To determine which object reaches 100 feet in the least amount of time, we can analyze the slopes of each line:
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Line A passes through (0, 0) and (3, 6):
- The slope (representing speed) can be calculated as change in distance divided by change in time: \[ \text{slope of A} = \frac{6 - 0}{3 - 0} = \frac{6}{3} = 2 \text{ feet/second} \]
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Line B passes through (0, 0) and (6, 6):
- The slope is: \[ \text{slope of B} = \frac{6 - 0}{6 - 0} = \frac{6}{6} = 1 \text{ foot/second} \]
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Line C passes through (0, 0) and (6, 3):
- The slope is: \[ \text{slope of C} = \frac{3 - 0}{6 - 0} = \frac{3}{6} = 0.5 \text{ feet/second} \]
Now, to find the time taken to reach 100 feet for each object, we can use the formula: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \]
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For Line A: \[ \text{time for A} = \frac{100 \text{ feet}}{2 \text{ feet/second}} = 50 \text{ seconds} \]
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For Line B: \[ \text{time for B} = \frac{100 \text{ feet}}{1 \text{ foot/second}} = 100 \text{ seconds} \]
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For Line C: \[ \text{time for C} = \frac{100 \text{ feet}}{0.5 \text{ feet/second}} = 200 \text{ seconds} \]
Based on this analysis, object A would reach 100 feet in the least amount of time, which is 50 seconds.
Response: object A
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