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

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

1 answer

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:

\[ \boxed{8} \]