Which of the following is an equivalent expression to 1/2(9−7⁰)+(−29)⁰

Question

? (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 minus 1

1/2(9−1)+1

Answer 1

To find an equivalent expression 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 into the expression: \[ \frac{1}{2}(9 - 1) + (-29)^0 \]

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

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

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

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

Now, we can check which of the provided options gives us an equivalent expression:

1. Option 1: \(\frac{1}{2}(2) + 1\) \[ \frac{1}{2}(2) + 1 = 1 + 1 = 2 \quad \text{(not equivalent)} \]

2. Option 2: \(\frac{1}{2}(9 - 0) + 0\) \[ \frac{1}{2}(9) + 0 = 4.5 \quad \text{(not equivalent)} \]

3. Option 3: \(\frac{1}{2}(9 - 1) - 1\) \[ \frac{1}{2}(8) - 1 = 4 - 1 = 3 \quad \text{(not equivalent)} \]

4. Option 4: \(\frac{1}{2}(9 - 1) + 1\) \[ \frac{1}{2}(8) + 1 = 4 + 1 = 5 \quad \text{(equivalent)} \]

Therefore, the answer is: \[ \frac{1}{2}(9 - 1) + 1 \]