Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.4 Linear Functions - 2.4 Exercises - Page 228: 39


$$\color{blue}{\bf\text{A, C, D, E}}$$

Work Step by Step

If a ramp $\bf{\text{rises }2.5ft}$ over a $\bf{\text{run of }10 ft}$, our slope is: $\bf{\frac{\text{rise}}{\text{run}}}$=$\bf{\frac{2.5}{10}}$ Let's look at each option to see which equal $\bf{\frac{2.5}{10}}$: $\bf{\text{A: }0.25}$ $2.5\div10=0.25$ so $\bf{\text{A is true }}$ $\bf{\text{B: }4}$ $4=\frac{4}{1}\ne\frac{2.5}{10}$ so $\bf{\text{B is false }}$ $\bf{\text{Reality check:}}$ A slope of $\bf4$ would be $\bf{\text{very}}$ steep, far too steep for a wheelchair. (see graph) $\bf{\text{C: }\frac{2.5}{10}}$ Which is the $\frac{\text{rise}}{\text{run}}$ form we already found so $\bf{\text{C is true }}$ $\bf{\text{D: 25%}}$ ${\text{25% = }0.25}$ so $\bf{\text{D is true}}$ $\bf{\text{E: }\frac{1}{4}}$ $\frac{1}{4}=0.25$ so $\bf{\text{E is true }}$ $\bf{\text{F: }\frac{10}{2.5}}$ $\bf\frac{10}{2.5}$ would represent a $\bf{\text{rise}}$ of $\bf10\text{ft}$ over a $\bf{\text{run}}$ of $\bf2.5\text{ft}$ Which is a slope of $\bf4$ so $\bf{\text{F is false }}$ $\bf{\text{G: 400%}}$ $\bf{\text{400%}=\frac{400}{100}=4}$ so $\bf{\text{G is false }}$ $\bf{\text{H: 2.5%}}$ $\bf{\text{2.5%}=\frac{2.5}{100}=\frac{1}{40}}$so $\bf{\text{H is false }}$ $\bf{\text{Reality check:}}$ A slope of $\bf\frac{1}{40}$ would be $\bf{\text{very}}$ shallow, so it would have to be extremely long for a wheelchair ramp. (see graph) So the correct options are: $$\color{blue}{\bf\text{A, C, D, E}}$$
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