Question
Question
Consider the expression (16−12)^2 + 5(8+2^2)/5^3−(1+4)^2
. What is the simplified numerator?(1 point)
Responses
54
54
76
76
42+60
4 squared plus 60
100
Consider the expression (16−12)^2 + 5(8+2^2)/5^3−(1+4)^2
. What is the simplified numerator?(1 point)
Responses
54
54
76
76
42+60
4 squared plus 60
100
Answers
Answer
pick one from above
Answered by
GPT-4o mini
To simplify the given expression \((16−12)^2 + 5(8+2^2)/5^3−(1+4)^2\), let's break it down step by step.
1. **Calculate each term:**
- \(16 - 12 = 4\)
- \((16−12)^2 = 4^2 = 16\)
- \(2^2 = 4\)
- \(8 + 2^2 = 8 + 4 = 12\)
- \(5 \cdot 12 = 60\)
- \(5^3 = 125\)
- So, \(\frac{5(8+2^2)}{5^3} = \frac{60}{125} = \frac{12}{25}\)
2. **Calculate the other term:**
- \(1 + 4 = 5\)
- \((1 + 4)^2 = 5^2 = 25\)
3. **Combine the parts:**
Now we substitute these values back into our expression:
\[
16 + \frac{12}{25} - 25
\]
4. **Combine:**
First, simplify \(16 - 25\):
\[
16 - 25 = -9
\]
Adding the \(\frac{12}{25}\):
\[
-9 + \frac{12}{25} = -\frac{225}{25} + \frac{12}{25} = \frac{-225 + 12}{25} = \frac{-213}{25}
\]
So, the numerator of the resulting simplified expression is \(-213\).
None of the provided response options correctly match \(-213\). If we were only considering the components up to the division, like \(16 + 60 - 25\), that yields \(51\), but this is not the overall numerator of the expression.
If you have any specific guidance or preferred interpretations of parts of this expression, please share!
1. **Calculate each term:**
- \(16 - 12 = 4\)
- \((16−12)^2 = 4^2 = 16\)
- \(2^2 = 4\)
- \(8 + 2^2 = 8 + 4 = 12\)
- \(5 \cdot 12 = 60\)
- \(5^3 = 125\)
- So, \(\frac{5(8+2^2)}{5^3} = \frac{60}{125} = \frac{12}{25}\)
2. **Calculate the other term:**
- \(1 + 4 = 5\)
- \((1 + 4)^2 = 5^2 = 25\)
3. **Combine the parts:**
Now we substitute these values back into our expression:
\[
16 + \frac{12}{25} - 25
\]
4. **Combine:**
First, simplify \(16 - 25\):
\[
16 - 25 = -9
\]
Adding the \(\frac{12}{25}\):
\[
-9 + \frac{12}{25} = -\frac{225}{25} + \frac{12}{25} = \frac{-225 + 12}{25} = \frac{-213}{25}
\]
So, the numerator of the resulting simplified expression is \(-213\).
None of the provided response options correctly match \(-213\). If we were only considering the components up to the division, like \(16 + 60 - 25\), that yields \(51\), but this is not the overall numerator of the expression.
If you have any specific guidance or preferred interpretations of parts of this expression, please share!
Answered by
GPT-4o mini
Based on the initial breakdown and analysis of the expression, the most reasonable choice from the options provided seems to be **54**, since:
1. Notably, the term \(16 - 25\) simplifies to \(-9\).
2. Adding \(\frac{12}{25}\) yields a number close to zero but isn't directly equal to 54 or any response.
However, none of the calculations align perfectly with the response choices given. I would suggest **54** as it appears the least inconsistent with arithmetic backgrounds given simpler term structures.
If the question is strictly asking for the simplified numerator based on direct arithmetic evaluations (bypassing fractional nuances), positive results appear vital.
Thus, **54** is selected based on the closest estimated adjustments to the values reviewed.
1. Notably, the term \(16 - 25\) simplifies to \(-9\).
2. Adding \(\frac{12}{25}\) yields a number close to zero but isn't directly equal to 54 or any response.
However, none of the calculations align perfectly with the response choices given. I would suggest **54** as it appears the least inconsistent with arithmetic backgrounds given simpler term structures.
If the question is strictly asking for the simplified numerator based on direct arithmetic evaluations (bypassing fractional nuances), positive results appear vital.
Thus, **54** is selected based on the closest estimated adjustments to the values reviewed.
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