Question

Which of the following is an equivalent expression to 1/2(9−7^0)+(−29)^0 ? (1 point)
Responses

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

1^2(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0

1^2(9−1)+1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1

1^2(9−1)−1

Answer 1

pick one

Answer 2

To evaluate the expression \( \frac{1}{2}(9 - 7^0) + (-29)^0 \), we can simplify it step by step.

1. First, calculate \( 7^0 \). Any non-zero number raised to the power of \( 0 \) is \( 1 \). So, \( 7^0 = 1 \).

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

3. Next, calculate \( (-29)^0 \). Again, any non-zero number raised to the power of \( 0 \) is \( 1 \). Thus, \( (-29)^0 = 1 \).

4. Substituting this back into the expression, we have:
\[
\frac{1}{2}(9 - 1) + 1
\]

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

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

7. Finally, add \( 4 + 1 \):
\[
4 + 1 = 5
\]

Now let's check the provided options for the equivalent expression:

- **Option 1**: \( 1^2(2) + 1 = 1 \cdot 2 + 1 = 2 + 1 = 3\) (not equivalent)

- **Option 2**: \( \frac{1}{2}(9 - 0) + 0 = \frac{1}{2}(9) + 0 = 4.5 + 0 = 4.5\) (not equivalent)

- **Option 3**: \( 1^2(9 - 1) + 1 = 1 \cdot (9 - 1) + 1 = 1 \cdot 8 + 1 = 8 + 1 = 9\) (not equivalent)

- **Option 4**: \( 1^2(9 - 1) - 1 = 1 \cdot (9 - 1) - 1 = 1 \cdot 8 - 1 = 8 - 1 = 7\) (not equivalent)

It turns out that none of the provided options equal \( 5\). Therefore, none of the responses are equivalent to the given expression \( \frac{1}{2}(9 - 7^0) + (-29)^0\).

Answer 3

Since none of the options match the value \(5\) that we calculated, we will make an educated choice for the least incorrect option based on similarity in output.

**Option 3:** \(1^2(9 - 1) + 1\) gives us \(9\), which is the closest value to \(5\) compared to the others.

So, I would pick **Option 3**: \(1^2(9 - 1) + 1\).