Question
(16−12)^2+5(8+22)
_______________
5^3−(1+4)^2
. What is the simplified numerator?(1 point)
Responses
76
4^2 + 60
100
54.
_______________
5^3−(1+4)^2
. What is the simplified numerator?(1 point)
Responses
76
4^2 + 60
100
54.
Answers
GPT-4o mini
To simplify the numerator of the expression \((16-12)^2 + 5(8+22)\), we will calculate each part step by step.
1. Calculate \(16 - 12\):
\[
16 - 12 = 4
\]
2. Square that result:
\[
(16 - 12)^2 = 4^2 = 16
\]
3. Calculate \(8 + 22\):
\[
8 + 22 = 30
\]
4. Multiply by 5:
\[
5(8 + 22) = 5 \times 30 = 150
\]
5. Combine both results to find the numerator:
\[
(16 - 12)^2 + 5(8 + 22) = 16 + 150 = 166
\]
Now let's look at the provided options:
- 76
- \(4^2 + 60\) (which equals \(16 + 60 = 76\))
- 100
- 54
Since \(166\) is not directly one of the provided responses, the values offered do not appear to match our calculations. Please verify if the question or responses were transcribed correctly or provide more context.
1. Calculate \(16 - 12\):
\[
16 - 12 = 4
\]
2. Square that result:
\[
(16 - 12)^2 = 4^2 = 16
\]
3. Calculate \(8 + 22\):
\[
8 + 22 = 30
\]
4. Multiply by 5:
\[
5(8 + 22) = 5 \times 30 = 150
\]
5. Combine both results to find the numerator:
\[
(16 - 12)^2 + 5(8 + 22) = 16 + 150 = 166
\]
Now let's look at the provided options:
- 76
- \(4^2 + 60\) (which equals \(16 + 60 = 76\))
- 100
- 54
Since \(166\) is not directly one of the provided responses, the values offered do not appear to match our calculations. Please verify if the question or responses were transcribed correctly or provide more context.