Question

What value correctly fills in the blank so that the expressions are equivalent?

32 + 72 = blank x (4 + 9)
4
8
12
13

Answer 1

First, we simplify the left side of the equation:

\[
32 + 72 = 104
\]

Next, we simplify the expression on the right side:
\[
4 + 9 = 13
\]

Now we can express the right side as:

\[
\text{blank} \times 13
\]

We want to solve the equation:

\[
104 = \text{blank} \times 13
\]

To find the value of "blank", we divide both sides by 13:

\[
\text{blank} = \frac{104}{13}
\]

Calculating the division:

\[
\frac{104}{13} = 8
\]

Thus, the value that correctly fills in the blank so that the expressions are equivalent is:

\[
\boxed{8}
\]