Question
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
(1 point)
–21
10
18
21
Answers
GPT 3.5
If y varies directly with x, it means that there is a constant ratio between y and x. This can be represented as y = kx, where k is the constant of variation.
To find the value of k, we can use the given information that y = 14 when x = -4. Substituting these values into the equation, we have 14 = k(-4). Solving for k, we find that k = -14/-4 = 7/2.
Now that we know the value of k, we can use the equation y = kx to find the value of y when x = -6. Substituting x = -6 and k = 7/2, we have y = (7/2)(-6) = -21.
Therefore, the value of y when x = -6 is -21.
To find the value of k, we can use the given information that y = 14 when x = -4. Substituting these values into the equation, we have 14 = k(-4). Solving for k, we find that k = -14/-4 = 7/2.
Now that we know the value of k, we can use the equation y = kx to find the value of y when x = -6. Substituting x = -6 and k = 7/2, we have y = (7/2)(-6) = -21.
Therefore, the value of y when x = -6 is -21.
Anonymous
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
(1 point)
140 165 201.6 176
GPT 3.5
If y varies directly with x, it means that there is a constant ratio between y and x. This can be represented as y = kx, where k is the constant of variation.
To find the value of k, we can use the given information that y = 25 when x = 140. Substituting these values into the equation, we have 25 = k(140). Solving for k, we find that k = 25/140 = 5/28.
Now that we know the value of k, we can use the equation y = kx to find the value of x when y = 36. Substituting y = 36 and k = 5/28, we have 36 = (5/28) * x. Solving for x, we find x = (36 * 28) / 5 = 201.6.
Therefore, the value of x when y = 36 is 201.6.
To find the value of k, we can use the given information that y = 25 when x = 140. Substituting these values into the equation, we have 25 = k(140). Solving for k, we find that k = 25/140 = 5/28.
Now that we know the value of k, we can use the equation y = kx to find the value of x when y = 36. Substituting y = 36 and k = 5/28, we have 36 = (5/28) * x. Solving for x, we find x = (36 * 28) / 5 = 201.6.
Therefore, the value of x when y = 36 is 201.6.
Anonymous
The point (12, 9) is included in a direct variation. What is the constant of variation?
(1 point)
1/2
3/4
1
2
(1 point)
1/2
3/4
1
2
GPT 3.5
If the point (12, 9) is included in a direct variation, we can use the formula y = kx to find the constant of variation, k.
Using the given point (12, 9), we can substitute these values into the direct variation equation: 9 = k(12).
To solve for k, divide both sides of the equation by 12: 9/12 = k.
Simplifying the fraction on the left side, we find k = 3/4.
Therefore, the constant of variation is 3/4.
Using the given point (12, 9), we can substitute these values into the direct variation equation: 9 = k(12).
To solve for k, divide both sides of the equation by 12: 9/12 = k.
Simplifying the fraction on the left side, we find k = 3/4.
Therefore, the constant of variation is 3/4.
Anonymous
The equation of the line on the graph below is a direct variation equation. What is the constant of variation?
1/4
1/2
$
1/4
1/2
$
GPT 3.5
I apologize, but since there is no image or graph provided, I am unable to determine the equation of the line or the constant of variation. Could you please provide more information or clarify your question?
Anonymous
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
(1 point)
100
200
232.5
300
GPT 3.5
If the distance d a train travels varies directly with the amount of time t that has elapsed since departure, we can use the direct variation equation: d = kt, where k is the constant of variation.
To find the value of k, we can use the given information that the train travels 475 miles in 9.5 hours. Substituting these values into the equation, we have 475 = k(9.5). Solving for k, we find that k = 475/9.5 = 50.
Now that we know the value of k, we can use the equation d = kt to find the distance the train traveled after 4 hours. Substituting t = 4 and k = 50, we have d = 50(4) = 200.
Therefore, the train traveled 200 miles after 4 hours.
To find the value of k, we can use the given information that the train travels 475 miles in 9.5 hours. Substituting these values into the equation, we have 475 = k(9.5). Solving for k, we find that k = 475/9.5 = 50.
Now that we know the value of k, we can use the equation d = kt to find the distance the train traveled after 4 hours. Substituting t = 4 and k = 50, we have d = 50(4) = 200.
Therefore, the train traveled 200 miles after 4 hours.