Question
Question
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Which of these objects would reach 100 feet in the least amount of time?
(1 point)
Responses
object B
object B
object A
object A
They would all reach 100 feet at the same time.
They would all reach 100 feet at the same time.
object C
object C
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Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Which of these objects would reach 100 feet in the least amount of time?
(1 point)
Responses
object B
object B
object A
object A
They would all reach 100 feet at the same time.
They would all reach 100 feet at the same time.
object C
object C
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which object reaches 100 feet in the least amount of time, we need to analyze the lines on the graph, which represent the relationships between time (x-axis) and distance (y-axis).
1. **Object A** passes through the points (0,0) and (3,6). The slope (rate of distance per time) can be calculated as follows:
- Slope = (6 - 0) / (3 - 0) = 6/3 = 2 feet per second.
- This means it covers 2 feet in 1 second.
2. **Object B** passes through the points (0,0) and (6,6). The slope is:
- Slope = (6 - 0) / (6 - 0) = 6/6 = 1 foot per second.
- This means it covers 1 foot in 1 second.
3. **Object C** passes through the points (0,0) and (6,3). The slope is:
- Slope = (3 - 0) / (6 - 0) = 3/6 = 0.5 feet per second.
- This means it covers 0.5 feet in 1 second.
To find out how long each object takes to reach 100 feet:
- **Object A**:
- Time = Distance / Speed = 100 feet / 2 feet per second = 50 seconds.
- **Object B**:
- Time = Distance / Speed = 100 feet / 1 foot per second = 100 seconds.
- **Object C**:
- Time = Distance / Speed = 100 feet / 0.5 feet per second = 200 seconds.
### Conclusion
Object A would reach 100 feet in the least amount of time, taking 50 seconds. Thus, the answer is:
**object A**
1. **Object A** passes through the points (0,0) and (3,6). The slope (rate of distance per time) can be calculated as follows:
- Slope = (6 - 0) / (3 - 0) = 6/3 = 2 feet per second.
- This means it covers 2 feet in 1 second.
2. **Object B** passes through the points (0,0) and (6,6). The slope is:
- Slope = (6 - 0) / (6 - 0) = 6/6 = 1 foot per second.
- This means it covers 1 foot in 1 second.
3. **Object C** passes through the points (0,0) and (6,3). The slope is:
- Slope = (3 - 0) / (6 - 0) = 3/6 = 0.5 feet per second.
- This means it covers 0.5 feet in 1 second.
To find out how long each object takes to reach 100 feet:
- **Object A**:
- Time = Distance / Speed = 100 feet / 2 feet per second = 50 seconds.
- **Object B**:
- Time = Distance / Speed = 100 feet / 1 foot per second = 100 seconds.
- **Object C**:
- Time = Distance / Speed = 100 feet / 0.5 feet per second = 200 seconds.
### Conclusion
Object A would reach 100 feet in the least amount of time, taking 50 seconds. Thus, the answer is:
**object A**
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