91Ó°ÊÓ

Suppose that a polynomial contains four terms. Explain how to use factoring by grouping to factor the polynomial.

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.

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?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A model that describes the average cost of tuition and fees at private U.S. colleges for the school year ending x years after 2000 cannot be used to estimate the cost of private education for the school year ending in 2000.

Will help you prepare for the material covered in the next section. A. Find \(\sqrt{16} \cdot \sqrt{4}\) B. Find \(\sqrt{16 \cdot 4}\) C. Based on your answers to parts (a) and (b), what can you conclude?

If 6.2 is multiplied by \(10^{3},\) what does this multiplication do to the decimal point in 6.2?