75) a2 19 8a 76) v2 4v 8 0 77) m2 3m 40 0 78) p2 5p 4 0 79) x2 7x 12 0 80) d 2 d 72 0 81) r2 r 3 82) y2 3y 7 83) c2 5c 7 0 84) b2 14 7b 85) 3k2 6k 12 0 86) 4f 2 16f 48 0 87) 4r2 24r 8 88) 3h2 6h 15 89) 10d 2d 2 12 90) 54x 6x2 48 91) 2n2 8 5n 92) 2t2 3t 4 0 93) 4a2 7a 3 0 94) n 2 3n2 95) (y 5)(y 3) 5 96) (b 4)(b 10) 17 97) (2m 1)(m 3) 7 98) (3c 4)(c 2) 3 Use the Pythagorean theorem and the square root property to fi nd the length of the missing side. 99) 100) a 1 b 5 1 101) 102) c 2 5 a 1 2 Write an equation, and solve. (Hint: Draw a picture.) 103) The width of a rectangle is 4 in., and its diagonal is 2113 in. long. What is the length of the rectangle? 104) Find the length of the diagonal of a rectangle if it has a width of 5 cm and a length of 412 cm. Write an equation, and solve. 105) A 13-ft ladder is leaning against a wall so that the base of the ladder is 5 ft away from the wall. How high on the wall does the ladder reach? 1 ft 5 ft Complete the square for each expression to obtain a perfect square trinomial. Then, factor. Fill It In Fill in the blanks with either the missing mathematical step or reason for the given step. 53) w2 8w Find half of the coeffi cient of w. Square the result. Add the constant to the expression. The perfect square trinomial is The factored form of the trinomial is 54) n2 n 1 2 (1) 1 2 a 1 2 b 2 1 4 n2 n 1 4 The perfect square trinomial is The factored form of the trinomial is 55) a2 12a 56) g2 4g 57) c2 18c 58) k2 16k 59) t2 5t 60) z2 7z 61) b2 9b 62) r2 3r 63) x2 1 3 x 64) y2 3 5 y Objective 5: Solve a Quadratic Equation by Completing the Square 65) What is the fi rst thing you should do if you want to solve 2p2 7p 8 by completing the square? 66) Can x3 10x 3 0 be solved by completing the square? Give a reason for your answer. Solve by completing the square. 67) x2 6x 8 0 68) t2 12t 13 0 69) k2 8k 15 0 70) v2 6v 27 0 71) u2 9 2u 72) s2 10 10s 73) p2 10p 26 74) t2 2t 9 622 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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