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

1/2(2)+1

1/2(9−1)−1

1/2(9−1)+1

1/2(9−0)+0

1 answer

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

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

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

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

  4. Simplify inside the parentheses: \[ 9 - 1 = 8 \]

  5. Now, substitute that back in: \[ \frac{1}{2}(8) + 1 \]

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

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

Now let's evaluate each of the given options for equivalency:

  1. \( \frac{1}{2}(2) + 1 \): \[ \frac{1}{2}(2) = 1 \quad \text{thus,} \quad 1 + 1 = 2 \quad \text{(not equal to 5)} \]

  2. \( \frac{1}{2}(9 - 1) - 1 \): \[ 9 - 1 = 8 \quad \text{thus,} \quad \frac{1}{2}(8) - 1 = 4 - 1 = 3 \quad \text{(not equal to 5)} \]

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

  4. \( \frac{1}{2}(9 - 0) + 0 \): \[ \frac{1}{2}(9) + 0 = 4.5 + 0 = 4.5 \quad \text{(not equal to 5)} \]

The expression \( \frac{1}{2}(9 - 1) + 1 \) is equivalent to the original expression.

Thus, the correct answer is: \( \frac{1}{2}(9 - 1) + 1 \)