Which of the following is an equivalent expression to 12(9−70)+(−29)0? (1 point) Responses 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 12(9−1)+1

Answer 1

To find an equivalent expression to \( 12(9−70)+(−29)0 \), we should first simplify the original expression step by step.

1. Calculate \((-29)0\): Any number multiplied by 0 is 0, so \((-29)0 = 0\).

2. Now substitute into the expression: \[ 12(9 - 70) + 0 \]

3. Simplify \( (9 - 70) \): \[ 9 - 70 = -61 \]

4. Now multiply: \[ 12(-61) = -732 \]

5. Finally, account for the \( + 0 \): \[ -732 + 0 = -732 \]

Now, we have that the expression \( 12(9 - 70) + (-29)0 \) simplifies to -732.

Next, we check each of the options provided to see if any of them also evaluates to -732.

1. Option 1: \( 12(9 - 0) + 0 \): \[ 12(9) + 0 = 108 + 0 = 108 \]

2. Option 2: \( \frac{1}{2}(9 - 0) + 0 \): \[ \frac{1}{2}(9) + 0 = 4.5 + 0 = 4.5 \]

3. Option 3: \( 12(9 - 1) - 1 \): \[ 12(8) - 1 = 96 - 1 = 95 \]

4. Option 4: \( \frac{1}{2}(2) + 1 \): \[ \frac{1}{2}(2) + 1 = 1 + 1 = 2 \]

5. Option 5: \( 12(9 - 1) + 1 \): \[ 12(8) + 1 = 96 + 1 = 97 \]

None of the options evaluates to -732. Since the options do not match the value of the original expression, it appears that there may have been an error in the choices provided. If you were looking for an alternative way to express the original computation, we may need different values or a revised set of responses.