If y varies directly with x, find the constant of variation with x = 4 and y = -24

If y varies inversely with x, find the constant of variation with x=5 and y = 10

If y varies directly with x, and y = 35 when x = 5 , find x when y = -7

If y varies directly with x, and y = -12 when x = 6, find x when y = -4

If y varies inversely with x, and y = 8 when x = 10 , find x when y = 4

If y varies inversely with x, and y = -5 when x = 20, find x when y = -4

I need the answer to these very, very, badlyyyyy!!!

There were 6 rows of these I completed the first rows, this a row, and I'm currently working on the last row.

No problem! I'll be happy to help you with these questions step-by-step. Let's start with the first question:

1. If y varies directly with x, we can express this relationship as y = kx, where k is the constant of variation.

Given x = 4 and y = -24, we can substitute these values into the equation and solve for k:
-24 = k * 4

Divide both sides of the equation by 4:
-6 = k

So, the constant of variation is -6.

Now let's move on to the second question:

2. If y varies inversely with x, we can express this relationship as y = k/x, where k is the constant of variation.

Given x=5 and y=10, we can substitute these values into the equation and solve for k:
10 = k/5

Multiply both sides of the equation by 5:
50 = k

So, the constant of variation is 50.

Let's proceed to the third question:

3. If y varies directly with x, and y = 35 when x = 5, we need to find x when y = -7.

Using the given relationship y = kx, we can substitute y = -7 and solve for x:
-7 = k * x

To find x, we can rearrange the equation:
x = -7 / k

However, since we don't know the value of k, we can't find the exact value of x. We need the constant of variation (k) in order to solve for x.

Next, let's tackle the fourth question:

4. If y varies directly with x, and y = -12 when x = 6, we need to find x when y = -4.

Using the given relationship y = kx, we can substitute y = -4 and solve for x:
-4 = k * x

To find x, we can rearrange the equation:
x = -4 / k

However, since we don't know the value of k, we can't find the exact value of x. We need the constant of variation (k) in order to solve for x.

Moving on to the fifth question:

5. If y varies inversely with x, and y = 8 when x = 10, we need to find x when y = 4.

Using the given relationship y = k/x, we can substitute y = 4 and solve for x:
4 = k / x

Rearranging the equation, we get:
x = k / 4

To find x, we also need to know the value of k. However, the value of k is not given, so we cannot determine the exact value of x.

Finally, let's tackle the last question:

6. If y varies inversely with x, and y = -5 when x = 20, we need to find x when y = -4.

Using the given relationship y = k/x, we can substitute y = -4 and solve for x:
-4 = k / x

Rearranging the equation, we get:
x = k / -4

Similar to the previous question, we need to know the value of k to find the exact value of x. Without the given value of k, we cannot determine the value of x.

I hope this helps clarify the process for finding the constant of variation and solving for x in these types of problems. Let me know if you have any further questions!

To find the constant of variation in direct or inverse variation, we can use the formulas:

1. Direct Variation: y = kx
2. Inverse Variation: y = k/x

For the first question, if y varies directly with x and we have x = 4 and y = -24, we can substitute these values into the direct variation formula to solve for the constant of variation (k):

-24 = k * 4

To isolate k, divide both sides of the equation by 4:

k = -24 / 4
k = -6

Therefore, the constant of variation in this case is -6.

For the second question, if y varies inversely with x and we have x = 5 and y = 10, we can substitute these values into the inverse variation formula to solve for the constant of variation:

10 = k / 5

To isolate k, multiply both sides of the equation by 5:

k = 10 * 5
k = 50

Therefore, the constant of variation in this case is 50.

For the third question, we need to find x when y = -7 and y varies directly with x. Given that y = 35 when x = 5, we can set up a proportion based on direct variation:

y₁ / x₁ = y₂ / x₂

Substituting the known values:

35 / 5 = -7 / x₂

To solve for x₂, cross-multiply:

35 * x₂ = -7 * 5

Divide both sides of the equation by 35:

x₂ = (-7 * 5) / 35
x₂ = -1

Therefore, when y = -7, x is equal to -1.

For the fourth question, we can use the same method as the third question. Given that y = -12 when x = 6, and we need to find x when y = -4:

-12 / 6 = -4 / x₂

Cross-multiplying:

-12 * x₂ = -4 * 6

Dividing by -12:

x₂ = (-4 * 6) / -12
x₂ = 2

Therefore, when y = -4, x is equal to 2.

For the fifth question, if y varies inversely with x and y = 8 when x = 10, we can use the inverse variation formula:

y = k / x

Substituting the values:

8 = k / 10

To solve for k, multiply both sides of the equation by 10:

k = 8 * 10
k = 80

Now, we need to find x when y = 4:

4 = 80 / x₂

Cross-multiplying:

4 * x₂ = 80

Dividing by 4:

x₂ = 80 / 4
x₂ = 20

Therefore, when y = 4, x is equal to 20.

For the sixth question, if y varies inversely with x and y = -5 when x = 20, we will again use the inverse variation formula:

y = k / x

Substituting the values:

-5 = k / 20

To solve for k, multiply both sides of the equation by 20:

k = -5 * 20
k = -100

Now, we need to find x when y = -4:

-4 = -100 / x₂

Cross-multiplying:

-4 * x₂ = -100

Dividing by -4:

x₂ = -100 / -4
x₂ = 25

Therefore, when y = -4, x is equal to 25.

I hope this explanation helps you understand how to solve these types of problems! Let me know if you have any further questions.

direct: y = kx, so k = y/x

inverse: xy = k

If y varies directly with x, find the constant of variation with x = 4 and y = -24
k = y/x = -24/4 = -6

If y varies inversely with x, find the constant of variation with x=5 and y = 10
k = xy = 5*10 = 50

and do the others in like wise.