Question

Which of the following is an equivalent expression to 1/2(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(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 determine which of the given expressions is equivalent to \( \frac{1}{2}(9 - 7^0) + (-29)^0 \), we first need to simplify the original expression.

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

2. Substitute \( 7^0 \) in the expression:
\[
\frac{1}{2}(9 - 1) + (-29)^0
\]

3. Calculate \( (-29)^0 \):
\[
(-29)^0 = 1
\]

4. Now substitute this back in:
\[
\frac{1}{2}(9 - 1) + 1
\]

5. Simplify \( 9 - 1 \):
\[
9 - 1 = 8
\]

6. Now, calculate \( \frac{1}{2}(8) + 1 \):
\[
\frac{1}{2}(8) = 4
\]
\[
4 + 1 = 5
\]

So, the original expression simplifies to \( 5 \).

Now let's check each response to see which one also equals \( 5 \):

- **Response 1: \( \frac{1}{2}(9 - 1) + 1 \)**
\[
= \frac{1}{2}(8) + 1 = 4 + 1 = 5 \quad \text{(This is equivalent)}
\]

- **Response 2: \( \frac{1}{2}(2) + 1 \)**
\[
= 1 + 1 = 2 \quad \text{(Not equivalent)}
\]

- **Response 3: \( \frac{1}{2}(9 - 0) + 0 \)**
\[
= \frac{1}{2}(9) + 0 = 4.5 + 0 = 4.5 \quad \text{(Not equivalent)}
\]

- **Response 4: \( \frac{1}{2}(9 - 1) - 1 \)**
\[
= \frac{1}{2}(8) - 1 = 4 - 1 = 3 \quad \text{(Not equivalent)}
\]

Thus, the only equivalent expression is:

\[
\frac{1}{2}(9 - 1) + 1 \quad \text{(Response 1)}
\]