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A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing equipment at a gym is 10 feet high and extends 6 feet horizontally.

Which statement best compares the slopes of the two pieces of equipment?

A. Because [tex]\(\frac{5}{3}\ \textgreater \ \frac{3}{2}\)[/tex], the slope of the climbing equipment at the gym is greater.
B. Because [tex]\(\frac{5}{3}\ \textless \ \frac{3}{2}\)[/tex], the slope of the climbing equipment at the playground is greater.
C. Because [tex]\(\frac{3}{5}\ \textgreater \ \frac{2}{3}\)[/tex], the slope of the climbing equipment at the gym is greater.
D. Because [tex]\(\frac{3}{5}\ \textless \ \frac{2}{3}\)[/tex], the slope of the climbing equipment at the playground is greater.

Sagot :

GinnyAnswer
To compare the slopes of the two pieces of climbing equipment, we first need to calculate the slopes for each.

1. Calculate the slope of the playground equipment:

The slope is calculated by dividing the vertical height by the horizontal distance.
- Vertical height of playground equipment [tex]\( = 6 \)[/tex] feet
- Horizontal distance of playground equipment [tex]\( = 4 \)[/tex] feet

The slope is:
[tex]\[ \text{slope}_{\text{playground}} = \frac{6}{4} = 1.5 \][/tex]

2. Calculate the slope of the gym equipment:

Similarly, the slope for the gym equipment is calculated by dividing the vertical height by the horizontal distance.
- Vertical height of gym equipment [tex]\( = 10 \)[/tex] feet
- Horizontal distance of gym equipment [tex]\( = 6 \)[/tex] feet

The slope is:
[tex]\[ \text{slope}_{\text{gym}} = \frac{10}{6} \approx 1.6667 \][/tex]

3. Compare the slopes:

Now we compare the calculated slopes:
- Slope of the playground equipment [tex]\( = 1.5 \)[/tex]
- Slope of the gym equipment [tex]\( \approx 1.6667 \)[/tex]

Since:
[tex]\[ 1.6667 > 1.5 \][/tex]

The slope of the gym equipment is greater than the slope of the playground equipment.

Therefore, the correct statement that best compares the slopes is:
[tex]\[ \text{Because } \frac{5}{3} > \frac{3}{2}, \text{ the slope of the climbing equipment at the gym is greater.} \][/tex]
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