Question

Which of the following is an equivalent expression to 12(9−7(0))+(−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(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0

12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1

12(2)+1
Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1

Answer 1

To evaluate the expression \( 12(9−7(0))+(−29)(0) \), we start by simplifying it step by step.

1. **Calculate \( 7(0) \)**:
\[
7(0) = 0
\]

2. **Substitute back into the expression**:
\[
9 - 7(0) = 9 - 0 = 9
\]

3. **Substitute into the original expression**:
\[
12(9 - 7(0)) + (-29)(0) = 12(9) + (-29)(0)
\]

4. **Calculate \( (-29)(0) \)**:
\[
(-29)(0) = 0
\]

5. **Now substitute this result back**:
\[
12(9) + 0 = 12 \cdot 9 = 108
\]

Now we need to evaluate which of the options given is equivalent to 108:

- **Option 1**: \( 12(9−1)+1 \)
\[
= 12(8) + 1 = 96 + 1 = 97 \quad \text{(Not equal to 108)}
\]

- **Option 2**: \( 12(9−0)+0 \)
\[
= 12(9) + 0 = 108 + 0 = 108 \quad \text{(Equal to 108)}
\]

- **Option 3**: \( 12(9−1)−1 \)
\[
= 12(8) - 1 = 96 - 1 = 95 \quad \text{(Not equal to 108)}
\]

- **Option 4**: \( 12(2)+1 \)
\[
= 24 + 1 = 25 \quad \text{(Not equal to 108)}
\]

The only expression that is equivalent to \( 12(9−7(0))+(−29)(0) \) is **Option 2: \( 12(9−0)+0 \)**.