 1 0.457m < 1.26m
15
4
9
2. 2 25
3. 2 49
68
2
6. 2 15
7. 6x
1
6
10. 2
14.
sq in.
27
100
62
3 hr
2
5
11.
153
8
8. 56y
3z
5
sq in.
21.
12. 216x
15.
21
2
sq in.
18. 25.438
17. 3.167
3
20. 20
5 20 23 hr
4. 2 91
5
9
40
23. \$30,600
■ Lesson 7.5
c. \$4838
16.
12. < 0.676 2 0.626 < 0.05
22.
1
b. \$508
1
6.
30
19.
4
1
27. a. \$488 5 \$482
3
4
1 59 < 1.06
16. 0.545
26. 506 inches
1.
8
16
17. < 4x 2 s0.556x 2 1.333xd < 4.78x
9. 22c
19
12. 2
5k
15. 21
14. 3
19
5. 2 3
2
5
4.
8.
1
3
5
6 1 8 1 24
24
24 5 1
c.
5
12
4
9
5
6
1 14 5 24
1 24
1 24
1 24
5
5
1
2.
y
7
3.
4
3z
1
4
5.
6. 28m
29
16x
7. Did not multiply by the reciprocal.
4. 2
16
1
10 4 3 5 10 4
5
5
5
5 10 ?
16
10 ? 5
5
16
25
5
8
■ Lesson 7.3
1. 0.96
5. 7.877
2. 0.693
6. 4.247
4. 21.39
3. 9.05
7.
5
16
1
2
6
< 0.65
Passport to Algebra and Geometry
8. Did not multiply by the reciprocal.
21.
2 1 2 6
4 5 ?
3 6 3 1
2?6
5
3?1
14.
19.
24.
64
189
28.
69
8
25.
11.
16.
21.
19
5z
3
32
9
8
6
5
5
12. 12
17. 32
22. 2 72
7
7p
23
26.
13.
18.
5
18
5
3
23.
2 74
7
ounces s 858 d; 23
8 ounces s 28 d
2. 70%
3. 40%
4. 50%
7. 48%
9. 65%
10. 60%
Fraction
Bored
36%
0.36
9
25
Moving
19%
0.19
19
100
New Furniture
15%
0.15
3
20
Redecorating
16%
0.16
4
25
Other
14%
0.14
7
50
90
70
50
30
Bored Moving
15. \$1500
■ Lesson 7.8
Percent
34%
Food
28%
Car payment
10%
Electricity
4%
Water
6%
Heat
2%
Phone
1%
Entertainment
5%
Clothing
10%
1. 0.18, 144
2. 0.23, 27.6
4. 1.75, 70
5. 0.006, 3.24
7. c, 4
8. d, 30
11. 5 squares
13. 40.7
9. a, 13.3
10. b, 6.6
17. 21.05
15. 197.88
18. 254.52
20. Perimeter 5 16 cm, area 5 15 sq cm
■ Lesson 7.7
3 cm
2. 0.16
3. 2.50
5. 0.005
6. 0.384
9. 165%
10. 0.8%
12. 38.4%
13. 5
132
6. 0.035, 5.25
19. Perimeter 5 48 cm, area 5 135 sq cm
17. c, because the shaded region is 50% of the
entire area. The other three figures all have
17.
3. 3.6, 28.8
12. 15 squares
14. 7.02
16. 273.6
16. >
Other
Reason
1. 0.48
New RedecFurniture orating
11. 49%
House payment
31. 31.25%
Decimal
8. 40%
16. Area
30. 58.3%
28. 225%
10
5. The least is d, 25%. The greatest is a, 75%.
6. 10%
27. 22%
Percent
Percent
1. 36%
24. 65%
Reason
33.
■ Lesson 7.6
23. 87.5%
26. 375%
29. 55.5%
32.
21
20
17
25
18.
4. 0.842
7. 63%
8. 92%
21. Perimeter 5 16 cm.
Yes, it is a linear measure.
11. 2.1%
14. <
7
20
19.
15. >
79
100
5 cm
20.
5
4
Passport to Algebra and Geometry
9.
1
10. 8
15. 34
20. 10
3
22.
25. 40%
54
3
16
5
24
5
2
69
20
1
22. Area 5 45 cm 2. No, because 333 % of 135 Þ
1
1
s 333 % of 15d 3 s 333 % of 9d. You can see that
the percentage rate is multiplied twice on the
right and only once on the left.
24. < \$657.44
23. \$63.96
1. \$8.43
2. \$62.91
4. 0.2%
5. 11.9%
6. 4.6%
8. 0.3%
9. 7.2%
10. 4.4%
12. 1.4%
13. 6.8%
3. \$144.15
14. 2.5%
7. 3.7%
11. 4.8%
15. 0.2%
16. Amount of raise 5 \$1206.80
New salary 5 \$18,446.80
18. 980 freshmen
19. Increase: \$2056.50
Current Price: \$22,621.50
19
2. A ratio, 36 or 19 to 36
hits
11114game
2
3 miles
1 miles
5
5 0.125 miles per
24 minutes 8 minute
minute; a rate because different units of
measure
10 students 1
5 or 1 to 6; a ratio because same
5.
60 students 6
units of measure
2 inches
1 inches
5
5 0.05 inch per
40 minutes 20 minutes
minute; a rate because different units of
measure
2 pictures 2
5 or 2 to 3; a ratio because same
7.
3 pictures 3
units of measure
144 in.
5 9 to 1
16 in.
36 hr
10.
5 3 to 14
168 hr
19. Ratio of the perimeters is 24 5 3 to 2.
72
Ratio of the areas is 24 5 3 to 1.
■ Lesson 8.2
1. Yes, 1 ? 42 5 6 ? 7
2. No, 2 ? 9 Þ 3 ? 4
6. 80
7. 36
4. 3
8. 7
9. 6
x
12
2
y
11.
5 ,x54
5 ,y58
5 15
12 3
4 24
y
7
12. 5 , z 5 54
13.
5 , y 5 63
9
z
11 99
3
w
27
3
6
t
14. 5 , w 5
15.
5 ,t5
4 18
2
10 35
7
16. 30.33
17. 3.2
18. 14.06
10.
1. A rate, 8 feet per second
8.
18. Ratio of the perimeters is 14
24 5 7 to 12.
12
Ratio of the areas is 24 5 1 to 2.
5. 12
■ Lesson 8.1
6.
17. a, the 36-ounce box for \$3.72 is the better
bargain because you pay about \$0.10 per
ounce, whereas, the other is about \$0.11 per
ounce.
3. No, 5 ? 120 Þ 12 ? 10
21. < 71.7% in December
< 28.3% in other months
4.
16. b, one gallon for \$4.25 is the better bargain
because you pay about \$1.06 per quart whereas
the other is about \$1.08 per quart.
36
20. < 19.6% laid off, < 80.4% retained
Yes, 80.4% of 153 < 123 people, which is the
number of employees retained.
3. A rate, < 1.27 hits per game
15. a. 24.25 miles per gallon
b. < 59.7 miles per hour
■ Lesson 7.9
17. 78,540 seats
32 oz
36 in.
13.
5 9 to 7
5 4 to 3
28 in.
24 oz
14. 50 cubic feet per hour
12.
32000 m
5 8 to 1
4000 m
7 pt
11.
5 7 to 16
16 pt
9.
Passport to Algebra and Geometry
19. d 5 24, e 5 18
21. 5 bags
20. q 5 13, r 5 5
22. 300 cement blocks
23. 2000 defective parts
■ Lesson 8.3
1. 105 teachers
2. a. 56 kph
b. Yes, you are traveling 68.75 mph.
3. 1834 cups of flour
5. 110 employees
7.
9334
pounds
4. 85 inches of snow
6. 22 days
8. 4623 minutes
9. < 21,691 people
■ Lesson 8.4
12.
1. 3.2%
2. 86.4
3. 39.56
5. 21.6
6. 1368
7. 1569.5
9. 106.98%
13. 10%
10. 45
4. 650
11. 100
Country
Percent
Population
China
21%
1.151 3 109
8. 14
India
16%
8.768 3 108
12. 300
former
Soviet Union
5%
2.74 3 108
United States
5%
2.74 3 108
Indonesia
4%
2.192 3 108
Brazil
3%
1.644 3 108
14. 150
p
25
5
, p 5 3.70%
15.
675 100
a
52
16.
5
, a 5 84.24
162 100
17. p 5 25%
18. a 5 20
Possible model:
Possible model:
13. \$21,116.67
14. They played 40 games and won 38.
15. \$17.31
■ Lesson 8.6
Each
=5
Each
=1
19. b 5 80 Possible model:
1
1. A 25% increase
2. A 333 % decrease
3. A 20% decrease
4. A 163 % increase
5. A 25% decrease
6. A 5% increase
2
7. < a 1.7% increase
8. < a 7.7% decrease
9. < a 12.7% increase
10. < a 2.2% decrease
11. Each number is a 300% increase of the
preceding number. 512, 2048, 8192
12. Each number is a 50% decrease of the
preceding number. 40, 20, 10
13. Each number is a 900% increase of the
preceding number. 10,000, 100,000, 1,000,000
= 0.8
20. \$975.48
21. Sales tax 5 \$87, total bill 5 \$1537
22. \$3.05 is the tip. < 18.0% tip rate s17.99%d
23. < \$35,714.29
4. \$1500
2. \$3375
3. \$1125
5. 5.727 3 107 sq mi
6. 1.168 3 107 sq mi
7. 5.097 3 106 sq mi
8. 1.718 3 107 sq mi
9. 2.978 3 106 sq mi
10. 9.335 3 106 sq mi
11. 5.097 3 106 sq mi
134
15. False, four times a number is a 300% increase
of the number
16. True
■ Lesson 8.5
1. \$12,500
14. Each number is a 60% decrease of the
preceding number. 400, 160, 64
17. False, a 90% decrease of 60 is 60 2 54 5 6.
18. True
21.
Original Number
New Number
Percent Change
55
66
20% increase
55
44
20% decrease
200
350
75% increase
1400
350
75% decrease
60
75
25% increase
60
45
25% decrease
Passport to Algebra and Geometry
Each
22. 42.9%
■ Lesson 8.8
23. 34.5%
■ Lesson 8.7
1. 36 outcomes possible
1. 720 ways
2.
white shirt-dark blue tie
white shirt-stripe blue tie
white shirt-paisley tie
white w/blue stripe shirt-dark blue tie
white w/blue stripe shirt-stripe blue tie
white w/blue stripe shirt-paisley tie
off white shirt-dark blue tie
off white shirt-stripe blue tie
off white shirt-paisley tie
light blue shirt-dark blue tie
light blue shirt-stripe blue tie
light blue shirt-paisley tie
light blue w/stripe shirt-dark blue tie
light blue w/stripe shirt-stripe blue tie
light blue w/stripe shirt-paisley tie
3.
C
D
D
B
C
D
D
B
B
C
C
B
B
A
C
D
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
B
D
D
A
B
D
D
A
A
B
B
A
A
C
B
D
1
1
1
2
2
2
3
3
1
3
2
3
4
4
4
5
5
5
6
6
6
1
1
1
2
2
2
3
3
3
5
4
6
4
4
4
5
5
5
6
6
6
3. Two is the smallest and 12 is the largest.
1
36
12
b. 36
6
c. 36
1
18
36 5 2
35
e. 36
7
f. 21
36 5 12
4. a.
d.
5 13
5 16
should approach theoretical probabilities as the
number of trials increase.
6. 64 ways
7.
9. 720 ways
1
64
10.
1
16
8.
1
720
11.
1
120
■ Lesson 9.1
C
D
D
A
C
D
D
A
A
C
C
A
A
B
C
D
B
C
C
A
B
C
C
A
A
B
B
A
A
D
B
C
1. 6, 26
4. 0.8, 20.8
1
125,000
5. 20, 220
7.
3. 1.4, 21.4
6. 56 , 2 56
8.
24 ways; the probability that Angel and Bo will
1
12
be standing next to each other is 24 5 2 .
4. 125,000 combinations;
2. !12, 2 !12
6 and 7
8 and 9
9.
5. 35,152 combinations of call letters
The probability that the second letter is a Q is
1352
35152
1
5 26
.
6. 180 times
Passport to Algebra and Geometry
5 and 6
10. 5, 25
11. 25, 225
12. 5.477, 25.477
13. 5.196, 25.196
14. 8, 28
15. 4, 24
■ Lesson 9.3
In Exercises 16–18, estimates may vary slightly.
1. c 5 10
2. b 5 36
16. 5.5, !30 < 5.477
4. b 5 40
5. a 5 7
7. c 5 35
8. b 5 30
17. 6.8, !45 < 6.708
18. 3.1, !10 < 3.162
19. x 5 !121, x 5 11
10.
20. q2 2 10 5 39, q 5 7, 27
A
37
12.
A
20
12
2. Rational, a quotient of integers
3. Irrational, cannot be written as a quotient of
integers (or decimal is non-terminating,
non-repeating)
B
4. Rational, 2 !16 5 24, an integer is always a
rational number
13.
25
15.
8. Sometimes, for example !4 is rational but !2
is irrational.
B
10. Always, real numbers are rational and
irrational.
12. 23, rational, result is an integer
, irrational, not a quotient of integers
−5
24. >
29. <
136
−4
−3
−2
25. <
30. !32
−1
0
1
26. >
31. !50
2
27. <
4
5
27
45
36
C
19. a 5 48
20. b 5 60
22. About 130.3 feet s127.3 1 3d
28. >
32. !4.5 or !
C
21. The maximum height the ladder will reach is
about 38.7 feet, and the minimum height is
9
2
3
4
A
18. b 5 52
18. d
12
17.
B
19–23.
− 16
5
16. Not a right triangle
11. !18, irrational, cannot be written as quotient
of integers (or non-terminating, non-repeating
decimal)
5
2
A
3
9. Never, integers are always rational.
− 16
3
C
9
2
Passport to Algebra and Geometry
7. Sometimes, for example is rational but not an
integer.
17. e
20
14. Not a right triangle
3
2
16. a
C
B
A
6. Rational, !94 5 32 , a quotient of integers
15. b
16
15
5. Irrational, cannot be written as a quotient of
integers (or decimal is non-terminating,
non-repeating)
14. c
C
11. Not a right triangle
25. < 20.4 ft
1. Rational, a quotient of integers
6
35
B
■ Lesson 9.2
!2
9. a 5 18
23. 26 sq ft
24. < 5.1 ft by 5.1 ft
13.
6. c 5 53
12
21. 25y 2 5 49, y 5 75 , 2 75
22. 12 ft by 12 ft
3. a 5 40
■ Lesson 9.4
18. x < 2
1. P 5 82 units, A 5 420 sq units
−1
2. P 5 20 units, A 5 25 sq units
3. P 5 108 units, A 5 306 sq units
0
1
2
3
−5
−4
−3
−2
12
13
14
15
19. y < 23
4. 6 feet from the base
5. < 180.3 miles
−6
6. < 43.0 yards
7. < 204.9 feet (60 1 60 1 84.9d
20. r ≤ 14
■ Lesson 9.5
1.
11
0
1
2
3
4
21. 28 < t
2.
−3
−2
−1
0
−9
1
3.
−7
−6
−5
7
8
9
10
22. 7 < x
−11
−10
−9
−8
−7
6
4.
−6
−5
−4
−3
−2
23. 5 ≤ x, 5 is less than or equal to x.
24. 210 ≥ t, 210 is greater than or equal to t.
5.
8
9
10
11
12
25. 24 < w, 24 is less than w.
26. q 1 12 < 24, q < 216
6.
3
4
5
6
8. x ≤ 15
7. x > 22
10. x ≥ 0
11. x ≤ 3
7
9. x < 0
12. x > 25
13. x < !10
−8
27. z 2 10 ≤ 5, z ≤ 15
28. p 2 16 > 212, p > 4
29. 42 ≥ t 1 22, 20 ≥ t
2
3
4
5
2
3
4
5
6
1
5
? 5x
≤
1
5
? s232d
x ≤ 2 32
5.
−3
−2
−1
0
16. x ≤ 2 !15
−5
−4
−3
−2
17. w ≥ 21
−2
■ Lesson 9.6
15. x ≥ 2 !5
−6
33. h > 2
1. The direction of the inequality symbol is not
reversed when you multiply both sides by a
positive number. Line 2 should be
14. x > !11
−4
32. t ≤ 25
31. h > 18
1
30. a ≥ 13
2. The direction of the inequality symbol is
reversed when you multiply both sides by a
negative number. Line 2 should be
1
22 ? s 2 2 dz < 22 ? s25d
z < 10.
3. c
−1
0
1
4. b
5. a
6. d
2
Passport to Algebra and Geometry
7. n <
19. At least 345 pounds
12
5
20. At least 56.6 mph
−1
0
1
2
3
21. \$15.00 per square yard
22. 20 singles
11
8. m > 2 3
■ Lesson 9.7
−5
−4
−3
−2
−1
24
25
26
27
−1
0
1
2
−2
−1
0
1
9. x ≥ 24
23
5
3
≥ k
−2
3
11. 2 32 > c
7
23x
≥
23
23
7
x ≥ 2 .
3
2. The direction of the inequality symbol is not
reversed when you add a negative number to
both sides. Line 3 should be
15y 1 10 2 10 > 23 2 10
−3
15y > 213
13
y > 2 15 .
12. 2 35 ≤ w
3. Never
−2
−1
0
1
2
5. b
4. Always
6. a
12. x ≤ 40
−26
14.
−25
−24
−23
−22
−5
13. x ≥ 5
11. a < 3
19
14. x > 2 2
15. 2n 1 2n 1 2 1 2n 1 4 ≤ 18; n ≤ 2
16. 2n 1 2n 1 2 1 2n 1 4 > 66; n > 10
≤ m
2 19
6
8. d
10. z ≥ 2180
9. x < 23
13. p ≥ 225
7. c
−4
−3
−2
−1
17. 2n 1 2n 1 2 1 2n 1 4 < 212; n < 23
18. x ≤ 12
19. x > 5
20. You must earn at least a 92 on the sixth exam.
15. 37.5 < p
■ Lesson 9.8
36
37
38
39
40
1. No, 2 1 5 >/ 8
3. No, 8 1 10 >/ 18
16. a < 272
5.
−75
−74
−73
−72
−71
17. d < 2 32
−4
−3
−2
−1
0
18. w > 20.4
−1
138
0
1
2
2. Yes
4. Yes
Measure of Side 3
is greater than
Measure of Side 3
is less than
6 in.
14 in.
8 cm
26 cm
8 ft
32 ft
30 m
120 m
45 yd
295 yd
3
Passport to Algebra and Geometry
10.
1. The direction of the inequality symbol is
reversed when you divide both sides by a
negative number. Line 3 should be
6. Yes
7. Yes
8. Yes
10. No
11. No
12. e 1 d
13. b
14. a
9. Yes
5. c
6. a
7. d
8. b
9.
10.
15. d
16. 2 in., 6 in., 6 in.; 3 in., 5 in., 6 in.: 4 in., 4 in.,
6 in.; 4 in., 5in., 5 in.
17. a. Yes, a triangle can be formed by side lengths
of three consecutive integers except for the
case of lengths 1, 2, 3.
b. Yes, a triangle can be formed by side lengths
of three consecutive even integers except for
the case of lengths 2, 4, 6.
c. Yes, a triangle can be formed by side lengths
of three consecutive odd integers except for
the case of lengths 1, 3, 5.
18. 35 ft < 3rd side < 585 ft; at least 1170 feet;
less than 550 feet
■ Lesson 10.1
1. OP, PU, OU
→ → → → →
2. PO, PQ, PR, PN, PU
↔
↔ ↔
↔
3. NR and OU, MS and OU
↔
↔
→ →
→
4. NR and MS
5. OP, PU, or OU
6. RP
7. a ray
8. a line
9. The length of a line segment
10. a line segment
11. 7
12. A, B, C, D, E or F, G, H, I, J
↔ ↔ ↔
→→ →
13. DE, GH, FJ
14. IC, IH, IJ
15.
17. Yes
11. 808
12. 1308
13. 808 acute angle
15. c
16. a
14. 142.58 obtuse angle
17. b
■ Lesson 10.3
1. m i n
2. No, l and p are not parallel, so their
corresponding angles are not congruent.
3. /12, /10
4. /2, /4, /8, /6
5. /1 and /5, /4 and /8, /2 and /6,
/3 and /7
6. /1 > /2 Corresponding angles of i lines > or
/1 > /6 corresponding angles of i lines >
/2 > /3 Vertical angles > or
/2 > /5 Corresponding angles of i lines >
/3 > /4 Corresponding angles of i lines >
/4 > /5 Vertical angles >
/5 > /6 Corresponding angles of i lines >
7.
Danver
105° FH
BS
Ryan
75°
MB
Morgan
16.
18. Yes
19. planes
■ Lesson 10.2
1. /ZVW or /YVW, /ZYW, /ZYX, /WYX,
/YWX, /VWZ, /YWZ
2. /VWY, /XWZ
3. /WZV, /WZY, /YXW
4. /VWZ, /YWZ, /XWY, /VWY, /XWZ,
/XWV
Passport to Algebra and Geometry
8. Accept all reasonable answers. Consider
Morgan Road at the intersection with Danver
Drive to be a straight angle. Therefore, the
angle at which the fire hydrant is placed has a
measure of 758, 1808 2 1058 5 758. Since this
angle and the angle given at Ryan Street and
Morgan Road are congruent, it can be shown
that Danver Drive and Ryan Street are parallel.
(Actually, we will prove formally later in the
text.)
9. The fire hydrant, bus stop, and mailbox are all
placed at 758 angles.
■ Lesson 10.5
10.
In Exercises 1–3, sketches may vary slightly.
1.
■ Lesson 10.4
2.
3.
4. Acute isoceles
1. A vertical line of symmetry
2. A rotational symmetry of 1808, and 2 lines of
symmetry
3. A horizontal line, a vertical line of symmetry, a
rotational symmetry of 1808
6. Right isoceles
In Exercises 7 and 8, sketches may vary slightly.
4. 908 or 1808 in either direction
7. Right isoceles
5. 608, 1208, or 1808 in either direction
8. Acute scalene
B
A
6. 458, 908, 1358 or 1808 in either direction
5. Right scalene
A
B
C
C
9. Perimeter 5 8 1 4!2 units < 13.66 units
Area 5 8 square units
y
B (−3, 4)
A (2, 4)
y
B (−2, 4)
2
4
C (−3, −4)
x
−4 −2
−2
4 x
D (2, −1)
1. Parallelogram
18. Sometimes
C (−2, 0)
2
−4
−4
A (0, −5)
2. Rhombus
3. Trapezoid
y
4
x
17. Never
15. Sometimes
■ Lesson 10.6
y
4
13. Right scalene
14. Equilateral, equiangular
16. Never
−4
B (2, 0)
11. Perimeter 5 6 1 3!2 units < 10.24 units
9
Area 5 2 square units
12. Acute isoceles
−4
C (−2, −1)
D (2, −4)
2
A (2, 4)
2
−4 −2
−2
C (0, 5)
4
10. Perimeter 5 4 1 4!2 units < 9.66 units
Area 5 4 square units
4. Sometimes, A rectangle with 4 equal sides is a
square.
B (2, 0)
4
A (0, −5)
x
5. Never, A parallelogram has opposite sides
parallel, a trapezopid only has one pair of
opposite sides parallel
6. x 5 8 cm, y 5 14 cm
7. x 5 y 5 16 yd
8. Not possible
9. Check studentÕs sketches.
Accept all parallelograms.
140
Passport to Algebra and Geometry
10.
15. 688, 888, 1088, 1288, 1488
16. 82.58, 97.58, 112.58, 127.58, 142.58, 157.58
18 in.
18 in.
12 in.
■ Lesson 10.9
12 in.
36 in.
1. MK shortest, LK longest
2. AB shortest, AC longest
12 in.
18 in.
3. XZ shortest, ZY longest
12 in.
36 in.
4. /C smallest, m/A 5 m/B largest
12 in.
5. /G smallest, /F largest
12 in.
6. /H smallest, /I largest
36 in.
7. AC, AB, BC, DC, BD
11. 2 trapezoids, 3 rectangles
8. KM, KL, LM, LN, NM
12. The two trapezoids that are the sides of the box
are congruent. The two rectangles that are the
face and base of the box are congruent.
9. x 5 15, /B smallest, /A largest, AC smallest,
BC longest
■ Lesson 10.7
1. b
2. a
3. c
11. b.; An equilateral triangle is also equiangular.
4. equilateral: a, c; equiangular: a, b; regular: a
5. equilateral
10. x 5 10, /F smallest, /FED largest, DE
smallest, DF largest
12. c.; An isoceles triangle has two angles of equal
measure.
6. equiangular
7. equilateral, equiangular, regular
8. x 5 3
13. a.; Length of the sides satisfies the
Pythagorean theorem.
9. x 5 4
14.
5
BS
N
10
12
10
m/AF 5 608
N
W
12
E
S
15
m/BS 5 408
10°
60
15
m/SJ 5 808
30°
10
10
60°
15
80°
40
AF
5
SJ
E
S
10. x 5 4
Therefore, Angel Falls and Buck Springs are
furthest apart. Angel Falls and San JosŽ are
closest. The distance between Buck Springs
and San JosŽ 40 < d < 60.
13
13
13
13
13
13
■ Lesson 11.1
1. 108 units2, 3s108d 5 324 units2 or
1
2
2 s12 1 24d ? 18 5 324 units
13
13
11. 1358
12. 4
13. 32 units
14. 10808
■ Lesson 10.8
1. 408
2. 908
6. 12
7. 9
11. 1208, 608
3. 1108
8. 6
9. 3
12. 1608, 208
4. 5
5. 9
10. 1448, 368
13. 8
Passport to Algebra and Geometry
2. 25!3 units2, 2s 25!3 d 5 50!3 units2 or
s10ds 5!3 d 5 50!3 units2
3. 4 3 Area of triangle 5 Area of hexagon,
4s 36!3 d 5 144!3 units2; P 5 36 units;
P 5 72 units
14. 10
4. 6 3 Area of triangle 5 Area of hexagon,
6s 4!3 d 5 24!3 units2; P 5 12 units;
P 5 24 units
5. X9 5 s23, 4d, Y9 5 s21, 2d, Z9 5 s24, 1d
6.
7.
In Exercises 5 and 6, one possible answer is given.
5.
8.
12 units2
16 units
9. Yes
10. No
12.
6.
11. No
13.
y
4
y
2
−2
−2
6 units2
12 1 2!2 units
7. 1800 ft2
−4 −2
−2
x
4
−4
8. 8712 ft2
9. 106 units2
■ Lesson 11.2
1. /X
2. YZ
3. /Z
5. /B
6. AC
7. DF
8. /N
9. m/X
11. a and d; b and c
2
14.
x
−4
y
4
2
4. BC
−4
2
4x
10. NO
12. c and d
15. A, H, I M, O, T, U, V, W, X, Y
13.
16. ÒOH MOM MY MOUTH TOO HOT Ó
14.
■ Lesson 11.4
16.
1. 908
2. 1808
4. 808 clockwise
3. 908
5. 1208 counterclockwise
6. 358 counterclockwise
17.
18.
7. DE
8. KF
11. nHAB
10. OQ
13.
19. 16
1. X9 5 s23, 24d, Y9 5 s21, 22d,
Z9 5 s24, 21d
2. X9 5 s3, 4d, Y9 5 s1, 2d, Z9 5 s4, 1d
3. X9 5 s3, 24d, Y9 5 s1, 22d, Z9 5 s4, 21d
4. X9 5 s3, 24d, Y9 5 s1, 22d, Z9 5 s4, 21d
142
Y
X′
X
A′
15.
Z
O
B′
■ Lesson 11.3
12. QLMO
14.
B
A
20. 9
9. PK
O
Y′
Z′
L
K
M
N
K′
N′
L′
O
M′
Passport to Algebra and Geometry
15.
■ Lesson 11.5
7. m/J 5 53.38; JL 5 !101
1. b.; 5 units left and 6 units up.
2. c.; 3 units left and 5 units down.
3. a.; 5 units left and 4 units down.
4. c
5. a
7.
8.
C′
B′
A′
C
A
tan J 5
C′
1. a and c
5
4. Yes, 4
2. a and c
3. a and b
5. No
6.
AB BC CD DA
(or reciprocals)
5
5
5
JK
KL
LM
MJ
7.
2
1
8. a. 16,
b. 17,
9. L
3 20
10. 1 , 3
4 3
11. 1 , 2
3
12. 2 , 2
1. 5.8 ft high, 5.5 ft wide, 12.8 ft long
3. < 616 m
5. < 4.8 acres
4. < 19,360 m 2
6. < 278 miles
yd wide by 3 yd long
2
2
8. 346 3 yd, 83 yd
1
10. 13 in. by 3 in.
9. 40 times longer
11. Yes
12. 7 ft 6 in.
■ Lesson 11.8
22
< 0.940
1.
!548
8
< 0.342
3.
!548
5.
11
4
5 2.75
6.
8
< 0.342
2.
!548
22
< 0.940
4.
!548
4
11
sin A 5 15
17
8
sin B 5 17
8
cos A 5 17
cos B 5 15
17
tan A 5 15
8
8
tan B 5 15
9.
N
5 0.36
10.
N
25
43
4
c. 13
■ Lesson 11.7
2. < 80 ft
< 1.34
8. m/B 5 28.18; BC 5 15
■ Lesson 11.6
7.
6
6
< 0.597
!101
!65
< 0.802
cos L 5
!101
6
tan L 5
< 0.744
!65
C
C′
10. ANGEL
1
13
!65
< 0.597
sin L 5
C
B
B′
A′
!101
A
B
A
9.
6
cos J 5
B
< 0.802
!101
6. b
B′
A′
!65
sin J 5
M
7
O
24
M
27
O
11. x
808
408
208
108
58
18
sin x
0.985
0.643
0.342
0.174
0.087
0.017
tan x
5.671
0.839
0.364
0.176
0.087
0.017
12. As x gets smaller the values of sin x and tan x
get closer.
13. As x gets smaller, the hypotenuse and the
adjacent side become closer to the same length.
Therefore, the ratios become closer.
14. and 15.
Length of
guy wire (ft)
50
100
150
200
Vertical distance
to guy wire (ft)
25
50
75
10
sine ratio
25
50
50
100
75
100
100
200
16. The sine ratio of opposite side to the
hypotenuse remains constant.
Passport to Algebra and Geometry
■ Lesson 11.9
4. 15.49
1. 401.9 cm 2
2. 88.0 in.2
6. 5.71
4. 251.2 cm 2
5. 156 m 2
8. m/R 5 618
p 5 6.65
q 5 13.72
7. 263.8 m 2
2. 0.5446
3. 0.9998
5. 9.54
7. m/N 5 488
o 5 20.07
n 5 22.29
9. m/V 5 288
t 5 15.05
s 5 17.04
11. < 184 ft
10. < 2145 ft
■ Lesson 12.4
1. 216 cm3
4. 4676 cm 3
2
1. 38.3 in., 116.8 in.
2
2. 6.9 in., 3.8 in.
2
3. 8.8 ft, 6.2 ft
4. 89.2 in., 633.1 in.
5. 15.3 in., 30.6 in.
3 in.
1 ft
4 in.
3 in.
3 in.
5 in.
16 in.
11. Each pillar requires 48 in.3. All four require
192 in.3.
■ Lesson 12.2
2. Cylinder
3. Cone
5.
■ Lesson 12.5
1. 50.24 m3
4. < 3679.69 cm3
5. 56.52 mm3
6. 628 ft3
7. 1017.36 in.3
7.
b. 12 vertices,
11. a. 5 faces,
b. 6 vertices,
b. 16 vertices,
8. 226.08 in.3
11. 19 mm
9. 22 in.
12. 2.5 ft
13. r 5 3.5 in., h 5 2 in., V 5 76.93 in.3,
The radius of the cylinder is half of the width
of the base of the prism. The height of the
cylinder and prism are the same.
Extra space 5 119.07 in.3
9.
10. a. 8 faces,
2. 49,062.5 in.3
3. 803.84 in.3
10. 7 cm
c. 18 edges
c. 9 edges
c. 24 edges
14. Volume 5 4421.12 in.3
Time < 36.8 minutes
■ Lesson 12.6
1. 128 cm3
3. 201.0 m3
144
9. V 5 108 in.3
10. V 5 96 in.3
12. Yellow area < 12.6 in.2,
red area < 100.5 in.2,
blue area < 201 in.2
12. a. 10 faces,
6. 18 cm
8. V 5 128 in.3
8 in.
11. Middle radius 5 6 in.,
8.
5. 16 in.
4 in.
10. 85,486.5 ft
6.
3. 360 m3
6. 9.2 cm, 18.4 cm
2
4.
2. 90 in.3
7. 10 m
8. 28.5 in.2
9. 518.1 ft
9. 126 in.2
12. Answers may vary slightly. < 753.6 mm 2
2
1. Prism
8. 54 in.2
11. 126 in.2
■ Lesson 12.1
7. 29.4
6. 178 ft2
10. No, where the faces meet, the surface area has
been eliminated.
12. < 499 ft
cm 2
3. 33.5 in.2
2. 160 in.3
4. 5887.5 cm 3
Passport to Algebra and Geometry
1. 1.8807
■ Lesson 12.3
5.
6.
3 cm
4 in.
3 in.
5 cm
5 cm
V 5 25 cm
V < 37.68 in.
3
3
7. 682.7 cm3
8. 962.9 cm3
x
28
24
0
4
8
y
9
6
3
0
23
9. 24 in.3
10. Yes, volume of cone < 150.72 yd3.
x
26
24
22
0
2
4
6
y
8
7
6
5
4
3
2
11. 6,250,000 tons
12. No, each cone requires < 5.02 grams. For
twelve the jeweler would need < 60.24 grams.
7. Yes, for each 1 unit increase in x, there is a
corresponding 4 unit increase in y.
■ Lesson 12.7
8. Yes, for each 1 unit decrease in x, there is a
corresponding 3 unit decrease in y.
1. 4.5p < 14.1 in.3
2. 166.6p < 523.3 cm
1
9. 3x 1 2 y 5 10,
Answers vary: s0, 20d, s1, 14d, s2, 8d
3
3. 221.83p < 696.6 in.3
10. x 2 4y 5 212,
Answers vary: s24, 2d, s0, 3d, s4, 4d
4. 3.6586p < 11.5 m3
5. 2.61 3 1011, 1.46 3 1010, 2.23 3 1011,
3.93 3 1010, 3.65 3 1014, 2.21 3 1014,
1.75 3 1013, 1.53 3 1013, 1.51 3 109
11. b, Answers vary: s80, 75d, s100, 55d, s90, 65d
12. c, Answers vary: s110, 70d, s100, 80d, s90, 90d
13. a, Answers vary: s70, 20d, s10, 80d, s30, 60d
6. 38.1 minutes
7. < 385,173.3 ft3
14. 1920
8. < 41,809.2 cm3
9. 20 mm, 20p mm, 1.333.3p mm3 or
4000
3 p
mm3
17. 2700
2. a
3. c
4. Yes
5. Yes
11. 5 yd, 10 yd, 10p yd
6. No possible solution: s24, 24d
■ Lesson 12.8
8.
1. Yes, 2:1
2. Yes, 2:3
3. Not similar
6. 324 cm3, 1:3
−4 −2
9. 108
10. 288
cm2,
72
in.3,
240
−4 −2
−2
4x
2
675
cm3,
in.2,
18
10.
11.
y
1125 in.
cm2,
−4 −2
2
4x
y
x
2
−2
−4
3
79.39 ft
12.
■ Lesson 13.1
1. Yes
4
2
2
3.75 cm3
12. 113.04 in.3, 7234.56 in.3
13. 267.95
4x
3
11. 50 cm3, 1350 cm2
ft3,
2
7. 243 ft2, 182.25 ft3
8. 533.8 in.2, 942.0 in.3, 4804.2 in.2, 25,434 in.3
in.2,
y
2
2
5. 2432p in.2, 15360p in.3
7. Yes
9.
y
4
4. 256 in.2, 224 in.3
16. 60
■ Lesson 13.2
1. b
10. 18 in., 36 in., 17,496p in.3
15. 2340
2. No
13.
y
y
6
3. Yes
4
(2, 4)
4
2
x
23
22
21
0
1
2
3
y
27
26
25
24
23
22
21
Passport to Algebra and Geometry
x
−2
2
4
−8 −6 −4
(−2, −2)
2x
6
14. c 5 3
15. c 5 26
16.
■ Lesson 13.4
1. Falls to the right
5. m 5 26 is steeper.
2
6. m 5 5
10 15 20 25 30 40
Altitude (in thousands of feet)
6
4
6.
2
y
−2
4x
x
8. d
4x
9. c
5
12. m 5 2 2
y
−4
(−2, −1) −2
4x
2
(−1, −2)
−6
1
13. m 5 3
14
14. m 5 17
2
x
(0, −6)
8
15. m 5 15
5
16. m 5 2 12
17. m 5 15
18. m 5 43
8
↔ ↔ ↔
↔
19. MN i XY, m MN 5 3 5 m XY
↔ ↔ ↔
↔
20. MN yi XY, m MN 5 12 , m XY 5 2 12
↔ ↔ ↔
↔
21. MN yi XY, m MN 5 5, m XY 5 15
↔ ↔ ↔
↔
22. MN i XY, m MN 5 23 5 m XY
4
2
4x
2
(−3, −2)
2
2x
−2
2
y
−4 −2
−2
−2
y
−4
−2
−6
11. m 5 0
−4 −2
−2
2
(−3, 0)
2
−4
(0, 4)
2
4
3. x-intercept: 2, y-intercept: 4
5.
4
(2, 6)
(−3, 4)
2. x-intercept: 2, y-intercept: 24
y
y
y
6
1. x-intercept: 23, y-intercept: 3
4.
3
8. m 5 2 5
4
10. m 5 3
h
■ Lesson 13.3
10. a
11. x-intercept: 1.98, y-intercept: 4.25
12. x-intercept: 2.81, y-intercept: 210.25
■ Lesson 13.5
14. s0, 16,500d, After 0 years of ownership the car
has value \$16,500. s11, 0d, The car has \$0
value after 11 years.
2. m 5 2 12 ,
y-intercept: 2
1. m 5 2,
y-intercept: 4
6
13. s0, 32d, 08C is equivalent to 328F.
s217.7, 0d, 08F is equivalent to 217.78C.
146
5
7. m 5 2 6
2
9. m 5 5
The points are close to being linear, but not
exactly. The change in altitude is 5000 feet
while the speed of sound drops 19 feet per
second, then 20 feet per second, then 20, then
21, then 21, then 20 and lastly 22. The change
is not exactly uniform, but very close.
7. b
4. m 5 4 is steeper.
3. Horizontal
5
−4
2. Rises to the right
Speed of sound
(in feet per second)
v
1125
1100
1075
1050
1025
1000
975
y
y
4
4
−4
−2
2
x
−2
−2
2
4
x
Passport to Algebra and Geometry
3. m 5 3,
y-intercept: 22
4. m 5 24,
y-intercept: 7
■ Lesson 13.6
1.
90 s
y
y
86
Scores
8
2
6
−4 −2
−2
2
4x
82
78
74
70
−6 −4 −2
1
5. m 5 2 10
,
y-intercept: 0
1 2 3 4 5 6 7 8 9
Hours
6. m 5 22,
y-intercept: 9
y
12
6
2
x
2
2.
8
−6
4
−4
−4
Wind chill
20
10
x
−10
4
h
For 9 hours of practice the estimated score is
approximately 70.
y
10
−6
66
4x
8 12
−20 −10
Actual
temp.
10 20 30
−20
7. c
8. a
9. d
1
3;
11. False, m 5
10. b
y-intercept: 2 43
13. False, m 5 2 32 , falls to right
14. True, m 5
origin.
1
3,
rises to right and passes through
15. m 5 1.79; y-intercept: 42.76
17. 57.08 pounds
At a temperature of 208F the wind chill factor
is approximately 38F. At a temperature of 108F
the wind chill factor is approximately 288F.
3. a. Verbal Model:
C
0.25 3
3
60
Number of
quarters
Number
of dimes
1 0.10
5 50
50
0.25q 1 0.10d 5 50
or
25q 1 10d 5 5000
Algebraic
Model:
40
30
20
10
1 2 3 4 5 6 7 8 9 t
Year
1
19. y 5 2 x 1 2
b. q
200
190
160
140
100
d
0
25
100
150
250
q
80
60
40
20
0
d
300
350
400
450
500
20. y 5 3x 2 1
21. y 5 23x 2 3
q
200
Quarters
18.
Consumption (in pounds)
16. 1.79 pounds
−50
12. True
150
100
50
50 150 250 350 450 d
Dimes
Passport to Algebra and Geometry
3. c. s0, 200d 0 dimes and 200 quarters totals
\$50.
s500, 0d 500 dimes and 0 quarters totals
\$50.
10.
y
10
6
2
−6
Sales of sale
4. a. 0.03 3 priced goods 1 0.04
3
Sales of regular
priced goods
6
−6
5 \$250 commission
Possible solutions: s0, 4d, s0, 5d, s3, 6d
11.
0.03s 1 0.04r 5 250
b. s
x
2
0
1000
2000
3000
4000
r
6250
5500
4750
4000
3250
s
5000
6000
7000
8000
8333.33
r
2500
1750
1000
250
0
y
Sales of regular priced
1
6500
−4 −2
−2
2
4x
Possible solutions: s21, 21d, s22, 0d,
s23, 26d
r
12.
y
2
5500
4500
−2
3500
2
2500
−2
1500
−4
4x
500
s
c. s0, 6250d \$0 sales of sale priced goods 1
\$6250 of sales of regular priced goods totals
\$250 commission.
s8333.33, 0d \$8333.33 sales of sale priced
goods 1 \$0 of sales of regular priced goods
totals \$250 commission.
5. a. The times are decreasing almost linearly.
b. The pattern is close to linear. If the pattern
continues in 2000, the winning time could
be approximately 48 seconds.
Possible solutions: s0, 23d, s1, 24d, s2, 25d
13. b 1 2g < 45
14. P ≤ 400 or 2l 1 2w ≤ 400
15. d 2 c ≥ 42
16. j 1 p > 70
17. a. 625a 1 500r ≥ 25,000
b.
50
40
30
20
10
r
5 10 15 20 25 30 35 40 a
All terrain bikes
■ Lesson 13.7
1. Yes
2. No
3. No
5. Yes
6. Yes
7. b
4. Yes
8. c
9. a
c. Possible solutions: s0, 50d, s10, 40d,
s20, 28d, s30, 15d, s40, 0d
18. y < 2x 1 1
19. y ≥ 2x
20. y < 2x 2 2
148
Passport to Algebra and Geometry
3000
5000
7000
Sales of sale priced
Racer bikes
1000
■ Lesson 13.8
3.
y
Frequency
1. Estimates vary, !72 < 8.49
2. Estimates vary, !80 < 8.94
3. Estimates vary, !73 < 8.54
4. Estimates vary, s 2 , 2 d
4
3
2
1
7 1
5. Estimates vary, s 2 2 , 0d
5
1.0-1.9 2.0-2.9 3.0-3.9
Number
6. Estimates vary, s 2 2 , 2 2 d
1
1
7. Center at s0, 0d, radius < 4.1
8. WY 5 XZ 5 !40 < 6.32
9. b.
■ Lesson 14.1
1. 31, 30.5, 30
3. 9, 9, 8
2. 17.6, 17.45, no mode
4. 47, 48, 48
6. 12.8, 14, 14
5. 20
8.–10. Measures and explanations vary.
12. < 2.8, 3, 3
11. 5
13. Possible answer: The mode would be the best
measure because the comparison was one of
quantity.
14. 71,000; 65,500; 96,000
|
5. 0.39
0.38
0.37
0.36
0.35
0.34
0.33
0.32
0.31
6.
0
8
133468
067899
133
233679
99
8
y
6
Frequency
■ Lesson 14.2
1. 30, 42, 43, 52, 53, 53, 54, 61, 67, 67, 68, 70,
71, 72, 72, 73
5
4
3
2
1
y
.310
.330
5
Frequency
x
4. 6
002
5
011133
4
123779
3
0233345667999
2
0033445567889
1
236677899
6 0 represents 60.
15. Possible answer: The median because the very
high priced homes distort the mean.
Group #1
Group #2
5
.350
.370
Batting Average
.390
x
■ Lesson 14.3
4
3
1. 1 and 40
2
3. 75%
1
6.
1
30 35 40 45 50 55 60 65 70 75 x
Number
2. Group #1: 2.6, 2.7, 2.8, 2.9, 3.3, 3.5, 3.5
Group #2: 1.9, 2.0, 2.1, 3.8, 3.8, 3.9
Passport to Algebra and Geometry
2. 7, 18 and 29
4. 25%
16
5. 50%
34
99
82
8.
80
88
81
84.5
87
9. 23y3 2 2y 1 10, 23y3, 22y, 10
9.
Winning Scores
55
14
30
38
10
14
12. 215x2 1 11
13.
14. t
Losing Scores
3
11. z 4 2 7z 2 1 z
19
11. Data can vary. Possible real-life situations:
exam scores with extra credit, golf scores, or
■ Lesson 14.4
3
5
6
,
23
21
15
3
2
1
2
3
4
5
h
1438
1390
1310
1198
1054
t
6
7
8
9
10
h
878
670
430
158
2146
43
26 23
8 , 29
25
8
10
0
29
15. 878 ft
16. Between 9 and 10 seconds
17. 54 ft, 2262 ft; It takes between 10 and 11
seconds for the penny to strike the ground.
■ Lesson 14.6
29
3
43
4
3
5
9
15
5
,
2. 3
6
14 3 212
34
1
2
0
5
,3
3. 3
4
17 23 11
23
4.
2 17
31
0
1.
9
19 2
5m
1.
24x3 1 2x2
24
1 2x 1 8
123x3
27x 1
3
2 210
3
7
4
4
2.
1 2x 1 4
2x2
3x3 1 2x2 2 6x 1 7
2 s2x3 2 6x2 2 4x 2 8d
x3 1 8x2 2 2x 1 15
3. 5x2 1 x 2 10
3
5. a 5 2 , b 5 6, c 5 3, d 5 4
4. 2k3 2 3k2 1 2k 1 12
5. 4w3 2 w2 2 2w 2 18
6. 22d 4 2 d 3 2 9d 2 2 6d 2 18
7. 6x3 2 13x2 1 12x 2 5
3
43
635 758 215 295
8. 785 823 , 293 320
814 730 345 292
8. 3y 4 2 17y 3 2 13y 2 1 12y 2 21
4
9. 216x 1 23
11. w 2 1 11w 2 8
3
12. x3 1 x2 1 4x 2 9
13. 3x2 1 9x 2 34, 230
9. Stand 1 - August
Stand 2 - July
420 463
10. 492 503
470 438
10. 29k2 2 14k 1 18
16. 23x2 1 36x 1 80, 161
15. 7x2 1 11x, 96
4
14. x2 1 7x 1 4, 124
■ Lesson 14.7
1. 12x3 2 6x
2. 23t 5 2 2t 3 1 3t 2
3. 6w5 2 18w3 2 6w
4. 212c 4 1 24c 2
11. Stand 2 - \$1404 profit
5. 26x 4 1 6x3 2 12x 2 1 15x
■ Lesson 14.5
6. 2n7 1 3n6 2 2n5 1 6n3
1. Yes, a trinomial
2. Yes, a binomial
3. Not a polynomial
4. b
5. c
8. 6x 1
150
1 2
2x
6. a
2 2x,
8. 218k 4 1 12k 2 1 42k
9. 3p4 2 2p3 1 6p2
10. I: 4x2 1 3x, II: 10x2 2 20x, III: 4x2 1 3x
7. 22z3 1 14z2 1 3z, 22z3, 14z2, 3z
4
7. 7z3 2 3z2 1 2z
6x 4, 1 x2,
2
22x
11. 18x2 2 14x
12. 12 s2xdfs5x 2 10d 1 s13x 2 4dg 5 18x2 2 14x
Passport to Algebra and Geometry
24
10. 22x2 1 10x
13. They are equivalent.
14. nsn 2 3d 5 n2 2 3n
15. x2s2x 1 5d 5 2x3 1 5x2
16. 12 s5xds6x 1 2d 5 15x2 1 5x
17. 150x3 1 50x2
18. 220x2 1 40x
19. V 5 4500 cm2; SA 5 2100 cm2
■ Lesson 14.8
1. s3x 1 5ds2x 1 4d 5 s3x 1 5ds2xd 1 s3x 1 5ds4d
5 6x2 1 10x 1 12x 1 20
5 6x2 1 22x 1 20
2. 5x2 1 11x 1 2
3. 3x2 1 19x 1 20
4. 2x2 1 15x 1 28
5. 12x2 1 30x 1 12
6. 2x2 1 17x 1 36
7. 15x2 1 19x 1 6
8. 12x2 1 60x 1 72
9. 20x2 1 91x 1 99
10. 42x2 1 142x 1 120
11. x2 1 15
2x 1 9
12. 5x2 1 35
2 x 1 15
13. 6x2 1 11x 1 4
14. x2 1 14x 1 30
15. 8x 1 18
16. s4x 1 2d by s3x 1 2d
Area 5 12x2 1 14x 1 4
17. s4x 1 5d by s3x 1 4d
Area 5 12x2 1 31x 1 20
Passport to Algebra and Geometry