By Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
"College Algebra" sequence is designed to provide scholars an exceptional grounding in pre-calculus themes in a common 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 motivate scholars to imagine significantly approximately mathematical thoughts. All labored examples are via Matched difficulties that toughen the techniques being taught. New to those variations, expertise Connections illustrate how thoughts 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 in order that they don't turn into calculator-dependent. additionally, each one textual content within the sequence comprises an abundance of workouts - together with quite a few calculator-based and reasoning and writing routines - and a large choice of real-world purposes illustrating how math comes in handy.
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Extra info for College Algebra, 8th Edition
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.
161ր2 and (؊16)1ր2 are not the same. ؍؊4 2. If n is even and b is negative, then b1͞n does not represent a real number. ) (؊16)1͞2 is not real. 3. If n is odd, then b1͞n represents the real nth root of b (there is only one). 321ր5 ؍2 4. 01րn ϭ 0 EXAMPLE 4 01ր9 ؍0 (؊32)1ր 5 ؍؊2 01ր6 ؍0 Principal nth Roots (A) 91ր2 ϭ 3 (B) Ϫ91ր2 ϭ Ϫ3 1ր2 (C) (Ϫ9) Compare parts (B) and (C). is not a real number. (E) (Ϫ27)1ր3 ϭ Ϫ3 (D) 271ր3 ϭ 3 (F) 01ր7 ϭ 0 bar67388_chR_014-035 20 11/02/06 CHAPTER R 00:52 Page 20 BASIC ALGEBRAIC OPERATIONS MATCHED PROBLEM 4 Find each of the following: (A) 41ր2 (B) Ϫ41ր2 (C) (Ϫ4)1ր2 (D) 81ր3 (E) (Ϫ8)1ր3 (F) 01ր8 How should a symbol such as 72ր3 be defined?
2 25 2 10 24. 16114 25. 29x8y4 26. 216m4y8 4 27. 216m4n8 5 28. 232a15b10 4 29. 2 m2 10 6 30. ͙ n 5 3 31. 2 1 xy 4 32. 2 15x 3 3 33. 29x2 29x 34. 12x18xy In Problems 35–46, rationalize denominators, and write in simplified form. 35. 38. 1 215 10 25 4 36. 1 317 37. 39. 2 144 40. 41. 6x 13x 42. 44. 4 16 Ϫ 2 45. 12y 2 16y 12 16 ϩ 2 1 17 3 3 254 3 43. 2 12 Ϫ 1 46. 12 110 Ϫ 2 In Problems 47–54, write in simplified form. 5 6 7 11 47. x 2 3xy 50. 5 2 32u12v8 uv 4 2 32m7n9 2mn 3 48. 2a2 8a8b13 49. 3 4 9 3 ab 51.