### All Algebra II Resources

## Example Questions

### Example Question #1 : Variable Relationships

varies directly with the square root of . If , then . What is the value of if ?

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

If varies directly with the square root of , then for some constant of variation ,

If , then ; therefore, the equation becomes

,

or

.

Divide by 5 to get , making the equation

.

If , then .

### Example Question #2 : Variable Relationships

If varies directly with and when , due to the effect of a constant, what is the value of when ?

**Possible Answers:**

**Correct answer:**

Since varies directly with , where is a constant.

1. Solve for when and .

2. Use your equation to solve for when .

### Example Question #3 : Variable Relationships

If varies indirectly with and when , due to the effect of a constant, what is the value of when ?

**Possible Answers:**

**Correct answer:**

Since varies indirectly with ,

1. Solve for when and .

2. Use the equation you found to solve for when .

### Example Question #4 : Variable Relationships

varies directly with . If , what is if ?

**Possible Answers:**

**Correct answer:**

1. Since varies directly with :

with K being some constant.

2. Solve for K using the x and y values given:

3. Use the equation you solved for to find the value of y:

### Example Question #5 : Variable Relationships

varies inversely with . If , then what is equal to when ?

**Possible Answers:**

**Correct answer:**

1. Since varies indirectly with :

2. Use the given x and y values to determine the value of K:

3. Using the equation along with the value of K, find the value of y when x=5:

### Example Question #6 : Variable Relationships

varies directly with and when . What is when ?

**Possible Answers:**

**Correct answer:**

1. Since varies directly with :

2. Use the values given for x and y to solve for K:

3. Use your new equation with the K you solved for to solve for y when x=27:

### Example Question #7 : Variable Relationships

varies inversely with . When . What is the value of when ?

**Possible Answers:**

**Correct answer:**

1. Since y varies indirectly with :

2. Solve for K using the x and y values given:

3. Using the equation you created by solving for K, find y when x=100:

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