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Chapter 0: Problem 142
Exercises \(142-144\) will help you prepare for the material covered in the next section. $$\text { Multiply: }\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)$$
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Factor and simplify each algebraic expression. $$(4 x-1)^{\frac{1}{2}}-1(4 x-1)^{\frac{3}{2}}$$
Will help you prepare for the material covered in the next section. Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$\frac{x^{2}+6 x+5}{x^{2}-25}$$
You had \(\$10,000\) to invest. You put x dollars in a safe, government-insured certificate of deposit paying 5% per year. You invested the remainder of the money in noninsured corporate bonds paying 12% per year. Your total interest earned at the end of the year is given by the algebraic expression $$0.05 x+0.12(10,000-x)$$ a. Simplify the algebraic expression. b. Use each form of the algebraic expression to determine your total interest earned at the end of the year if you invested $6000 in the safe, government-insured certificate of deposit.
Place the correct symbol, \(>\) or \(<,\) in the shaded area between the given numbers. Do not use a calculator. Then check your result with a calculator. a. \(3^{\frac{1}{2}} \quad 3^{\frac{1}{3}}\) b. \(\sqrt{7}+\sqrt{18} \sqrt{7+18}\)
a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$\text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. }$$ How old is the son? b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?
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