By Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
"College Algebra" sequence is designed to provide scholars an excellent grounding in pre-calculus themes in a straight forward demeanour. The sequence emphasizes computational talents, principles, and challenge fixing instead of conception. Explore/Discuss packing containers built-in all through each one textual content inspire scholars to imagine severely approximately mathematical options. All labored examples are by means of Matched difficulties that toughen the techniques being taught. New to those variants, expertise Connections illustrate how recommendations that have been formerly defined in an algebraic context can also be solved utilizing a graphing calculator. scholars are consistently proven the underlying algebraic tools first so they don't develop into calculator-dependent. moreover, every one textual content within the sequence comprises an abundance of routines - together with a variety of calculator-based and reasoning and writing workouts - and a large choice of real-world functions illustrating how math comes in handy.
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Extra info for College Algebra, 8th Edition
Simplify and express answers using positive exponents. 83. (a3րnb3րm)1ր3 84. (anր2bnր3)1րn 85. (xmր4ynր3)Ϫ12 86. (amր3bnր2)Ϫ6 87. If possible, find a real value of x such that: (A) (x2)1ր2 x (B) (x2)1ր2 ϭ x (C) (x3)1ր3 x 88. If possible, find a real value of x such that: (A) (x2)1ր2 Ϫx (B) (x2)1ր2 ϭ Ϫx (C) (x3)1ր3 ϭ Ϫx 89. If n is even and b is negative, then b1րn is not real. If m is odd, n is even, and b is negative, is (bm)1րn real? 90. If we assume that m is odd and n is even, is it possible that one of (b1րn)m and (bm)1րn is real and the other is not?
Statement (A) (7x)y ϭ 7(xy) (B) a(b ϩ c) ϭ (b ϩ c)a (C) (2x ϩ 3y) ϩ 5y ϭ 2x ϩ (3y ϩ 5y) (D) (x ϩ y)(a ϩ b) ϭ (x ϩ y)a ϩ (x ϩ y)b (E) If a ϩ b ϭ 0, then b ϭ Ϫa. MATCHED PROBLEM Property Illustrated Associative (ؒ) Commutative (ؒ) Associative (ϩ) Distributive Inverse (ϩ) 2 Which real number property justifies the indicated statement? (A) 4 ϩ (2 ϩ x) ϭ (4 ϩ 2) ϩ x (B) (a ϩ b) ϩ c ϭ c ϩ (a ϩ b) (C) 3x ϩ 7x ϭ (3 ϩ 7)x (D) (2x ϩ 3y) ϩ 0 ϭ 2x ϩ 3y (E) If ab ϭ 1, then b ϭ 1րa. Z Further Operations and Properties Subtraction of real numbers can be defined in terms of addition and the additive inverse.
892 ϫ 1016 5 5 71. 2 9ϩ 1 9 3 3 72. 2 2ϩ 1 2 3 8 7 For what real numbers are Problems 73–76 true? 73. 2x2 ϭ Ϫx 74. 2x2 ϭ x 3 3 75. 2 x ϭx 3 3 76. 2 x ϭ Ϫx In Problems 77 and 78, evaluate each expression on a calculator and determine which pairs have the same value. Verify these results algebraically. 77. (A) 13 ϩ 15 (C) 1 ϩ 13 (E) 28 ϩ 160 (B) 22 ϩ 13 ϩ 22 Ϫ 13 3 (D) 2 10 ϩ 6 13 (F) 16 3 78. (A) 2 2 2 ϩ 15 (C) 13 ϩ 17 (E) 210 ϩ 184 (B) 18 (D) 23 ϩ 18 ϩ 23 Ϫ 18 (F) 1 ϩ 15 In Problems 79–82, rationalize denominators.