*********** Use the definitions of even, odd, prime, and compositive numbers to justify your answers for (a)-(c). Assume that r and s are particular integers. (a) Is Srs even? O Yes, because 8rs = 2(4rs) + 1 and 4rs is an integer. O Yes, because 8rs = 2(4rs) and 4rs is an integer. O No, because 8rs = 2(4rs) and 4rs is an integer. O No, because 8rs = 2(4rs) + 1 and 4rs is an integer. (b) Is 2r + 4s² + 9 odd? O Yes, because 2r + 4s² + 9 = 2(r + 2s2 + 4) + 1 and r + 2s² + 4 is an integer. O Yes, because 2r + 4s² + 9 = 2(r + 2s² + 4) and r + 2s² + 4 is an integer. O No, because 2r + 4s² + 9 = 2(r + 2s² + 4) + 1 and r + 2s² + 4 is an integer. O No, because 2r + 4s² + 9 = 2(r + 2s² + 4) and r + 2s² + 4 is an integer. (c) If r and s are both positive, is 2² + 2rs + s² composite? O Yes, because ² + 2rs + s² = (r + s)2 and r + s is an integer. O Yes, because r2 + 2rs + s2 = (r + s)2 and r + s is not an integer. O No, because 2² + 2rs + s² = (r + s)2 and r + s is not an integer. O No, because 2 + 2rs + s² = (r + s)2 and r + s is an integer.

*********** Use the definitions of even, odd, prime, and compositive numbers to justify your answers for (a)-(c). Assume that r and s are particular integers. (a) Is Srs even? O Yes, because 8rs = 2(4rs) + 1 and 4rs is an integer. O Yes, because 8rs = 2(4rs) and 4rs is an integer. O No, because 8rs = 2(4rs) and 4rs is an integer. O No, because 8rs = 2(4rs) + 1 and 4rs is an integer. (b) Is 2r + 4s² + 9 odd? O Yes, because 2r + 4s² + 9 = 2(r + 2s2 + 4) + 1 and r + 2s² + 4 is an integer. O Yes, because 2r + 4s² + 9 = 2(r + 2s² + 4) and r + 2s² + 4 is an integer. O No, because 2r + 4s² + 9 = 2(r + 2s² + 4) + 1 and r + 2s² + 4 is an integer. O No, because 2r + 4s² + 9 = 2(r + 2s² + 4) and r + 2s² + 4 is an integer. (c) If r and s are both positive, is 2² + 2rs + s² composite? O Yes, because ² + 2rs + s² = (r + s)2 and r + s is an integer. O Yes, because r2 + 2rs + s2 = (r + s)2 and r + s is not an integer. O No, because 2² + 2rs + s² = (r + s)2 and r + s is not an integer. O No, because 2 + 2rs + s² = (r + s)2 and r + s is an integer.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 64RE

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