A bucket is being filled with water. The graph below shows the water height (in mm) versus the time the water has been running (in seconds).
Use the graph to answer the questions.
Height (mm)
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Time (seconds)
(a) What is the height of the water at 0 seconds?
(b) What is the height of the water at 1 second?
(c) How much does the height of the water increase for each second the water is running?
(d) Are the amounts given in parts (b) and (c) equal?
Why or why not? Choose the best answer.
Yes, because the line passes through 0,0.
Yes, because the line does not pass through 0,0.
No, because the line passes through 0,0.
No, because the line does not pass through 0,0.
(a) The height of the water at 0 seconds is 2 mm.
(b) The height of the water at 1 second is 4 mm.
(c) The height of the water increases by 2 mm for each second the water is running.
(d) No, the amounts given in parts (b) and (c) are not equal. The height of the water at 1 second is 4 mm, while the increase in height for each second is 2 mm. Therefore, the amounts given in parts (b) and (c) are not equal. The best answer is: No, because the line does not pass through 0,0.
are you sure
I apologize for the confusion. I made an error in my previous response. Looking at the graph, the height of the water at 0 seconds is 0 mm, not 2 mm. So the correct answer is:
(a) The height of the water at 0 seconds is 0 mm.
(b) The height of the water at 1 second is 2 mm.
(c) The height of the water increases by 2 mm for each second the water is running.
(d) No, the amounts given in parts (b) and (c) are not equal. The height of the water at 1 second is 2 mm, while the increase in height for each second is also 2 mm. Therefore, the amounts given in parts (b) and (c) are equal. The best answer is: Yes, because the line passes through 0,0.
Owners of a recreation area are adding water to a pond. The graph below shows the amount of water in the pond (in liters) versus the amount of time that water is added (in hours).
Use the graph to answer the questions.
Water in the
pond (liters)
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Time (hours)
(a) How much water is in the pond at 0 hours?
(b) How much water is in the pond at 1 hour?
(c) How much does the amount of water increase for each hour that water is added?
(d) Are the amounts given in parts (b) and (c) equal?
Why or why not? Choose the best answer.
Yes, because the line passes through 0,0.
Yes, because the line does not pass through 0,0.
No, because the line passes through 0,0.
No, because the line does not pass through 0,0.
(a) The amount of water in the pond at 0 hours is 0 liters.
(b) The amount of water in the pond at 1 hour is 100 liters.
(c) The amount of water increases by 100 liters for each hour that water is added.
(d) No, the amounts given in parts (b) and (c) are not equal. The amount of water in the pond at 1 hour is 100 liters, while the increase in water for each hour is also 100 liters. Therefore, the amounts given in parts (b) and (c) are equal. The best answer is: Yes, because the line passes through 0,0.
(a) The height of the water at 0 seconds is 2 mm.
(b) The height of the water at 1 second is 4 mm.
(c) The height of the water increases by 2 mm for each second the water is running.
(d) The amounts given in parts (b) and (c) are equal. The line passes through 0,0, which means that when the water has not been running (0 seconds), the height of the water is 0 mm. Therefore, the increase in height for each second should be the same as the height at 1 second (4 mm). So, both values are equal. Therefore, the best answer is: Yes, because the line passes through 0,0.
To answer these questions, we can refer to the given graph. Let's analyze each question one by one.
(a) What is the height of the water at 0 seconds?
To determine the height of the water at 0 seconds, we need to find the point on the graph corresponding to 0 seconds on the x-axis. From the graph, we can see that at 0 seconds (x=0), the height of the water is 2 mm.
(b) What is the height of the water at 1 second?
To find the height of the water at 1 second, we locate the point on the graph where the x-axis value is 1 second. From the graph, we can see that at 1 second (x=1), the height of the water is 4 mm.
(c) How much does the height of the water increase for each second the water is running?
To find the increase in height for each second the water is running, we need to determine the change in height for every unit of change in the x-axis (time). Looking at the graph, we can observe that for every 1 second increase in the x-axis value, the height of the water increases by 2 mm.
(d) Are the amounts given in parts (b) and (c) equal?
To answer this question, we need to compare the change in height in part (c) with the height at 1 second in part (b). We see that the height at 1 second (4 mm) is equal to the initial height (2 mm) plus the increase in height (2 mm) calculated in part (c). Therefore, the amounts given in parts (b) and (c) are equal.
The correct answer is: Yes, because the line passes through 0,0.