Question

Consider the expression (16−12)2+5(8+22)53−(1+4)2. What is the simplified numerator?(1 point)
Responses

54
4^2+60
76
100

Answer 1

Let's simplify the expression step by step:

The expression is:

\[
(16-12)^2 + 5(8 + 22) \cdot 53 - (1 + 4)^2
\]

1. Calculate the components in the parentheses:
- \(16 - 12 = 4\)
- \(1 + 4 = 5\)
- \(8 + 22 = 30\)

2. Substitute these values back into the expression:
- So we have:
\[
(4)^2 + 5(30) \cdot 53 - (5)^2
\]

3. Compute the squares:
- \(4^2 = 16\)
- \(5^2 = 25\)

4. Substitute these values back into the expression:
- Now we have:
\[
16 + 5(30) \cdot 53 - 25
\]

5. Compute \(5(30)\):
- \(5 \cdot 30 = 150\)

6. Substitute back into the expression:
- So we have:
\[
16 + 150 \cdot 53 - 25
\]

7. Now, calculate \(150 \cdot 53\):
- \(150 \cdot 53 = 7950\)

8. Substitute this back:
- We now have:
\[
16 + 7950 - 25
\]

9. Finally, perform the remaining arithmetic:
- \(16 - 25 = -9\)
- \(-9 + 7950 = 7941\)

So the simplified expression is \(7941\). If we need to find the numerator of the expression, it's unclear what the problem means since it doesn't indicate a fraction. However, based on the provided options, let's go over them once more to check:

Responses:
- 54
- \(4^2 + 60\) which is \(16 + 60 = 76\) — this is close to 76
- 76 — (This looks correct if these numbers are not fractions)
- 100

The correct simplified numerator based on the computation is not distinctly available in the given options because we found \(7941\).

If we consider any portions of the expression leading to 100, we note that it’s not part of it. So out of the provided options, **76** seems the most plausible response because \(4^2 + 60\) sums up to 76.

Thus, the final answer is:

**76**