Name the property of real numbers illustrated by the equation.
π⋅3=3⋅π
(1 point)
Responses
Commutative Property of Addition
Commutative Property of Addition
Closure Property
Closure Property
Commutative Property of Multiplication
Commutative Property of Multiplication
Associative Property of Multiplication
Commutative Property of Multiplication
Which of the following correctly demonstrates the use of the Commutative Property of Multiplication?
a. 11(b+z)=11b+11z
b. 2(b^(10)-z^(11))=(b^(10)+z^(11))*2
c. z^(11)*2=z^(11)+2
d. 3(b^(10)+4)=3(4+b^(10))3
a. 11(b+z)=11b+11z
Which of the following correctly demonstrates the Commutative Property of Addition?
123+456=579
abcxyz=zyxcba
0+579=579
abc+xyz=xyz+abc
abc+xyz=xyz+abc
Use the Commutative Property to determine the missing step in proving the equivalence of 12a+10+a=10+a+12a.
Step 1: [missing]
Step 2: 10+13a=10+13a
Step 3: The expressions are equivalent because they both equal the same value.
10+12a+a=10+13a
12a+10+a−a=10+a+12a−a
12a+10=10+12a
12a+10+a−10=10+a+12a−10
Step 1: 12a+10+a = a+10+12a (Using the Commutative Property of Addition to change the order of terms)
Use the Commutative Property to determine the missing step in proving the equivalence of 12a+10+a=10+a+12a.
a. 10+12a+a=10+13a
b. 12a+10+a−a=10+a+12a−a
c. 12a+10=10+12a
d. 12a+10+a−10=10+a+12a−10
The missing step is:
d. 12a+10+a−10=10+a+12a−10 (Using the Commutative Property of Addition to reorder the terms)
Substituting 1 for x in the equation 5x + 3=x⋅5 + 3 is a test case for which property?
The Commutative Property of Multiplication
The Associative Property of Multiplication
The Commutative Property of Addition
The Associative Property of Addition
The Commutative Property of Multiplication
Which step contains an error using the Commutative Property of Addition in verifying 8+x^(2)+17x-x^(2)+4=10+4x^(2)+10x-4x^(2)+2+7x
Step 1: 8+4+x^(2)-x^(2)+17x=10+2+10x-4x^(2)+7x+4x^(2)
Step 2: 8+4+17x+x^(2)-x^(2)=10+2+4x^(2)-4x^(2)+10x+7x
Step 3: 12+17x+x^(2)=12-x^(2)+17x
The error is in Step 2. The Commutative Property of Addition states that the order of terms can be changed, but in this step, the terms are not in the same order on both sides of the equation. Specifically, the terms 4x^2 and -4x^2 should have been switched to maintain the same order of the terms.
Which step contains an error using the Commutative Property of Addition in verifying 8+x^(2)+17x-x^(2)+4=10+4x^(2)+10x-4x^(2)+2+7x
Step 1: 8+4+x^(2)-x^(2)+17x=10+2+10x-4x^(2)+7x+4x^(2)
Step 2: 8+4+17x+x^(2)-x^(2)=10+2+4x^(2)-4x^(2)+10x+7x
Step 3: 12+17x+x^(2)=12-x^(2)+17x
A. No mistake was made.
B. Step 1
C. Step 2
D. Step 3
The correct answer is C. Step 2
In Step 2, there is an error in using the Commutative Property of Addition. The terms 4x^2 and -4x^2 were not switched in the same order on both sides of the equation.
rewrite 8+4+17x+x^(2)-x^(2)
The expression can be simplified as:
8 + 4 + 17x + x^2 - x^2 = 12 + 17x
Which step contains an error using the Commutative Property of Addition in verifying 8+x^(2)+17x-x^(2)+4=10+4x^(2)+10x-4x^(2)+2+7x
Step 1: 8+4+x^(2)-x^(2)+17x=10+2+10x-4x^(2)+7x+4x^(2)
Step 2: 8+4+17x+x^(2)-x^(2)=10+2+4x^(2) - 4x^(2)+10x+7x
Step 3: 12+17x+x^(2)=12-x^(2)+17x
The correct answer is B. Step 1.
In Step 1, there is an error in using the Commutative Property of Addition. The terms x^2 and -x^2 were not switched in the same order on both sides of the equation.
Which step contains an error using the Commutative Property of Addition in verifying 8 + x^(2) + 17x - x^(2) + 4 = 10 + 4x^(2) + 10x - 4x^(2) + 2 + 7x
Step 1: 8 + 4 + x^(2) - x^(2) + 17x = 10 + 2 + 10x - 4x^(2) + 7x + 4x^(2)
Step 2: 8 + 4 + 17x + x^(2) - x^(2) = 10 + 2 + 4x^(2) - 4x^(2) + 10x + 7x
Step 3: 12 + 17x + x^(2) = 12 - x^(2) + 17x
The correct answer is C. Step 2.
In Step 2, there is an error in using the Commutative Property of Addition. The terms 4x^2 and -4x^2 were not switched in the same order on both sides of the equation.