By Ron Larson
University Algebra with functions for company and lifestyles Sciences meets the call for for classes that emphasize challenge fixing, modeling, and real-world purposes for enterprise and the lifestyles sciences. The authors supply a company beginning in algebraic innovations and instructed scholars to use their realizing to suitable examples and functions they're more likely to stumble upon in collage or of their careers. extra know-how elements to be had via CL MATHSpace improve guide and encourage newcomers. this system addresses the desires of scholars in any respect levels--and particularly those that can have struggled in past algebra courses--offering an abundance of examples and workouts that make stronger options and make studying extra dynamic. The early creation of services in bankruptcy 1 guarantees compatibility with syllabi and offers a framework for pupil studying. non-compulsory Discovery and Exploration actions are built-in through the textual content; teachers may also choose to use graphing know-how as a device for challenge fixing and assessment or retention.
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Extra info for College Algebra with Applications for Business and the Life Sciences
1. If a ϩ c ϭ b ϩ c, then a ϭ b. 2. If ac ϭ bc and c 0, then a ϭ b. So, you can also subtract the same number from each side of an equation as well as divide each side of an equation by the same nonzero number. Calculators and Rounding The table below shows keystrokes for several similar functions on a standard scientific calculator and a graphing calculator. These keystrokes may not be the same as those for your calculator. Consult your user’s guide for specific keystrokes. Graphing Calculator Scientific Calculator ENTER ؍ ͧ؊ͨ ؉ր؊ > CHAPTER 0 yx x–1 1ր x For example, you can evaluate 133 on a graphing calculator or a scientific calculator as follows.
Use properties of rational exponents. ■ Combine radicals. ■ Use a calculator to evaluate a radical. ■ Use a radical expression to solve an application problem. Radicals and Properties of Radicals A square root of a number is defined as one of its two equal factors. For example, 5 is a square root of 25 because 5 is one of the two equal factors of 25. In a similar way, a cube root of a number is one of its three equal factors. Here are some examples. 25 ϭ ͑Ϫ5͒2 Number Equal Factors ͑Ϫ5͒͑Ϫ5͒ Ϫ5 (square root) Ϫ64 ϭ ͑Ϫ4͒3 ͑Ϫ4͒͑Ϫ4͒͑Ϫ4͒ Ϫ4 (cube root) 81 ϭ 34 3и3 и3и3 Root 3 (fourth root) Definition of nth Root of a Number Let a and b be real numbers and let n be a positive integer.
1, 3 In Exercises 9 and 10, evaluate the expression. Խ Խ ԽԽ Խ 9. com for worked-out solutions to odd-numbered exercises. In Exercises 1–6, identify the terms of the algebraic expression. 1. 7x ϩ 4 3. x2 Ϫ 4x ϩ 8 5. 2x Ϫ 9x ϩ 13 2 2. Ϫ5 ϩ 3x 4. 4x3 ϩxϪ5 6. 3x ϩ 2x Ϫ 1 4 3 In Exercises 7–10, simplify the expression. 7. ͑8 Ϫ 17͒ ϩ 3 8. Ϫ3͑5 Ϫ 2͒ 9. ͑4 Ϫ 7͒͑Ϫ2͒ 10. Ϫ5͑Ϫ2 Ϫ 6͒ In Exercises 11–16, evaluate the expression for each value of x. ) Expression Values 11. 4x Ϫ 6 (a) x ϭ Ϫ1 (b) x ϭ 0 12. 5 Ϫ 3x (a) x ϭ Ϫ3 (b) x ϭ 2 13.