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07/10/12 1 /MTH 098 ANSWERS TO FINAL EXAM REVIEW 3. 1 2 –52 5. 1 x=3 6. x=1 7. x = –3 8. a= 9. y= 1. x+4 1 or y = x + 2 2 2 a2 11. 9b4 13. 3a 5b2 15. a2 1 17. x −8 19. 6b2 + 11b – 10 20. 10x2 + 41x + 21 22. x2 – 49 24. y2 + 4y + 4 26. 5x2 + 5x – 3 28. –3y3 – 7y2 + 7y – 5 30. –15a5b3 32. x2 – 2x + 3 2 34. 3a – 4 + a x ( x + 4) 36. y ( x − 5) x (x + 1) 38. x + 2 40. 42. 44. 46. 48. 50. 52. 54. 56. 58. 60. 2x + 15 3x2 1 x−4 5a (a – 5) 4xy (2xy – 1) (x + 5) (x – 5) (b – 9c) (b + 9c) (x + 4) (x – 3a) (a – 7) (a + 3) (x + 7) (x – 2) x (x – 10) (x + 7) (4x – 3) (2x – 1) 2. –40 4. a = –1 3 − 3b + 10 or a = − b + 2 5 5 10. x6y8 2x5 12. y2 14. –5a2b2 3 16. 5 3x + 5 18. − x+4 2x2 – 13x + 6 16x2 – 1 9x2 – 24x + 16 5a2 – 7a – 3 x5y7 x4 + 3x3 – 2x2 –2a2 + 3a – 4 xb 35. a 3aby2 37. 8x 21. 23. 25. 27. 29. 31. 33. 39. 41. 43. 45. 47. 49. 51. 53. 55. 57. 59. 61. x( x + 2 y) 5(5x + y ) 4 + 5x x 3b + 2 b2 3 6 (x – 7x2 + 9) 4a2b (2a + 3b – ab) (3x + 8y) (3x – 8y) (a – b) (x + 2) (2y + 1) (4y + 3) (p + 8) (p – 3) a(x + 13) (x + 4)) (4x + 3) (3x – 5) 5 (5x – 1) (2x + 3) 07/10/12 2 62. (3x + 2y)2 5 ⎧ 5 ⎫ 64. x = 0, − ; ⎨− ,0⎬ 3 ⎩ 3 ⎭ 66. x = 10, –5; {–5, 10} 67. –12 68. x = 52 69. x = − 70. x ≤ 3 (–∞, 3] 63. 3a(a – 7)2 65. x = –5, 3; {–5,3} 3 2 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 71. y ≤ –4 (–∞, –4] -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 72. x ≥ 3 [3, ∞) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 73. x > –2 (–2, ∞) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 74. x < –6 (–∞, –6) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 76. –x5 78. 2xy2 80. 4 xy 3 3 y 75. 7 77. 3 3 79. 8x 2 y 5 x 1 81. midpoint = ⎛⎜ , 3 ⎞⎟ ; distance = 15 3 82. midpoint = ⎛⎜ , 0 ⎞⎟ ; distance = 5 83. midpoint = (4, 5); distance = 10 3 85. − 4 84. –3 4 86. − 3 1 88. 5 ⎝2 87. –2 1 89. 3 ⎠ ⎝2 ⎠ 07/10/12 3 2 2 90. y = − x + 2; m = − ; y-int. = (0, 2); x-int. = (3, 0) 3 3 y 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 91. 1 1 y = − x – 1; m = − ; y-int. = (0, –1); x-int. = (–3, 0) 3 3 y 5 4 3 2 1 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 5 92. y = 5x – 5; m = 1 ; y-int. = (0, –5); x-int = (1, 0) y 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 7 -2 -3 -4 -5 -6 -7 x 07/10/12 4 y 93. m = 0 7 6 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 x 1 2 3 4 5 -3 94. slope is undefined y 7 6 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 x 1 2 3 4 5 -3 95. 5 cm 96. 8 cm 97. z = 70°, x = 70°, y = 110° 98. a = 60°, b = 120°, c = 120° 99. (–3, –3) 100. Inconsistent system, no solution 101. (3, 4) 102. Dependent system, infinite solutions 103. length = 35 m 104. smaller angle = 20°, larger angle = 70° 105. smaller angle = 30°, larger angle = 150° 106. 8 lbs of sunflower seeds, 2 lbs of cracked corn 107. Area = 60 ft2 108. smaller number = 21 109. 37, 39, 41 110. $3000 @ 7.5%, $7000 @ 9% 111. 53.3 mph 112. 18 in 7 114. 1 hours 113. 114 ft 8