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Chapter 0: Problem 102
Write each algebraic expression without parentheses. $$\frac{1}{2}(2 y)+[(-7 x)+7 x]$$
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In parts (a) and (b), complete each statement. $$\text { a. } b^{4} \cdot b^{3}=(b \cdot b \cdot b \cdot b)(b \cdot b \cdot b)=b^{?}$$ $$\text { b. } b^{5} \cdot b^{5}=(b \cdot b \cdot b \cdot b \cdot b)(b \cdot b \cdot b \cdot b \cdot b)=b^{7}$$ c. Generalizing from parts (a) and (b), what should be done with the exponents when multiplying exponential expressions with the same base?
Factor Completely. $$(x+y)^{4}-100(x+y)^{2}$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ 4^{-2}<4^{-3} $$
It takes you 50 minutes to get to campus. You spend t minutes walking to the bus stop and the rest of the time riding the bus. Your walking rate is 0.06 mile per minute and the bus travels at a rate of 0.5 mile per minute. The total distance walking and traveling by bus is given by the algebraic expression $$0.06 t+0.5(50-t)$$ a. Simplify the algebraic expression. b. Use each form of the algebraic expression to determine the total distance that you travel if you spend 20 minutes walking to the bus stop.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. My mathematical model describes the data for tuition and fees at public four-year colleges for the past ten years extremely well, so it will serve as an accurate prediction for the cost of public colleges in 2050.
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