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)
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The person showing a proportional relationship between time and # of jumping jacks
The person that did the most jumping jacks initially before the time started
The person doing the most jumping jacks per minute
1) The person showing a proportional relationship between time and the number of jumping jacks: Katrina.
2) The person that did the most jumping jacks initially before the time started: Kimberly.
3) The person doing the most jumping jacks per minute: Katrina.
Match the description with the correct Function.
Function A:
Function B:
x y
0 1
4 9
8 17
Function C: y=x+20
(4 points)
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Function with the greatest rate of change
Function with the smallest y-intercept
Which function would benefit you the most if it represented your money earned per hour?
Function with the highest initial amount of money
1) Function with the greatest rate of change: Function B.
2) Function with the smallest y-intercept: Function A.
3) Function that would benefit you the most if it represented your money earned per hour: Function C (y=x+20).
4) Function with the highest initial amount of money: Function A.
According to the graph, which of these statements is/are true? Check all that apply.
(2 points)
Responses
The entry level worker has the same slope as the lawyer.
The entry level worker has the same slope as the lawyer.
The plumber has a steeper rate of change than the entry level worker.
The plumber has a steeper rate of change than the entry level worker.
The lawyer has a greater initial amount of earnings than the plumber.
The lawyer has a greater initial amount of earnings than the plumber.
The plumber initially earns more money than the lawyer, but the lawyer earns more as more hours are worked.
The plumber initially earns more money than the lawyer, but the lawyer earns more as more hours are worked.
Bill Gates has the same y - intercept as the entry level worker
According to the graph, the correct statements are:
1) The plumber has a steeper rate of change than the entry level worker.
2) The lawyer has a greater initial amount of earnings than the plumber.
3) The plumber initially earns more money than the lawyer, but the lawyer earns more as more hours are worked.
Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain. The river was 22 feet before the rain began.(4 points)
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a. What is the rate of change (slope) for this scenario? Response area
b. What is the y-intercept for this scenario? Response area
c. Write an equation for the scenario in slope-intercept form. Response area
d. Write this equation in standard form.
a. What is the rate of change (slope) for this scenario?
To find the rate of change (slope), we can use the formula: slope = (change in y) / (change in x).
In this scenario, the change in y is 62 - 34 = 28 (feet), and the change in x is 10 - 3 = 7 (days).
So, the slope is 28 / 7 = 4 (feet per day).
b. What is the y-intercept for this scenario?
The y-intercept represents the starting point or initial value. In this scenario, the river was 22 feet before the rain began. Therefore, the y-intercept is 22.
c. Write an equation for the scenario in slope-intercept form.
The slope-intercept form of an equation is y = mx + b, where m represents the slope and b represents the y-intercept.
In this scenario, the slope is 4 and the y-intercept is 22.
So, the equation in slope-intercept form is y = 4x + 22.
d. Write this equation in standard form.
The standard form of an equation is Ax + By = C, where A, B, and C are constants.
To convert the equation y = 4x + 22 to standard form, we need to eliminate the decimals.
Multiply through by 4 to get 4y = 16x + 88.
Rearrange the terms to get 16x - 4y = -88.
So, the equation in standard form is 16x - 4y = -88.
r 10 days of rain. The river was 22 feet before the rain began.(4 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.
a. What is the rate of change (slope) for this scenario? Response area
b. What is the y-intercept for this scenario?
c. Write an equation for the scenario in slope-intercept form.
d. Write this equation in standard form.
a. What is the rate of change (slope) for this scenario?
To find the rate of change (slope), we can use the formula: slope = (change in y) / (change in x).
In this scenario, the change in y is 62 - 22 = 40 (feet), and the change in x is 10 (days).
So, the slope is 40 / 10 = 4 (feet per day).
b. What is the y-intercept for this scenario?
The y-intercept represents the starting point or initial value. In this scenario, the river was 22 feet before the rain began. Therefore, the y-intercept is 22.
c. Write an equation for the scenario in slope-intercept form.
The slope-intercept form of an equation is y = mx + b, where m represents the slope and b represents the y-intercept.
In this scenario, the slope is 4 and the y-intercept is 22.
So, the equation in slope-intercept form is y = 4x + 22.
d. Write this equation in standard form.
The standard form of an equation is Ax + By = C, where A, B, and C are constants.
To convert the equation y = 4x + 22 to standard form, we need to eliminate the decimals.
Multiply through by 4 to get 4y = 16x + 88.
Rearrange the terms to get 16x - 4y = -88.
So, the equation in standard form is 16x - 4y = -88.
incorrect
I apologize for the incorrect response. Let's recalculate the correct answers:
a) To find the rate of change (slope), we can use the formula: slope = (change in y) / (change in x). In this scenario, the change in y is 62 - 22 = 40 (feet), and the change in x is 10 - 0 = 10 (days). So, the slope is 40 / 10 = 4 (feet per day).
b) The y-intercept represents the starting point or initial value. In this scenario, the river was 22 feet before the rain began. Therefore, the y-intercept is 22.
c) The equation in slope-intercept form can be found using the slope (m) and the y-intercept (b). So, the equation in slope-intercept form is y = mx + b = 4x + 22.
d) To write this equation in standard form, we need to rearrange it to the form Ax + By = C, where A, B, and C are constants. In this case, the equation 4x + 22 can be rewritten as 4x - y = -22.
Please let me know if you need any further assistance.
Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain.
Given the two points we know: (3, 34) and (10, 62), what would the point-slope equation look like?
(1 point)
Responses
(y - 34) = 4 (x - 3)
(y - 34) = 4 (x - 3)
(y - 34) = 4 (x - 10)
(y - 34) = 4 (x - 10)
(y - 10) = 4 (x + 62)
(y - 10) = 4 (x + 62)
(y - 3) = 4 (x - 34)
Given the two points (3, 34) and (10, 62), we can use the point-slope form of an equation which is: y - y₁ = m(x - x₁), where (x₁, y₁) is one of the points and m is the slope.
Using the point (3, 34) as our reference point, we get:
(y - 34) = m(x - 3)
Now, we need to find the slope (m) using the two points:
m = (y₂ - y₁) / (x₂ - x₁) = (62 - 34) / (10 - 3) = 28 / 7 = 4
Substituting the slope (m = 4) into the point-slope equation:
(y - 34) = 4(x - 3)
Therefore, the point-slope equation would be:
(y - 34) = 4 (x - 3)
x/3 = -9
To solve the equation x/3 = -9, we can multiply both sides of the equation by 3 to isolate the variable x:
(x/3) * 3 = (-9) * 3
This simplifies to:
x = -27
Therefore, the solution to the equation x/3 = -9 is x = -27.
To solve the equation x/3 = -9, we can follow these steps:
1) To eliminate the fraction, we can multiply both sides of the equation by 3.
(3) * (x/3) = (-9) * (3)
2) Simplify each side of the equation.
(3/3) * x = -27
3) Simplify further.
1 * x = -27
4) The x-term on the left side simplifies to x, leaving us with:
x = -27
Therefore, the solution to the equation x/3 = -9 is x = -27.