Which of the following is an equivalent expression to 12(9−70)+(−29)0
? (1 point)
12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
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(2)+1
12(9−70)+(−29)0 simplifies to:
12(-61) + 0
The equivalent expression is: 12(-61)+0
Which of the following shows the correct process of solving −4(3+120)+150
by generating an equivalent expression using the Zero Power Rule? (1 point)
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 4 times 5 equals negative 20
−4(3+120)+150 =−4(15)+15=−60+15=−45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45
−4(3+120)+150=−4(15)+1=−60+1=−59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59
−4(3+120)+150 =−4(15)+15=−60+15=−45
The correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule is:
−4(3+120)+150 =−4(15)+15=−60+15=−45
To find the equivalent expression to 12(9−70)+(−29)0, let's simplify each option:
1. 12(9−1)−1
Simplifying the parentheses, we have 12(8)−1.
Multiplying, we get 96−1.
Therefore, the expression is equivalent to 95.
2. Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
Simplifying the parentheses, we have Start Fraction 1 over 2 End Fraction (8)−1.
Applying the fraction, we have 4(8)−1.
Multiplying, we get 32−1.
Therefore, the expression is equivalent to 31.
3. Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0
Simplifying the parentheses, we have Start Fraction 1 over 2 End Fraction (9)+0.
Applying the fraction, we have 4.5(9)+0.
Multiplying, we get 40.5+0.
Therefore, the expression is equivalent to 40.5.
4. 12(2)+1
Simplifying the parentheses, we have 12(2)+1.
Multiplying, we get 24+1.
Therefore, the expression is equivalent to 25.
Therefore, the equivalent expression to 12(9−70)+(−29)0 is 25.