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In Exercises 5–51, simplify the given algebraic expressions.
Research on a plastic building material leads to
Simplify this expression.
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Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus
- For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples. • In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2). • Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5). To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that x + 4 = (x + 2i)(x – 2i). 115. а. х - 9 116. а. х? - 100 117. а. х - 64 b. x + 9 b. + 100 b. x + 64 118. а. х — 25 119. а. х— 3 120. а. х — 11 b. x + 25 b. x + 3 b. x + 11arrow_forwardScientific Notation. In Exercises 9–12, the given expressions are designed to yield results expressed in a form of scientific notation. For example, the calculator-displayed result of 1.23E5 can be expressed as 123,000, and the result of 1.23E-4 can be expressed as 0.000123. Perform the indicated operation and express the result as an ordinary number that is not in scientific notation. 614arrow_forwardIn Exercises 15–20, simplify each expression. 15. 24 - 36 ÷ 4.3 16. (52 – 24) + [9 ÷ (-3)] (8 – 10) - (-4)² 17. - (-4) 2 + 8(2) ÷ 4 18. 7x – 4(3x + 2) – 10 19. 5(2у — 6) - (4у — 3) 20. 9х — [10 — 4(2х — 3)1arrow_forward
- In Exercises 83–92, factor by introducing an appropriate substitution. 83. 2r* – x? – 3 84. 5x4 + 2x2 3 85. 2r6 + 11x³ + 15 86. 2x + 13x3 + 15 87. 2y10 + 7y + 3 88. 5y10 + 29y – 42 89. 5(x + 1)2 + 12(x + 1) + 7 (Let u = x + 1.) 90. 3(x + 1) - 5(x + 1) + 2 (Let u = x + 1.) 91. 2(x – 3) – 5(x – 3) – 7 92. 3(x – 2) – 5(x – 2) – 2arrow_forwardIn Exercises 20–23, determine whether each statement is true or false. V3 V3 20. - 5 5 21. (x|x is a negative integer greater than -4} = {-4, –3, –2, –1} 22. -17 ¢ {x|x is a rational number} 23. -128 + (2·4) > (-128 ÷ 2) · 4arrow_forwardClassify the quadratic forms in Exercises 9–18. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P using the methods of Section 7.1. 11. 2x² + 10x1x2 + 2x3arrow_forward
- For Exercises 23–24, use the remainder theorem to determine if the given number c is a zero of the polynomial. 23. f(x) = 3x + 13x + 2x + 52x – 40 a. c = 2 b. c = 24. f(x) = x* + 6x + 9x? + 24x + 20 а. с 3D —5 b. c = 2iarrow_forwardQuestion 27 6x + 7 S- (x+2)2. 6 In x + 2 + 5(x + 2)−1 + C 6 In 1x + 21-5(x + 2)¯1 + C 5 In x + 2 + 6(x + 2)¯1 + C 5 In x + 21 - 6(x + 2)¯1 + C Evaluatearrow_forward10. Evaluate the expression (x +3)ē + (x – 3)º + (x + 2)¯³ when x = 6.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage