A-47 Answers to Selected Exercises 85. no; It increases by almost a factor of 8. 87. a + 871b + 11.5c + 3d = 239 a + 847b + 12.2c + 2d = 234 a + 685b + 10.6c + 5d = 192 a + 969b + 14.2c + 1d = 343 88. ≥ 1 1 1 1 871 847 685 969 11.5 12.2 10.6 14.2 3 2 5 1 4 239 234 192 343¥; a ≈ -715.457, b ≈0.348, c ≈48.659, d ≈30.720 21. 512, 326 23. 51-3, 026 25. E A1, 2 3B F 27. ∅ 29. E A 4y + 7 3 , yB F 31. 51-1, -2, 326 33. 51-1, 23, 1626 35. 512, 4, 526 37. E A1 2 , 1, - 1 2B F 39. 512, 1, -126 41. ∅ 43. E A -15z - 12 23 , z - 13 23 , zB F 45. 511, 1, 2, 026 47. 510, 2, -2, 126 49. 512, 326 51. 514, 5, 626 53. 511, -2, -326 55. 511, 2, -126 57. E A - 8 7, - 9 7, - 3 7B F 59. 511, 0, 2, -126 61. ∅ 63. 5111z + 8, 4z + 1, z26 65. A = 1 2 , B = - 1 2 67. A = 1 2 , B = 1 2 69. day laborer: $152; concrete finisher: $160 71. 12, 6, 2 73. 30.4 cm3 of 2%; 9.6 cm3 of 7% 75. $5000 at 1.5%; $10,000 at 2.2%; $10,000 at 2.4% 77. 44.4 g of A; 133.3 g of B; 222.2 g of C 79. (a) 65 or older: y = 0.0018x + 0.16; ages 25–39: y = -0.005x + 0.205 (b) 5119.5652, 0.195226; 2037; 19.5% (c) The percent of people in the U.S. population aged 25–39 is decreasing, but not necessarily the number of people in this category. 81. (a) using the first equation, 245 lb; using the second equation, 253 lb (b) for the first, 7.46 lb; for the second, 7.93 lb (c) 118 lb and 66 in. 15. 3x + 2y + z = 1 2y + 4z = 22 -x - 2y + 3z = 15 17. x = 2 y = 3 z = -2 19. x + y = 3 2y + z = -4 x - z = 5 83. n T 3 28 6 191 10 805 29 17,487 100 681,550 200 5,393,100 400 42,906,200 1000 668,165,500 5000 8.3 * 1010 10,000 6.7 * 1011 100,000 6.7 * 1014 89. F = -715.457 + 0.348A + 48.659P + 30.720W 90. 323; This estimate is very close to the actual value of 320. 9.3 Exercises 1. 0 3. x2 - 12 5. -3 or 3 7. -31 9. 7 11. 0 13. -26 15. 0 17. 2, -6, 4 19. -6, 0, -6 21. 186 23. 17 25. 166 27. 0 29. 0 31. 1 33. 2 35. -144 - 8210 37. -5.5 39. -3 41. 15 43. 3 45. 0 47. 0 49. 16 51. 17 53. 54 55. 0 57. 0 59. -88 61. 298 63. 512, 226 65. 512, -526 67. 512, 026 69. Cramer’s rule does not apply because D= 0; ∅ 71. Cramer’s rule does not apply because D= 0; E A2y + 4 3 , yB F 73. 51-4, 1226 75. 51-3, 4, 226 77. Cramer’s rule does not apply because D= 0; ∅ 79. Cramer’s rule does not apply because D= 0; E A 19z - 32 4 , -13z + 24 4 , zB F 81. 510, 0, -126 83. 510, 4, 226 85. E A31 5 , 19 10 , - 29 10B F 87. W1 = W2 = 10023 3 ≈58 lb 89. 1 unit2 91. 9.5 units2 93. 19,328.3 ft2 95. E - 4 3F 97. 5-1, 46 99. 5-46 101. 5136 103. E - 1 2F 105. 51-a - b, a2 + ab + b226 107. 511, 026 109. 51-1, 226 112. 102 113. 102; yes 114. no 9.4 Exercises 1. 3x12x + 12 3. 1x + 4213x2 + 12 5. x12x2 + 122 7. 5 3x + -10 312x + 12 9. 6 51x + 22 + 8 512x - 12 11. 5 61x + 52 + 1 61x - 12 13. 4 x + 4 1 - x 15. 15 x + -5 x + 1 + -6 x - 1 17. 2 1x + 222 + -3 1x + 223 19. 1 + -2 x + 1 + 1 1x + 122 21. 1 9 + -1 x + 25 1813x + 22 + 29 1813x - 22 23. -3 5x2 + 3 51x2 + 52 25. -2 71x + 42 + 6x - 3 713x2 + 12 27. 1 4x + -8 1912x + 12 + -9x - 24 7613x2 + 42 29. x3 - x2 + -1 312x + 12 + 2 31x + 22 31. -1 x + 2x 2x2 + 1 + 2x + 3 12x2 + 122 33. -1 x + 2 + 3 1x2 + 422 35. 5x2 + 3 x + -1 x + 3 + 2 x - 1 37. -1 41x + 12 + 1 41x - 12 + 1 21x2 + 12 39. 2 x + -1 x - 1 + 3 x + 2 Chapter 9 Quiz [9.1] 1. 51-2, 026 2. E Ax, -x + 2 2 B F , or 51-2y + 2, y26 3. ∅ 4. 513, -426 [9.2] 5. 51-5, 226 [9.3] 6. 51-3, 626 [9.1] 7. 51-2, 1, 226 [9.2] 8. 512, 1, -126 [9.3] 9. Cramer’s rule does not apply because D= 0; E A 2y + 6 9 , y, 23y + 6 9 B F [9.1] 10. at home: $4328.24; away from home: $3400.76 11. $1000 at 2%; $1500 at 3%; $2500 at 4%
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