Section 1.3 The Order of Operations, Algebraic Expressions, and Equations 39 48. 5x - 2 x for x = 1, 2, 3, and 4 49. x + 3 x - 1 for x = 2, 3, 4, and 5 50. x + 1 x - 2 for x = 3, 4, 5, and 6 Evaluate each expression for the given values of the variables. (See Objective 3.) 51. 2x + 3y for x = 0 and y = 2 52. 4x + y for x = 2 and y = 0 53. y2 - y1 x2 - x1 for x1 = 2, x2 = 5, = 4, and y2 = 6 y1 54. y2 - y1 x2 - x1 for x1 = 0, x2 = 3, y1 = 2, and y2 = 7 55. 1 2 bh for b = 4 and h = 5 56. 1 2 bh for b = 3 and h = 6 2 x 57. 2l + 2w for l = 8 and w = 10 58. 2l + 2w for l = 4 and w = 12 59. 1(x1 - x)2 + (y- y)2 for x 1, 21 21 = = 4, y1 = 12, y2 = 16 60. 1(x1 - x2)2 + (y1 - y2)2 for x1 = 0, x2 = 6, y1 = 3, y2 = 11 61. b2 - 4ac for a = 2, b = 5, c = 3 62. b2 - 4ac for a = 1, b = 6, c = 2 Determine if the given value is a solution of the equation. (See Objective 4 .) 63. 2x2 - 3x - 1 = x + 5; x = 2 64. y2 + 3y - 6 = y + 9; y = 3 65. a2 - 2a + 3 = 2a + 8; a = 5 66. 3b2 - 6b - 10 = 5b - 6; b = 4 67. 9x - 6(x - 1) = 4x + 2; x = 3 68. 4z - 2(z + 1) = z + 2; z = 5 69. 6y - 2(y - 3) = y + 9; y = 1 70. 8z - 4(z + 1) = 2z + 8; z = 6 Translate each phrase into an algebraic expression. Let x represent the unknown number. (See Objective 5.) 71. The sum of a number and 4 72. The sum of a number and 12 73. 2 more than three times a number 74. 6 more than four times a number 75. The difference of a number and 9 76. The difference of a number and 15 77. 3 less than four times a number 78. 3 decreased by twice a number 79. The product of a number and 10 80. The product of a number and 7 81. The product of 3 and the sum of a number and 15 82. The product of 4 and a number increased by 6 83. The sum of four times a number and 3 84. The sum of twice a number and 4 85. Twice the difference of a number and 7 86. Twice the difference of a number and 3 87. The quotient of three times a number and 4 88. The quotient of four times a number and 5 Write an algebraic expression that represents each unknown quantity. (See Objective 6.) 89. Shanika invested money in two different accounts. She invested a total of $5000. If x represents the amount she invested in the first account, write an expression that represents the amount she invested in the second account. 90. David invested money in two different accounts. He invested a total of $2000. If x represents the amount he invested in the first account, write an expression that represents the amount he invested in the second account. 91. In a rectangle, the length is three less than twice the width. If w represents the width, write an expression that represents the length of the rectangle. 92. In a rectangle, the width is four more than the length. If l represents the length, write an expression that represents the width of the rectangle. 93. In 2011, Oprah Winfrey and Tiger Woods were both among the 100 highest paid celebrities. Oprah Winfrey was paid $215 million more than Tiger Woods. If x represents the amount Tiger Woods was paid in millions, write an algebraic expression that represents how much Oprah Winfrey was paid. (Source: http://www.forbes.com) 94. In 2011, pop stars Lady Gaga and Justin Bieber were among the 100 highest paid celebrities. Justin Bieber was paid $37 million less than Lady Gaga. If x represents the amount Lady Gaga was paid in millions, write an algebraic expression that represents how much Justin Bieber was paid. (Source: http://www.forbes.com) Solve each problem. (See Objective 6.) 95. Find the perimeter of the Lincoln Memorial Reflecting Pool in Washington, D.C. The reflecting pool is approximately 2029 ft long and 167 ft wide. 96. The perimeter of a pentagon is five times the length of a side of the pentagon. If each outside wall of the Pentagon is 921 ft long, what is the perimeter of the Pentagon?
hendricks_beginning_intermediate_algebra_1e_ch1_3
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