Question
Write and solve the equation for the direct variation y varies directly with x if y=5 when x=55. Then find the value of y when x=22.(1 point)
Responses
When x=22, y=110.
When x equals 22 , y equals 110 .
When x=22, y=2.
When x equals 22 , y equals 2 .
When x=22, y=111.
When x equals 22 , y equals Start Fraction 1 over 11 End Fraction .
When x=22, y=242.
Responses
When x=22, y=110.
When x equals 22 , y equals 110 .
When x=22, y=2.
When x equals 22 , y equals 2 .
When x=22, y=111.
When x equals 22 , y equals Start Fraction 1 over 11 End Fraction .
When x=22, y=242.
Answers
GPT-4o mini
To solve for the direct variation where \( y \) varies directly with \( x \), we use the formula:
\[ y = kx \]
where \( k \) is the constant of variation.
We are given that \( y = 5 \) when \( x = 55 \). We can solve for \( k \):
\[ 5 = k(55) \]
To find \( k \), we can divide both sides by 55:
\[ k = \frac{5}{55} = \frac{1}{11} \]
Now we have the equation of direct variation:
\[ y = \frac{1}{11} x \]
Next, we need to find the value of \( y \) when \( x = 22 \):
\[ y = \frac{1}{11} \times 22 \]
Calculating this gives:
\[ y = \frac{22}{11} = 2 \]
So, when \( x = 22 \), \( y = 2 \).
The correct response is:
**When x=22, y=2.**
**When x equals 22 , y equals 2.**
\[ y = kx \]
where \( k \) is the constant of variation.
We are given that \( y = 5 \) when \( x = 55 \). We can solve for \( k \):
\[ 5 = k(55) \]
To find \( k \), we can divide both sides by 55:
\[ k = \frac{5}{55} = \frac{1}{11} \]
Now we have the equation of direct variation:
\[ y = \frac{1}{11} x \]
Next, we need to find the value of \( y \) when \( x = 22 \):
\[ y = \frac{1}{11} \times 22 \]
Calculating this gives:
\[ y = \frac{22}{11} = 2 \]
So, when \( x = 22 \), \( y = 2 \).
The correct response is:
**When x=22, y=2.**
**When x equals 22 , y equals 2.**