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In Exercises 85–116, simplify each exponential expression.
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EBK INTERMEDIATE ALGEBRA FOR COLLEGE ST
- In Exercises 7–12, describe the relationship between the two quantities.arrow_forwardConvert 8 – 7j to exponential form.arrow_forwardAmerica is getting older. The graph shows the projected elderly U.S. population for ages 65–84 and for ages 85 and older.The formula E = 5.8√x + 56.4 models the projected number of elderly Americans ages 65–84, E, in millions, x years after 2020.a. Use the formula to find the projected increase in the number of Americans ages 65–84, in millions, from 2030 to 2060. Express this difference in simplified radicalform.b. Use a calculator and write your answer in part (a) to the nearest tenth. Does this rounded decimal overestimate or underestimate the difference in the projected data shown by the bar graph ? By how much?arrow_forward
- Rewrite each of the expressions in Exercises 50–52 as thesum, difference, or multiple of logarithms.arrow_forwardIn Exercises 129–132, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 129. 9x? + 15x + 25 = (3x + 5) 130. x - 27 = (x – 3)(x² + 6x + 9) 131. x³ – 64 = (x – 4)3 132. 4x2 – 121 = (2x – 11)arrow_forwardIn Exercises 117–124, simplify each exponential expression. 9y* 117. 7x3 118. -3 + 119. -3\3 ху 120. 4,-1 -3. 121. (-4x³y$)(2x ®y5) 122. (-4x4y) (-2r'y-) 123. (3xy?)'(2x?y)2 (xy²)-{(x?y>y° 124.arrow_forward
- For Exercises 49–52, rewrite the equation so that the coefficient on x is positive.arrow_forwardIn Exercises 87–88, use the graph of f(x) = |4 – x| to solve each equation or inequality. y flx) = |4 – x| y = 53- y = 1 $ 9 10 87. 14 - x| = 1 88. 14 - x| < 5arrow_forwardIn Exercises 90–104, simplify each exponential expression. Assume that no denominators are 0. 90. (-3x")(-5x“) 91. ху 5 93. (х3) 6 92. y-7 94. (7x³y) 16y3 95. -2y10 96. (-3x)(4х 11) 12x7 97. 4x -10a b6 98. 99. (-3xy*)(2r3)° 20a 3611 1 ot * 2 101. (5x²y4)-3 100. 2-2 + 102. (3x*y 2)(-2r°y³) 3xy 5x3y 2 103. -2..3 -20xy -3 104. 10x'y-6arrow_forward
- In Exercises 132–137, factor each polynomial. Assume that all variable exponents represent whole numbers. 132. 9x2" + x" – 8 133. 4x2n – 9x" + 5 134. an+2 – a"+2 – 6a? 135. b2n+2 + 3b"+2 10b2 136. 3c"+2 10c"+1 + 3c" 137. 2d"+2 5d"+1 + 3d"arrow_forwardIn Exercises 106–108, factor and simplify each algebraic expression. 106. 16x + 32r4 107. (x² – 4)(x² + 3) - (r? – 4)°(x² + 3)2 108. 12x+ 6xarrow_forwardSimplify. 102 (1+j) x (1+j) (1+j)x (1+j)"02 - 100 102 %3D (Simplify your answer. Type your answer using exponential notation.)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage