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
They would all reach 100 feet at the same time.
They would all reach 100 feet at the same time.
object C
object C
object A
object A
object B
object B
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The correct answer is object C.
To answer the question, we need to determine which object would reach 100 feet in the least amount of time.
Looking at the graph, we can see that object A has a steeper slope than object B, and object B has a steeper slope than object C.
A steeper slope represents a faster rate of change, meaning the object is covering more distance in less time.
Therefore, the object that would reach 100 feet in the least amount of time is object A.
To answer this question, we need to analyze the given information on the coordinate plane.
First, let's examine the solid line labeled A, which passes through the points (0,0) and (3,6). This line represents object A's distance in feet over time in seconds.
Next, let's look at the dotted line labeled B, which passes through the points (0,0) and (6,6). This line represents object B's distance in feet over time in seconds.
Finally, we have the dashed line labeled C, which passes through the points (0,0) and (6,3). This line represents object C's distance in feet over time in seconds.
The question asks which object would reach 100 feet in the least amount of time. To find this information, we need to determine the time it takes for each object to reach 100 feet on their respective lines.
For object A, we can see that it takes 3 seconds for the distance to increase from 0 to 6 feet. Since the line is linear, we can assume that it will take another 3 seconds to increase the distance from 6 to 12 feet. Thus, it will take a total of 6 seconds for object A to reach 100 feet, as calculated using proportions.
For object B, we can observe that it takes 6 seconds for the distance to increase from 0 to 6 feet. Since the line is also linear, we can assume that it will take another 6 seconds to increase the distance from 6 to 12 feet. Thus, it will take a total of 12 seconds for object B to reach 100 feet.
For object C, we can see that it takes 6 seconds for the distance to increase from 0 to 3 feet. Since the line is linear, we can assume that it will take another 6 seconds to increase the distance from 3 to 6 feet. Therefore, it will take a total of 12 seconds for object C to reach 100 feet.
Comparing the times for each object, we can determine that object A would reach 100 feet in the least amount of time, which is 6 seconds.
So, the correct answer is: object A.