68 Chapter 1 The Set of Real Numbers 78. Each month, Jared makes credit card payments of $115, $63, and $95. He also makes a student loan payment of $77 and another loan payment of $100. His monthly take-home pay is $2000. a. Use the definition given in Exercise 77 to determine Jared’s debt-to-income ratio. 0.225 b. To obtain a loan for a new home theater system his debt-to-income ratio must be less than 0.15. Does he 79. The area of a rectangle is given by where is the length of the rectangle and A /w, / P 2/ 2w 57,600 ft2 80. The perimeter of a rectangle is given by . Find the perimeter for the V /wh, / 25 yd 2 yd 20 yd w is the width. Find the area for the rectangle shown. rectangle shown. 1040 ft 81. The area of a trapezoid is given by 1b1 b22h, A b1 b2 12 where and are the lengths of the two parallel sides and h is the height. A window is in the shape of a trapezoid. Find the area of the trapezoid with dimensions shown in the figure. 21 ft2 b2 6 ft h 3 ft b1 8 ft 82. The volume of a rectangular solid is given by where is the length of the solid, w is the width, and h is the height. Find the volume of the box shown in the figure. 1000 yd3 Concept 4: Translations For Exercises 83–94, translate each English phrase into an algebraic expression. (See Example 6.) 83. The product of 3 and x 84. The sum of b and 6 85. The quotient of x and 7 86. Four divided by k 87. The difference of 2 and a 88. Three subtracted from t 89. x more than twice y 90. Nine decreased by the 91. Four times the sum of x and 12 product of 3 and p 92. Twice the difference of x and 3 93. Q less than 3 94. Fourteen less than t For Exercises 95–102, translate the English phrase into an algebraic expression. Then evaluate the expression for (See Example 7.) x 4, y 2, and z 10. 95. Two times y cubed 96. Three times z squared 97. The absolute value of the difference of z and 8 98. The absolute value of the difference of x and 3 0z 8 0; 2 0x 3 0; 1 99. The product of 5 and the square root of x 100. The square root of the difference of z and 1 51x; 10 1z 1; 3 101. The value x subtracted from the product 102. The difference of z and the product of x and y of y and z yz x; 16 z xy; 2 Expanding Your Skills For Exercises 103–106, use the order of operations to simplify the expressions. 103. 104. 105. 106. 1 04 02 22 1144 1 4 5 29 02 0 2 2 13 010 0 02 0 49 1 219 23 24 25 35 3x b 6 x 7 or x 7 4 or 4 k 2 a t 3 k 2y x 9 3p 41x 122 21x 32 3 Q t 14 2y3; 16 3z2; 300 160 ft 360 ft meet this criteria? No. 0.225 0.15 Writing Translating Expression Geometry Scientific Calculator Video
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