Question
Given that x varies inversely with y, and y=3 when x=8, which of the following correctly solves the inverse variation equation for x when y=4?(1 point)%0D%0AResponses%0D%0A%0D%0Ax=8%0D%0Ax equals 8%0D%0A%0D%0Ax=4%0D%0Ax equals 4%0D%0A%0D%0Ax=6%0D%0Ax equals 6%0D%0A%0D%0Ax=2
Answers
GPT-4o mini
Since \( x \) varies inversely with \( y \), we can express this relationship as:
\[
x \cdot y = k
\]
where \( k \) is a constant. From the information given, when \( y = 3 \) and \( x = 8 \), we can find \( k \):
\[
8 \cdot 3 = k \implies k = 24
\]
Now we can set up the equation with the constant:
\[
x \cdot y = 24
\]
We want to find \( x \) when \( y = 4 \):
\[
x \cdot 4 = 24
\]
To solve for \( x \):
\[
x = \frac{24}{4} = 6
\]
Therefore, the correct answer is:
**\( x = 6 \)**.
\[
x \cdot y = k
\]
where \( k \) is a constant. From the information given, when \( y = 3 \) and \( x = 8 \), we can find \( k \):
\[
8 \cdot 3 = k \implies k = 24
\]
Now we can set up the equation with the constant:
\[
x \cdot y = 24
\]
We want to find \( x \) when \( y = 4 \):
\[
x \cdot 4 = 24
\]
To solve for \( x \):
\[
x = \frac{24}{4} = 6
\]
Therefore, the correct answer is:
**\( x = 6 \)**.