Question

Which of the following is an equivalent expression to 12(9−70)+(−29)0 ? (1 point) Responses 12(9−1)+1 Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1 12(2)+1 Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1 12(9−0)+0 Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0 12(9−1)−1

Answer 1

To simplify the expression \( 12(9 - 70) + (-29)0 \), we start by simplifying the components step by step.

1. **Calculate the multiplication with 0**:
\( (-29)0 = 0 \).
So, the expression simplifies to:
\[
12(9 - 70) + 0 = 12(9 - 70)
\]

2. **Calculate the subtraction inside the parentheses**:
\( 9 - 70 = -61 \).
Now the expression is:
\[
12(-61)
\]

3. **Calculate the multiplication**:
\( 12 \times (-61) = -732 \).

Now we have simplified the expression to \( -732 \).

Next, we need to check which of the provided responses is equivalent to \( -732 \):

1. **Evaluate \( 12(9 - 1) + 1 \)**:
\[
= 12(8) + 1 = 96 + 1 = 97
\]

2. **Evaluate \( \frac{1}{2}(9 - 1) + 1 \)**:
\[
= \frac{1}{2}(8) + 1 = 4 + 1 = 5
\]

3. **Evaluate \( 12(2) + 1 \)**:
\[
= 12(2) + 1 = 24 + 1 = 25
\]

4. **Evaluate \( \frac{1}{2}(2) + 1 \)**:
\[
= \frac{1}{2}(2) + 1 = 1 + 1 = 2
\]

5. **Evaluate \( 12(9 - 0) + 0 \)**:
\[
= 12(9) + 0 = 108 + 0 = 108
\]

6. **Evaluate \( \frac{1}{2}(9 - 0) + 0 \)**:
\[
= \frac{1}{2}(9) + 0 = 4.5 + 0 = 4.5
\]

7. **Evaluate \( 12(9 - 1) - 1 \)**:
\[
= 12(8) - 1 = 96 - 1 = 95
\]

None of the options provided yield \( -732 \). After re-evaluating the original expression \( 12(9 - 70) + (-29)0 = 12(-61) = -732 \), it appears there may be an issue. If you intended to find a numerical equivalent expression among the options listed, none of them equal \( -732 \).

Please check again, or clarify if there was a specific method or condition that should be applied to the expressions that could yield \( -732 \).