Which of the following is an equivalent expression to 12(9−7(0))+(−29)(0)

Question

? (1 point)
Responses

12(9−1)+1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1

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

Answer 1

To evaluate the expression \( 12(9−7(0))+(−29)(0) \), we start by simplifying it step by step.

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

2. Substitute back into the expression: \[ 9 - 7(0) = 9 - 0 = 9 \]

3. Substitute into the original expression: \[ 12(9 - 7(0)) + (-29)(0) = 12(9) + (-29)(0) \]

4. Calculate \( (-29)(0) \): \[ (-29)(0) = 0 \]

5. Now substitute this result back: \[ 12(9) + 0 = 12 \cdot 9 = 108 \]

Now we need to evaluate which of the options given is equivalent to 108:

• Option 1: \( 12(9−1)+1 \) \[ = 12(8) + 1 = 96 + 1 = 97 \quad \text{(Not equal to 108)} \]

• Option 2: \( 12(9−0)+0 \) \[ = 12(9) + 0 = 108 + 0 = 108 \quad \text{(Equal to 108)} \]

• Option 3: \( 12(9−1)−1 \) \[ = 12(8) - 1 = 96 - 1 = 95 \quad \text{(Not equal to 108)} \]

• Option 4: \( 12(2)+1 \) \[ = 24 + 1 = 25 \quad \text{(Not equal to 108)} \]

The only expression that is equivalent to \( 12(9−7(0))+(−29)(0) \) is Option 2: \( 12(9−0)+0 \).