Use the following example to answer the question.
Antoine goes to the mall to buy new shoes and jerseys. He pays a set rate per pair of shoes and a set rate per jersey, and he pays more per jersey than he pays per pair of shoes. His total spending can be modeled by the equation 35x+55y
. Which of the statements correctly interprets a part of the expression?
Statement #1: Antoine spends $35.00 per pair of shoes.
Statement #2: Antoine spends $55.00 per pair of shoes.
Statement #3: Antoine spends $35.00 in total for shoes.
Statement #3: Antoine spends $35.00 in total for shoes.
Use the Commutative Property of Multiplication to rewrite the algebraic expression: k17⋅z33
.
The Commutative Property of Multiplication states that the order of the factors does not affect the product. Therefore, we can rearrange the factors in any order without changing the result.
Using the Commutative Property of Multiplication, we can rewrite the expression as:
17k ⋅ 33z
Which expression correctly demonstrates the Commutative Property of Multiplication?(1 point)
A. 15(x+4)=15(x⋅4)
B. x+4+15=15+4+x
C. 15⋅x⋅4=4+15+x
D. 15⋅(x)⋅4=4⋅15⋅(x)
D. 15⋅(x)⋅4=4⋅15⋅(x)
Write an equivalent expression to (a⋅b)⋅c using the Associative Property of Multiplication.
The Associative Property of Multiplication states that the grouping of factors does not affect the result of the multiplication.
Using the Associative Property of Multiplication, we can rewrite the expression as:
a⋅(b⋅c)
Which expression is equivalent to −3x−5?
A. −1+3x−(2x+6)
B. −1+(x−4x)+6
C. (x−7)+(2−4x)
D. (−4x−6)+(2+5x)
D. (-4x-6) + (2+5x)
How to use Distributive Property, to find the an expression that is equivalent to 4x3+8x2+12x
?
To use the Distributive Property, we need to factor out the common factor from each term in the expression.
The common factor in this case is 4x. We can factor out 4x from each term:
4x * 3 + 4x * 2 + 4x * 3
Now, we can simplify each term:
= 12x + 8x + 12x
= 20x + 12x
= 32x
Therefore, an expression that is equivalent to 4x^3 + 8x^2 + 12x is 32x.
According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x?
A. (2x2+4)(2x2+3)
B. 4x(4x+5x)
C. 4x(x2+2x+3)
D. (2x2+4)(2x−3)
To use the Distributive Property, we need to distribute the common factor to each term within the parentheses.
The common factor in this case is 4x.
Distributing 4x to each term in the expression gives us:
4x * 3 + 4x * 8x + 4x * 12
Simplifying each term, we get:
12x + 32x^2 + 48x
Therefore, the expression that is equivalent to 4x^3 + 8x^2 + 12x is 12x + 32x^2 + 48x.
Among the given options, the expression that is equivalent to 4x^3 + 8x^2 + 12x is not present.
According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x?
A. (2x^2+4)(2x^2+3)
B. 4x(4x+5x)
C. 4x(x^2+2x+3)
D. (2x^2+4)(2x−3)
According to the Distributive Property, the expression that is equivalent to 4x^3 + 8x^2 + 12x is:
C. 4x(x^2 + 2x + 3)
This is because when we distribute the 4x to each term inside the parentheses, we get:
4x * x^2 + 4x * 2x + 4x * 3 = 4x^3 + 8x^2 + 12x
Which of the following simplifies to the same expression as 4x2−3x2+5x−24?
A. (x+8)(x−3)
B. (x+6)(x−4)
C. 4x(x−6)
D. 2(x−12)
To find the expression that simplifies to the same expression as 4x^2 - 3x^2 + 5x - 24, we need to factor this expression.
4x^2 - 3x^2 + 5x - 24 simplifies to x^2 + 5x - 24.
Among the given options, the expression that simplifies to the same expression as 4x^2 - 3x^2 + 5x - 24 is:
B. (x + 6)(x - 4)
If we expand (x + 6)(x - 4), we get x^2 + 2x - 24, which is equivalent to x^2 + 5x - 24.
Add the polynomial expressions 5z−2z2−4z+5 and 6z2+3−7z.
A. 4z2−6z+8
4 z squared minus 6 z plus 8
B. 4z2−z+8
4 z squared minus z plus 8
C. 11z2+z−2
11 z squared plus z minus 2
D. 9z2−11z+8
To add the polynomial expressions 5z - 2z^2 - 4z + 5 and 6z^2 + 3 - 7z, we simply combine like terms.
The like terms are the terms with the same variables and the same powers.
Combining the terms, we get:
(-2z^2 + 6z^2) + (5z - 4z - 7z) + (5 + 3)
= 4z^2 - 6z + 8
Therefore, the correct option is:
A. 4z^2 - 6z + 8
Which of the following correctly simplifies (9x2+17x+13)−(2x2+12x+11)?
A. 7x2+5x+2
B. 7x2+29x+24
C. 9x2+17x+13−2x2−12x−11
D. 12x2+2
To simplify the expression (9x^2 + 17x + 13) - (2x^2 + 12x + 11), we distribute the negative sign to each term inside the parentheses and then combine like terms.
(9x^2 + 17x + 13) - (2x^2 + 12x + 11) = 9x^2 + 17x + 13 - 2x^2 - 12x - 11
Combining like terms, we get:
(9x^2 - 2x^2) + (17x - 12x) + (13 - 11) = 7x^2 + 5x + 2
Therefore, the correct option is:
A. 7x^2 + 5x + 2
Which of the following responses shows that polynomials form a closed system under multiplication?(1 point)
Responses
A. 6⋅−3
6 times negative 3
B. 3x24−1
Start Fraction 3 x squared over 4 minus 1 End Fraction
C. 4x3⋅5
4 x cubed times 5
D. (x)(12x)
left parenthesis x right parenthesis left parenthesis Start Fraction 1 over 2 End Fraction x right parenthesis
The correct response that shows that polynomials form a closed system under multiplication is:
C. 4x^3 ⋅ 5