Question

Suppose y varies inversely with​ x, and yequalsnegative 2 when xequals21. What is an equation for the inverse​ variation?

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Part 1
What is the equation for the inverse​ variation?
  
enter your response here ​(Type an equation. Simplify your​ answer.)

Answer 1

[AI-generated answer — Bot GPT 3.5]

y = k/x

where k is the constant of variation.

To find the value of k, we can use the given information y = -2 when x = 21:

-2 = k/21

Solving for k:

k = -2 * 21
k = -42

Therefore, the equation for the inverse variation is:

y = -42/x

Answer 2

Suppose y varies inversely with​ x, and yequalsnegative 4 when xequals17. What is an equation for the inverse​ variation?

Question content area bottom
Part 1
What is the equation for the inverse​ variation?
  
enter your response here ​(Type an equation. Simplify your​ answer.)

Answer 3

[AI-generated answer — Bot GPT 3.5]

Given that y varies inversely with​ x, the equation for inverse variation is y = k/x, where k is the constant of variation.

We are also given that y = -4 when x = 17, so we can find the value of k by substituting these values into the equation:

-4 = k/17

Solving for k:

k = -4 * 17
k = -68

Therefore, the equation for the inverse variation is:

y = -68/x

Answer 4

Suppose y varies inversely with​ x, and yequals6 when xequals9. Write an equation for the inverse variation.

Question content area bottom
Part 1
What is the equation for the inverse​ variation?
  
enter your response here ​(Type an equation. Simplify your​ answer.)

Answer 5

[AI-generated answer — Bot GPT 3.5]

Given that y varies inversely with​ x, the equation for inverse variation is y = k/x, where k is the constant of variation.

We are also given that y = 6 when x = 9, so we can find the value of k by substituting these values into the equation:

6 = k/9

Solving for k:

k = 6 * 9
k = 54

Therefore, the equation for the inverse variation is:

y = 54/x

Answer 6

Suppose y varies inversely with​ x, and yequals10 when xequals8. Write an equation for the inverse variation.

Question content area bottom
Part 1
What is the equation for the inverse​ variation?
  
enter your response here ​(Type an equation. Simplify your​ answer.)

Answer 7

[AI-generated answer — Bot GPT 3.5]

Given that y varies inversely with​ x, the equation for inverse variation is y = k/x, where k is the constant of variation.

We are also given that y = 10 when x = 8, so we can find the value of k by substituting these values into the equation:

10 = k/8

Solving for k:

k = 10 * 8
k = 80

Therefore, the equation for the inverse variation is:

y = 80/x

Answer 8

A family takes 1 and one half

h to drive from their house to a lake at 48 ​mi/h. The travel time varies inversely with the speed of the car. How long will the return trip take at 24 ​mi/h?
Question content area bottom
Part 1
The trip will take
  
enter your response here h.

Answer 9

[AI-generated answer — Bot GPT 3.5]

Let's denote the time for the return trip at 24 mi/h as T hours.

According to the given information, we know that the travel time varies inversely with the speed of the car. This means that the product of the speed and the time is constant.

For the first trip at 48 mi/h, which takes 1.5 hours, the product is:
48 * 1.5 = 72

For the return trip at 24 mi/h, let's denote the time as T:
24 * T = 72
T = 72 / 24
T = 3

Therefore, the return trip at 24 mi/h will take 3 hours.

Answer 10

Do the data in each table represent a direct variation or an inverse​ variation? Write an equation to model the data in the table.

x
y
2
1
5
0.4
8
0.25

Question content area bottom
Part 1
Do the data in each table represent a direct variation or an inverse​ variation?
Inverse variation
Your answer is correct.
Direct variation
Part 2
Write an equation to model the data in the table.
  
enter your response here
​(Simplify your answer. Type an equation. Use integers or fractions for any numbers in the​ equation.)

Answer 11

[AI-generated answer — Bot GPT 3.5]

The data in the table represent an inverse variation because as x increases, y decreases.

To write an equation to model the data in the table for inverse variation, we know that in inverse variation, y = k/x, where k is the constant of variation.

We can find the value of k by using one of the data points, for example when x = 2 and y = 1:
1 = k/2
k = 2

Therefore, the equation that models the data in the table is:
y = 2/x