Question

what value of m makes the equation 2/3(m-9)=1/3(m-27) true?

Responses:
-9
-3
-1
-6

Answer 1

if f(x)=x^2 and g(x)=f(x+7.2), what is the vertex of the graph of g?

Responses:
(7.2,0)
(-7.2,0)
(0,7.2)
(0,-7.2)

Answer 2

To solve the equation \( \frac{2}{3}(m - 9) = \frac{1}{3}(m - 27) \), we can eliminate the fractions by multiplying both sides by 3:

\[
3 \cdot \frac{2}{3}(m - 9) = 3 \cdot \frac{1}{3}(m - 27)
\]

This simplifies to:

\[
2(m - 9) = m - 27
\]

Now, distribute the 2 on the left side:

\[
2m - 18 = m - 27
\]

Next, we can get all terms involving \( m \) on one side by subtracting \( m \) from both sides:

\[
2m - m - 18 = -27
\]

This simplifies to:

\[
m - 18 = -27
\]

Now, add 18 to both sides:

\[
m = -27 + 18
\]

This gives us:

\[
m = -9
\]

Therefore, the value of \( m \) that makes the equation true is \( \boxed{-9} \).