To find the value of y when x = -6, we can use the direct variation formula:
y = kx
where k is the constant of variation.
To find the value of k, we can use the given data: y = 14 when x = -4.
14 = k(-4)
Divide both sides of the equation by -4 to solve for k:
k = -3.5
Now we can use the value of k to find the value of y when x = -6:
y = (-3.5)(-6) = 21
Therefore, the value of y when x = -6 is 21. So the correct answer is 21.
A)
Multiple Choice
Suppose y varies directly with x, and y = 14 when x = –4. What is the value of y when x = –
6?
(1 point)
–21
10
18
21
11 answers
A)
Suppose y varies directly with x, and y = 25 when x = 140. What is the value of x when y =
36?
(1 point)
140
165
201.6
176
Suppose y varies directly with x, and y = 25 when x = 140. What is the value of x when y =
36?
(1 point)
140
165
201.6
176
To find the value of x when y = 36, we can use the direct variation formula:
y = kx
where k is the constant of variation.
To find the value of k, we can use the given data: y = 25 when x = 140.
25 = k(140)
Divide both sides of the equation by 140 to solve for k:
k ≈ 0.17857
Now we can use the value of k to find the value of x when y = 36:
36 = 0.17857x
Divide both sides of the equation by 0.17857 to solve for x:
x ≈ 201.6
Therefore, the value of x when y = 36 is approximately 201.6. So the correct answer is 201.6.
y = kx
where k is the constant of variation.
To find the value of k, we can use the given data: y = 25 when x = 140.
25 = k(140)
Divide both sides of the equation by 140 to solve for k:
k ≈ 0.17857
Now we can use the value of k to find the value of x when y = 36:
36 = 0.17857x
Divide both sides of the equation by 0.17857 to solve for x:
x ≈ 201.6
Therefore, the value of x when y = 36 is approximately 201.6. So the correct answer is 201.6.
The point (12, 9) is included in a direct variation. What is the
constant of variation?
(1 point)
1/2
3/4
1
2
constant of variation?
(1 point)
1/2
3/4
1
2
To find the constant of variation, we can use the direct variation formula:
y = kx
where k is the constant of variation.
Given that the point (12, 9) is included in a direct variation, we can substitute the x and y values into the formula:
9 = k(12)
Now we can solve for k by dividing both sides of the equation by 12:
k = 9/12 = 3/4
Therefore, the constant of variation is 3/4. So the correct answer is 3/4.
y = kx
where k is the constant of variation.
Given that the point (12, 9) is included in a direct variation, we can substitute the x and y values into the formula:
9 = k(12)
Now we can solve for k by dividing both sides of the equation by 12:
k = 9/12 = 3/4
Therefore, the constant of variation is 3/4. So the correct answer is 3/4.
The equation of the line on the graph below is a direct variation
equation. What is the constant of variation?
(1 point)
1/4
1/2
3/4
1
equation. What is the constant of variation?
(1 point)
1/4
1/2
3/4
1
I apologize, but I am unable to see the graph you mentioned. Could you please provide some additional information or describe the equation of the line? This will help me assist you in finding the constant of variation.
the graph has a diangle line that starts (-4,-1) to (4,1)
To find the constant of variation from the given graph, we can use the formula for the equation of a line in slope-intercept form:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Given the points (-4, -1) and (4, 1), we can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - (-1)) / (4 - (-4))
= 2 / 8
= 1/4
The constant of variation in a direct variation equation represents the slope of the line, so the constant of variation for the given graph is 1/4. Therefore, the correct answer is 1/4.
y = mx + b
where m is the slope of the line and b is the y-intercept.
Given the points (-4, -1) and (4, 1), we can calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - (-1)) / (4 - (-4))
= 2 / 8
= 1/4
The constant of variation in a direct variation equation represents the slope of the line, so the constant of variation for the given graph is 1/4. Therefore, the correct answer is 1/4.
The distance d a train travels varies directly with the amount of
time t that has elapsed since departure. If the train travels 475
miles in 9.5 hours, how many miles did the train travel after 4
hours?
(1 point)
100
200
232.5
300
time t that has elapsed since departure. If the train travels 475
miles in 9.5 hours, how many miles did the train travel after 4
hours?
(1 point)
100
200
232.5
300
To find the distance the train traveled after 4 hours, we can use the direct variation formula:
d = kt
where d is the distance, k is the constant of variation, and t is the time.
Given that the train travels 475 miles in 9.5 hours, we can substitute these values into the formula:
475 = k(9.5)
Solve for k by dividing both sides of the equation by 9.5:
k = 475 / 9.5 = 50
Now we can use the value of k to find the distance the train traveled after 4 hours:
d = 50(4) = 200
Therefore, the train traveled 200 miles after 4 hours. So the correct answer is 200.
d = kt
where d is the distance, k is the constant of variation, and t is the time.
Given that the train travels 475 miles in 9.5 hours, we can substitute these values into the formula:
475 = k(9.5)
Solve for k by dividing both sides of the equation by 9.5:
k = 475 / 9.5 = 50
Now we can use the value of k to find the distance the train traveled after 4 hours:
d = 50(4) = 200
Therefore, the train traveled 200 miles after 4 hours. So the correct answer is 200.
1 answer