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.
Consider the expression (16 − 12)^2 + 5(8+2^2) / 5^3−(1+4)^2. What is the simplified numerator?
To simplify the numerator, we will start by following the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).
In the expression, we have:
(16 − 12)^2 + 5(8+2^2)
First, we will simplify the parentheses:
(16 − 12)^2 + 5(8+4)
Next, we will simplify the exponent:
(4)^2 + 5(8+4)
Now, we will simplify the addition inside the parentheses:
(4)^2 + 5(12)
We will square 4:
16 + 5(12)
Next, we will simplify the multiplication:
16 + 60
Finally, we will add:
76
Therefore, the simplified numerator is 76.
Which expression is equivalent to −3x − 5?
(x−7)+(2−4x)
−1+3x−(2x+6)
(−4x−6)+(2+5x)
−1+(x−4x)+6
The expression that is equivalent to -3x - 5 is (-4x - 6).
According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x?
4x(4x+5x)
4x(x2+2x+3)
(2x2+4)(2x−3)
(2x2+4)(2x2+3)
According to the Distributive Property, the expression that is equivalent to 4x^3 + 8x^2 + 12x is 4x(x^2 + 2x + 3).
Multiply the polynomials (3x−1)(2x+4)
.
To multiply the polynomials (3x - 1)(2x + 4), we will use the distributive property.
First, we will multiply the terms in the first parentheses by the terms in the second parentheses:
(3x)(2x) + (3x)(4) + (-1)(2x) + (-1)(4)
This simplifies to:
6x^2 + 12x - 2x - 4
Combining like terms, we have:
6x^2 + 10x - 4
Therefore, the product of (3x - 1)(2x + 4) is 6x^2 + 10x - 4.
None of the statements correctly interpret a part of the expression. Let's break down the equation to understand it better:
The equation 35x + 55y represents Antoine's total spending, where x represents the number of pairs of shoes and y represents the number of jerseys he buys.
The term 35x represents the total amount Antoine spends on shoes, as x represents the number of pairs of shoes he buys and 35 represents the cost per pair of shoes. However, it is important to note that this does not mean Antoine spends $35.00 per pair of shoes. It only represents the total amount he spends on shoes.
The term 55y represents the total amount Antoine spends on jerseys, as y represents the number of jerseys he buys and 55 represents the cost per jersey. Again, this does not mean Antoine spends $55.00 per pair of shoes. It only represents the total amount he spends on jerseys.
Therefore, none of the statements correctly interpret a part of the expression.
None of the statements correctly interpret a part of the expression.
The correct interpretation of the expression 35x + 55y is that Antoine spends 35 times the number of pairs of shoes, x, plus 55 times the number of jerseys, y.
Therefore, none of the statements accurately describe Antoine's spending on shoes.