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Which of the following is an equivalent expression to 12(9−70)+(−29)0 ? (1 point)Responses12(9−1)+1Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 112(9−0)+0Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 012(2)+1Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 112(9−1)−1

1 answer

To simplify the expression \( 12(9 - 70) + (-29)0 \), let's break it down step by step:

  1. Calculate \( (-29)0 \):

    • Any number multiplied by zero equals zero, so \( (-29)0 = 0 \).

  2. Simplify the expression: \[ 12(9 - 70) + 0 = 12(9 - 70). \]

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

  4. Substitute back into the expression: \[ 12(-61) = -732. \]

Now let's examine each of the given response options to find one that is equal to \(-732\).

  1. First option: \( 12(9 - 1) + 1 \)

    • \( 9 - 1 = 8 \)
    • \( 12(8) + 1 = 96 + 1 = 97 \) (not equal to -732)

  2. Second option: \( \frac{1}{2}(9 - 1) + 1 \)

    • \( 9 - 1 = 8 \)
    • \( \frac{1}{2}(8) + 1 = 4 + 1 = 5 \) (not equal to -732)

  3. Third option: \( 12(9 - 0) + 0 \)

    • \( 9 - 0 = 9 \)
    • \( 12(9) + 0 = 108 + 0 = 108 \) (not equal to -732)

  4. Fourth option: \( 12(2) + \frac{1}{2}(2) + 1 \)

    • \( 12(2) = 24 \)
    • \( \frac{1}{2}(2) = 1 \)
    • \( 24 + 1 + 1 = 26 \) (not equal to -732)

  5. Fifth option: \( 12(9 - 1) - 1 \)

    • \( 9 - 1 = 8 \)
    • \( 12(8) - 1 = 96 - 1 = 95 \) (not equal to -732)

None of the provided responses are equal to \(-732\). Please verify the equation you provided or check if there are additional response options.