Question

a walkway rises 8.5 ft for every 10 ft on the horizontal. find its slope (or grade). select all that apply. a. \\(\frac{10}{85}\\) b. \\(\frac{85}{10}\\) c. 85% d. 0.85 e. 8.5% f. 20 g. \\(\frac{17}{20}\\) h. 2000%

Explanation:

Step1: Recall the slope formula

Slope is defined as the ratio of the rise (vertical change) to the run (horizontal change). So, slope $= \frac{\text{rise}}{\text{run}}$. Here, rise is $8.5$ ft and run is $10$ ft. So, slope $= \frac{8.5}{10}$. So option B is correct.

Step2: Simplify the fraction

$\frac{8.5}{10}=\frac{85}{100}=\frac{17}{20}$? Wait, no, $8.5=\frac{85}{10}$, so $\frac{8.5}{10}=\frac{85}{100}=0.85$. Also, $0.85$ as a percentage is $0.85\times100 = 85\%$. Let's check each option:

• Option A: $\frac{10}{85}$ is run over rise, not slope. So A is wrong.
• Option B: $\frac{8.5}{10}$ is rise over run, which is slope. Correct.
• Option C: $85\%$ is $0.85$, which is the decimal form of slope (since slope as a percentage is often expressed as the decimal times 100). Wait, slope as a grade is often expressed as a percentage, where grade $= \text{slope} \times 100$. So slope is $0.85$, grade is $85\%$. So C is correct? Wait, no, slope is $\frac{rise}{run}=0.85$, and grade is slope $\times 100 = 85\%$. Wait, let's re - evaluate:

Slope $m=\frac{\text{rise}}{\text{run}}=\frac{8.5}{10}=0.85$.

• Option D: $0.85$ is the slope (decimal form). Correct.
• Option E: $8.5\%$ is $0.085$, not equal to $0.85$. Wrong.
• Option F: $20$ is not related. Wrong.
• Option G: Simplify $\frac{8.5}{10}=\frac{85}{100}=\frac{17}{20}$ (dividing numerator and denominator by $5$: $85\div5 = 17$, $100\div5 = 20$). So $\frac{17}{20}=0.85$. Correct.
• Option H: $2000\%$ is $20$, which is wrong.

Wait, let's correct the earlier mistake. Let's go step by step:

1. Calculate the slope: Slope $=\frac{\text{rise}}{\text{run}}=\frac{8.5}{10}$. So option B is correct.

1. Simplify $\frac{8.5}{10}$: Multiply numerator and denominator by $10$ to get $\frac{85}{100}$, then divide numerator and denominator by $5$: $\frac{85\div5}{100\div5}=\frac{17}{20}$. So option G is correct.

1. Convert $\frac{8.5}{10}$ to decimal: $\frac{8.5}{10}=0.85$. So option D is correct.

1. Convert the decimal slope to percentage (for grade): $0.85\times100 = 85\%$. So option C is correct.

Wait, let's re - check each option:

• Option B: $\frac{8.5}{10}$ is the slope (rise over run). Correct.
• Option C: $85\%$ is the grade (slope $\times100$). Since the question says "slope (or grade)", so grade is also acceptable. Correct.
• Option D: $0.85$ is the decimal form of the slope. Correct.
• Option G: $\frac{17}{20}=0.85$, which is equal to $\frac{8.5}{10}$. Correct.

Wait, let's verify $\frac{17}{20}$: $\frac{17}{20}=0.85$, and $\frac{8.5}{10}=0.85$. So they are equal.

So the correct options are B, C, D, G.

Wait, let's check again:

• Option B: $\frac{8.5}{10}$ (rise over run) – correct.
• Option C: $85\%$ (slope as a percentage, since grade = slope×100) – correct.
• Option D: $0.85$ (decimal form of slope) – correct.
• Option G: $\frac{17}{20}=0.85$ (simplified fraction of slope) – correct.

Option A: $\frac{10}{85}$ is incorrect (run over rise). Option E: $8.5\%$ is incorrect. Option F: $20$ is incorrect. Option H: $2000\%$ is incorrect.

Answer:

B. $\frac{8.5}{10}$, C. $85\%$, D. $0.85$, G. $\frac{17}{20}$