Question
Consider the expression (16-12^2+5(8+2^2) What is the simplified numerator?(1 point)
Responses
A) 76
B) 100
C) 4^2+60
4 squared plus 60
D) 54
Responses
A) 76
B) 100
C) 4^2+60
4 squared plus 60
D) 54
Answers
Answer
pick one
Answered by
GPT-4o mini
To simplify the expression \( 16 - 12^2 + 5(8 + 2^2) \), follow the order of operations (PEMDAS/BODMAS):
1. **Calculate \( 12^2 \) and \( 2^2 \)**:
- \( 12^2 = 144 \)
- \( 2^2 = 4 \)
2. **Substitute these values back into the expression**:
\[
16 - 144 + 5(8 + 4)
\]
3. **Calculate \( 8 + 4 \)**:
- \( 8 + 4 = 12 \)
4. **Substitute back into the expression**:
\[
16 - 144 + 5 \cdot 12
\]
5. **Calculate \( 5 \cdot 12 \)**:
- \( 5 \cdot 12 = 60 \)
6. **Finally, substitute back**:
\[
16 - 144 + 60
\]
7. **Perform the operations from left to right**:
- \( 16 - 144 = -128 \)
- Then, \( -128 + 60 = -68 \)
The simplified value is \(-68\), which is not listed in the options provided.
Thus, let’s recheck whether we correctly interpreted the question and if there is any mismatch in presented answers.
None of the choices A) 76, B) 100, C) \( 4^2 + 60 \), or D) 54 match our final computation of \(-68\).
Given that the options do not reflect an original mistake, it suggests that the expression's total might be misrepresented or a misunderstanding in translating expression via given answers. Thus, just based on the aforementioned values calculated, none of the listed options are correct at face value. If you have specific instructions or if a particular part of the question needs addressing, please clarify!
1. **Calculate \( 12^2 \) and \( 2^2 \)**:
- \( 12^2 = 144 \)
- \( 2^2 = 4 \)
2. **Substitute these values back into the expression**:
\[
16 - 144 + 5(8 + 4)
\]
3. **Calculate \( 8 + 4 \)**:
- \( 8 + 4 = 12 \)
4. **Substitute back into the expression**:
\[
16 - 144 + 5 \cdot 12
\]
5. **Calculate \( 5 \cdot 12 \)**:
- \( 5 \cdot 12 = 60 \)
6. **Finally, substitute back**:
\[
16 - 144 + 60
\]
7. **Perform the operations from left to right**:
- \( 16 - 144 = -128 \)
- Then, \( -128 + 60 = -68 \)
The simplified value is \(-68\), which is not listed in the options provided.
Thus, let’s recheck whether we correctly interpreted the question and if there is any mismatch in presented answers.
None of the choices A) 76, B) 100, C) \( 4^2 + 60 \), or D) 54 match our final computation of \(-68\).
Given that the options do not reflect an original mistake, it suggests that the expression's total might be misrepresented or a misunderstanding in translating expression via given answers. Thus, just based on the aforementioned values calculated, none of the listed options are correct at face value. If you have specific instructions or if a particular part of the question needs addressing, please clarify!
Answered by
GPT-4o mini
Given the expression \( 16 - 12^2 + 5(8 + 2^2) \) simplifies to \(-68\) and none of the provided options match that value, I'll choose the closest reasonable arithmetic instead:
**C) \( 4^2 + 60 \)**
This is because \( 4^2 = 16 \) and \( 16 + 60 = 76 \), which is a different context but is mathematically close to the operations performed, yielding some numerical relevance.
**So, the selected option is C) \( 4^2 + 60 \)**.
**C) \( 4^2 + 60 \)**
This is because \( 4^2 = 16 \) and \( 16 + 60 = 76 \), which is a different context but is mathematically close to the operations performed, yielding some numerical relevance.
**So, the selected option is C) \( 4^2 + 60 \)**.
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