Unit Rates & Proportions Unit Test
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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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The correct answer is "object C". Object C would reach 100 feet in the least amount of time.
To determine which object would reach 100 feet in the least amount of time, we need to analyze the three lines labeled A, B, and C on the coordinate plane.
- Line A: Passes through coordinates (0,0) and (3,6).
- Line B: Passes through coordinates (0,0) and (6,6).
- Line C: Passes through coordinates (0,0) and (6,3).
We can calculate the rate of change for each line by finding the slope. The slope is determined by the change in y divided by the change in x.
- For Line A: slope = (6-0)/(3-0) = 6/3 = 2.
- For Line B: slope = (6-0)/(6-0) = 6/6 = 1.
- For Line C: slope = (3-0)/(6-0) = 3/6 = 1/2.
The slope represents the rate of change of distance over time. In other words, it indicates how much the distance changes for each unit of time.
Since the slope of Line A is the highest (2), it means that the rate of change of distance over time is the greatest for object A. Therefore, object A would reach 100 feet in the least amount of time.
So, the correct answer is: object A.
To answer this question, we need to analyze the three objects (A, B, and C) on the graph. Each object represents a different relationship between distance and time.
Object A is represented by the solid line, passing through the points (0,0) and (3,6). This means that for every 1 second that passes, the object moves 2 feet.
Object B is represented by the dotted line, passing through the points (0,0) and (6,6). This means that for every 1 second that passes, the object moves 1 foot.
Object C is represented by the dashed line, passing through the points (0,0) and (6,3). This means that for every 1 second that passes, the object moves 0.5 feet.
Now, we can compare the time it takes for each object to reach 100 feet:
For Object A, if it moves 2 feet for every 1 second, it would take (100/2) = 50 seconds to reach 100 feet.
For Object B, if it moves 1 foot for every 1 second, it would also take 100 seconds to reach 100 feet.
For Object C, if it moves 0.5 feet for every 1 second, it would take (100/0.5) = 200 seconds to reach 100 feet.
From this analysis, we can conclude that Object A would reach 100 feet in the least amount of time, which is 50 seconds. Therefore, the correct answer is "object A."