349 Answers to Chapter 4 Exercises Exercise Set 4.1 1. –6 2. 7 3. 53 4. 49 5. –180 6. –225 7. 120 8. 135 9. –375 10. 300 11. –270 12. 675 13. 16 14. –16 15. 105 16. 165 17. –285 18. –1035 19. ! 25 69 20. 4 21. undefined 22. 5 2 23. ! 15 4 24. undefined 25. X = 31 26. Y = !4 27. Y = !91 28. X = !13 29. W = !9261 30. W = !576 31. W = 176 32. W = 216 33. M = ! 1 48 34. M = ! 7 72 35. M = ! 7 192 36. M = ! 17 240 37. Q = 0 38. Q = 0 39. Q is undefined 40. Q is undefined 41. ! 5 3 42. 2 43. 1 44. 6 45. ! 31 6 46. ! 11 6 47. ! 23 36 48. ! 23 18
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Answers to Chapter 4 Exercises - The First Step to Success · PDF file349 Answers to Chapter 4 Exercises Exercise Set 4.1 1. –6 2. 7 3. 53 4. 49 5. –180 6. –225
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25. X = 31 26. Y = !4 27. Y = !91 28. X = !13 29. W = !9261 30. W = !576 31. W = 176 32. W = 216
33. M = !1
48 34. M = !
7
72
35. M = !7
192 36. M = !
17
240
37. Q = 0 38. Q = 0 39. Q is undefined 40. Q is undefined
41. !5
3 42. 2
43. 1 44. 6
45. !31
6 46. !
11
6
47. !23
36 48. !
23
18
350
49. !3
2 50. !
5
3
51. !1
7 52. !
8
25
53. 7
30 54. !
5
3
55. P = 48 56. P = 64 57. P = 26.6 58. P = 36.6
59. P = 281
2 60. P = 22
5
6
61. A = 50.24 62. A = 452.16 63. A = 4.5216 64. A = 7.065 65. S = 125.6 66. S = 150.72 67. A = 84 68. A = 180 69. A = 36.55 70. A = 66.04
71. A = 312
3 72. A = 26
1
4
73. A = 1,632.96 74. A ≈ 2,809.86 75. A ≈ 3,401.22 76. A = 16,105.1 77. A ≈ 50,569.47 78. A ≈ 291,911.39 79. A ≈ $10,766.95 80. A ≈ $18,726.11 81. C = 194.05 82. C = 425.6 83. B = 72.85 84. B = 128.05 85. V ≈ 2482.7 cubic inches 86. V ≈ 8908.66 cubic inches 87. C = 15° 88. C = 30° 89. C = –40° 90. C = –25° 91. F = 86° 92. F = 113° 93. F = –4° 94. F = –40°
95. P = 512019683
! 0.2601 96. P = 15128
! 0.1172
97. P = 7
32! 0.2188 98. P = 448
6561! 0.0683
99. P ≈ $6,304.83 100. P ≈ $4,961.36 101. F ≈ $13,728.59 102. F ≈ $29,242.38 103. F ≈ $66,666.94 104. F ≈ $139,314.61
Exercise Set 4.3 1. x = !8 2. x = !6 3. x = 3 4. x = 5 5. y = !9 6. y = !13 7. a = !7 8. a = !5 9. v = !4 10. v = !5 11. b = 4 12. b = 5 13. x = !7 14. x = !10
353
15. x = !5 16. x = !5
17. x = !1
6 18. x = !
5
12
19. x = !1
2 20. x = !
1
4
21. y = !2.03 22. y = !4.32 23. t = !3.43 24. t = !2.28 25. x = !7 26. x = !16 27. y = !15 28. y = 12 29. s = 8 30. s = 11
31. t = !5
2 32. t = !
11
2
33. b = !9
2 34. b = !
14
3
35. a =9
2 36. a =
1
3
37. x = !18 38. x = 18 39. x = 12 40. x = !12
41. y =9
10 42. y =
5
3
43. a = !2
3 44. a =
4
3
45. x = !15 46. x = !28 47. x = 54 48. x = 36 49. x = !12.5 50. x = !22.8 51. y = !5.4 52. y = !16.9 53. x = 6 54. x = 5 55. y = 5 56. y = 5 57. a = !3 58. a = !5 59. b = !5 60. b = !4 61. s = 5 62. s = !4 63. t = 4 64. t = 6
65. u =7
3 66. u =
5
4
67. v = !7
2 68. v = !
8
3
69. x =1
2 70. x =
4
3
354
71. y = !3
2 72. y = !
1
4
73. x = 6 74. x = !10 75. y = 12 76. y = 12 77. a = 8 78. a = 30 79. x = !8 80. x = !21 81. y = !16 82. y = 30 83. a = 8 84. a = 12 85. b = !20 86. b = !30 87. x = –20 88. x = –11 89. x = 11.8 90. x = 6
91. x = !9
2 92. x = 3
93. y = 4 94. y = 2
95. a = 2 96. a =7
2
97. b =13
4 98. b =
17
2
99. s =10
9 100. s = 2
101. t = 177
102. t = 65
Exercise Set 4.4 1. x = 3 2. x = 3 3. x = !4 4. x = !8 5. y = !7 6. y = !7 7. y = !3 8. y = !3 9. a = !5 10. a = !5
11. a = 5 12. a =7
2
13. b =8
3 14. b =
5
2
15. any number solution 16. no solution 17. no solution 18. any number solution
19. s = !1 20. s = !3
2
355
21. t = 11 22. t = !4
23. t =5
2 24. t =
18
5
25. x =9
8 26. x =
3
4
27. y =6
5 28. y = 3
29. s =15
8 30. s =
25
2
31. t = !13
4 32. t = 3
33. a = !7
2 34. a = !
13
4
35. b = !3 36. b = 3
37. r = !9
2 38. r = !
11
4
39. t = 7,000 40. t = 10,000 41. x = 24 42. x = !1 43. y = 3 44. y = !2
45. a = !4 46. a = !15
2
47. b = !8
9 48. b = !
5
2
49. s = !6
11 50. s =
13
12
51. any number solution 52. no solution 53. no solution 54. any number solution
55. v =9
2 56. v = !
9
5
57. w = 2 58. w = !5 59. x = !5 60. x = !16 61. r = !4 62. r = 4 63. no solution 64. any number solution
65. a =7
8 66. a = !1
67. b = 11 68. b =1
6
356
69. v = !6 70. v =14
13
71. s =15
8 72. s = 0
73. g =9
13 74. p = !
13
4
75. x = !3
10 76. y = !
3
4
Exercise Set 4.5 1. 8 and 26 2. 11 and 38 3. 14 and 38 4. 15 and 39 5. –7 and – 39 6. –12 and –66 7. –25 and –162 8. –15 and –85 9. –8 10. –10 11. –6 12. –12 13. 21 in. and 27 in. 14. 32 in. and 40 in. 15. 20 in. and 40 in. 16. 15 in. and 45 in. 17. width = 6 in., length = 15 in. 18. width = 7 in., length = 15 in. 19. width = 5 m, length = 8 m 20. width = 7 m, length = 12 m 21. width = 6 ft, length = 15 ft 22. width = 9 ft, length = 21 ft 23. width = 8 ft, length = 20 ft 24. width = 8 ft, length = 28 ft 25. width = 7 m, length = 20 m 26. width = 8 m, length = 21 m 27. width = 10 ft, length = 12 ft 28. width = 21 in., length = 23 in. 29. width = 21 m, length = 22 m 30. width = 49 ft, length = 50 ft 31. 55°, 60°, 65° 32. 54°, 62°, 64° 33. 30°, 60°, 90° 34. 18°, 54°, 108° 35. 70°, 70° 36. 45°, 45° 37. 59°, 60°, 61° 38. 50°, 60°, 70° 39. Kyle is 16, Travis is 12 40. Brett is 18, Lia is 13 41. Marble is 25, Frank is 15 42. Jack is 24, Jill is 16 43. Jeremy is 30, Julia is 12 44. Janice is 30, Frank is 12 45. Don is 40, Darlene is 15 46. Fran is 10, Martha is 4 47. Lia is 15 48. Brett is 20 49. Louis is 17 50. Daniel is 13 51. 200 child tickets; 400 adult tickets 52. 250 student tickets; 150 general tickets 53. 800 $25 tickets; 1,200 $40 tickets 54. 1,400 $40 tickets; 1,100 $75 tickets 55. 12,000 $30 tickets; 4,000 $40 tickets 56. 10,000 $75 tickets; 5,000 $100 tickets 57. 60,000 people 58. 70,000 people
13. P = 15.4 14. A = 200.96 15. S = 188.4 16. A = 135 17. A ≈ 5,918.41 18. A = $4875 19. C = –25° 20. F ≈ $572,066.54 21. !14x ! 5 22. !156b
2
23. !1
5a2 24. 25
36y2
25. Inverse property of addition 26. Multiplication property of zero 27. Associative property of multiplication 28. Inverse property of multiplication 29. Distributive property 30. Identity property of addition 31. !14y
2 32. !64x2y3
33. !2x ! 6y 34. !18a2b3+ 7a
3b2
35. !5x2! 3x + 4 36. !19a ! 4ab + 2b
37. !10u2!16uv ! 9v
2 38. !5
12x !
3
4xy !
5
6y
39. 42x2! 63x ! 91 40. !30a
2+ 40a + 80
41. 8.5y2! 4y !17.5 42. 35x
2! 60xy ! 40x
2y +10x
43. 53a ! 91b 44. !5y2+ 9y + 8
358
45. 1.4x ! 2y 46. 1
45a !
3
44b
47. x = !13 48. v = !9 49. b = 7 50. y = !9
51. x = 9 52. t = !20
3
53. y = !39 54. a =3
4
55. x = !4 56. a = !5 57. t = 6 58. y = 6 59. a = !12 60. b = 36 61. x = !9 62. y = 14
63. a =14
3 64. b =
13
7
65. x = !5 66. y = 2 67. s = 3 68. t = 4
69. x = 1 70. t = !15
2
71. s = !7 72. y = !7
73. x = 7 74. y =5
18
75. s = !9 76. no solution
77. u = 0 78. v = !4
3
79. 12 and 21 80. –12 81. 2 ft and 3 ft 82. width = 15 m; length = 27 m 83. width = 47 in.; length = 49 in. 84. 67°, 67° 85. Jenny is 9, Frank is 5 86. Travis is 12 87. 180 adult tickets, 120 student tickets 88. 7,000 $60 tickets; 3,000 $75 tickets 89. 24 nickels, 12 quarters 90. 10 $1 chips, 20 $5 chips, 20 $10 chips