By Ron Larson

ALGEBRA AND TRIGONOMETRY: actual arithmetic, genuine humans, seventh variation, is a perfect scholar and teacher source for classes that require using a graphing calculator. the standard and volume of the workouts, mixed with attention-grabbing purposes and leading edge assets, make instructing more straightforward and aid scholars be triumphant. conserving the sequence’ emphasis on scholar help, chosen examples through the textual content contain notations directing scholars to prior sections to study innovations and abilities had to grasp the cloth to hand. The booklet additionally achieves accessibility via cautious writing and design—including examples with exact suggestions that start and finish at the related web page, which maximizes clarity. equally, side-by-side options convey algebraic, graphical, and numerical representations of the math and aid various studying types. Reflecting its subtitle, this crucial revision focuses greater than ever on displaying scholars the relevance of arithmetic of their lives and destiny careers.

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Algebra and Trigonometry: Real Mathematics Real People

ALGEBRA AND TRIGONOMETRY: genuine arithmetic, genuine humans, seventh version, is a perfect scholar and teacher source for classes that require using a graphing calculator. the standard and volume of the routines, mixed with fascinating functions and leading edge assets, make educating more uncomplicated and aid scholars prevail.

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A) [(x2y−2)−1]−1 (b) b−2 a 32. (a) 3 (5x z ) (5x z ) (4y ) (3y ) (b) 3 4 2 6 3 2 6 −3 Calculators and Exponents In Exercises 33–38, use a calculator to evaluate the expression. ) 33. (−4)3(52) 34. (8−4)(103) 35. 36 73 37. 43 − 1 32 − 2 38. 3−4 42 − 3 36. 45 93 Scientific Notation In Exercises 39–52, write the number in scientific notation. 39. 50 40. 2 41. 484 42. 525,252,118 43. 25 44. −5,222,145 45. 0002485 46. 0000025 47. 0000025 48. 000125005 49. Land area of Earth: 57,300,000 square miles 50.

3 Write the expressions (a) √ 27 and (b) √x 3y 5z in exponential form. 2 Write the expressions (c) (x − 7)−1͞2 and (d) −3b1͞3c 2͞3 in radical form. E XAM P L E 14 Simplifying with Rational Exponents 1 1 = (−2)4 16 b. (−5x 5͞3)(3x−3͞4) = −15x(5͞3) − (3͞4) = −15x11͞12, x ≠ 0 5 −32 a. (−32)−4͞5 = (√ ) −4 c. = (−2)−4 = 3 √125 = √ 6 125 = √ 6 √ (5)3 = 53͞6 = 51͞2 = √5 d. (2x − 1)4͞3(2x − 1)−1͞3 = (2x − 1)(4͞3) − (1͞3) = 2x − 1, Checkpoint c. com. Simplify each expression. a. (−125)−2͞3 x≠ b. (4x 2 y 3͞2)(−3x−1͞3y−3͞5) d.

Unless noted otherwise, when you are asked to factor a polynomial, you can assume that you are looking for factors with integer coefficients. If a polynomial cannot be factored using integer coefficients, then it is prime or irreducible over the integers. For instance, the polynomial x2 − 3 is irreducible over the integers. Over the real numbers, this polynomial can be factored as x2 − 3 = (x + √3 )(x − √3 ). A polynomial is completely factored when each of its factors is prime. So, x3 − x2 + 4x − 4 = (x − 1)(x2 + 4) Completely factored is completely factored, but x3 − x2 − 4x + 4 = (x − 1)(x2 − 4) Not completely factored is not completely factored.

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