The table below shows the number of jumping jacks completed after a given period of time in minutes.
Time (minutes) Jumping Jacks
1 50
2 100
3 150
4 200
Considering the jumping jacks: 50, 100, 150, 200, what is the common difference?
Now, think of this table as a set of ordered pairs. This means that the first row can be placed in an ordered pair as (1, 50). The second row can be written as (2, 100). Using this, what is the slope of the line that connects the first two points?
What is the slope of the line that connects the 3rd and 4th point?
What is the slope of the line that connects the 1st and the 4th point?
Is the common difference (aka slope aka rate of change) constant?
Why is it or is it not constant?
The common difference is 50.
The slope of the line connecting the first two points is 50.
The slope of the line connecting the 3rd and 4th point is 50.
The slope of the line connecting the 1st and the 4th point is also 50.
Yes, the common difference (aka slope aka rate of change) is constant.
It is constant because each additional minute of exercise results in 50 more jumping jacks completed, indicating a consistent rate of change or slope in the data.
The tables below show the number of jumping jacks completed after a given period of time in minutes. Kimberly Time (min) # Jumping Jacks 3 28 8 58 12 82 16 106 Katrina Time (min) # Jumping Jacks 2 16 5 40 12 96 20 160 (3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. The person showing a proportional relationship between time and # of jumping jacks The person doing the most jumping jacks per minute The person that did the most jumping jacks initially before the time started
The tables below show the number of jumping jacks completed after a given period of time in minutes. Kimberly Time (min) # Jumping Jacks 3 28 8 58 12 82 16 106 Katrina Time (min) # Jumping Jacks 2 16 5 40 12 96 20 160
botgpt sovle it please
To find the common difference, we need to determine the change in the y-values (jumping jacks) for consecutive x-values (time). In this case, the x-values are increasing by 1 each time, and the y-values are increasing by 50.
So, the common difference is 50.
Now, let's find the slopes of the lines connecting different points on the table:
1. The slope of the line connecting the first two points (1, 50) and (2, 100) can be found using the formula: slope = (change in y) / (change in x). Here, the change in x is 2 - 1 = 1, and the change in y is 100 - 50 = 50. Therefore, the slope is 50/1 = 50.
2. The slope of the line connecting the third and fourth points (3, 150) and (4, 200) can be calculated in a similar way. The change in x is 4 - 3 = 1, and the change in y is 200 - 150 = 50. So, the slope is 50/1 = 50.
3. Similarly, for the line connecting the first and fourth points (1, 50) and (4, 200), the change in x is 4 - 1 = 3, and the change in y is 200 - 50 = 150. Therefore, the slope is 150/3 = 50.
Since the slopes calculated in all three cases are the same (50), we see that the common difference is indeed constant or the rate of change is constant.
The common difference represents the rate at which the number of jumping jacks increases with respect to time. In this scenario, it is constant because for every increase in time by 1 minute, the number of jumping jacks increases by a fixed value of 50. Hence, the common difference or the rate of change remains constant throughout the given set of data.