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.

This statement is incorrect. The expression 35x represents the amount Antoine spends on shoes, but it does not provide the cost per pair of shoes.

So which option is it?

Statement #3: Antoine spends $35.00 in total for shoes.

This statement correctly interprets a part of the expression. The term 35x represents the amount Antoine spends on shoes, and it is multiplied by the number of pairs of shoes he buys, x. So, the total amount Antoine spends on shoes can be represented by the expression 35x.

Consider the expression (16−12)^2+5(8+2^2)/5^3−(1+4)^2 . What is the simplified numerator?

76
100
54
4^2+60

To simplify the numerator of the expression (16-12)^2 + 5(8+2^2), we first need to perform the necessary calculations within the parentheses and exponents.

(16-12)^2 = 4^2 = 16

2^2 = 4

Now, substituting the simplified values back into the original expression, we have:

16 + 5(8 + 4)/5^3 - (1+4)^2

Next, we simplify the expression within the parentheses:

8 + 4 = 12

1 + 4 = 5

So the expression becomes:

16 + 5(12)/5^3 - 5^2

Using the order of operations (PEMDAS/BODMAS), we perform the operations involving exponents:

5^3 = 125

5^2 = 25

Now, we substitute the simplified values:

16 + 5(12)/125 - 25

Multiplying 5 by 12:
= 60/125 - 25

Simplifying the fraction:
= 12/25 - 25

To subtract fractions, we need a common denominator. The common denominator is 25.

12/25 - 25/1 = (12 - 625)/25

= -613/25

Therefore, the simplified numerator is -613.

That is not an option

Apologies for the confusion. Let's revisit the expression and simplify the numerator correctly.

(16-12)^2 + 5(8+2^2)

Within the parentheses and exponents:

(16-12)^2 = 4^2 = 16

2^2 = 4

Now, substituting the simplified values back into the original expression:

16 + 5(8 + 4)

Simplifying within the parentheses:

8 + 4 = 12

Substituting the simplified value:

16 + 5(12)

Using the order of operations, we multiply:

16 + 60

Now, we add:

76

Therefore, the simplified numerator is 76.

Write an equivalent expression to (a⋅b)⋅c using the Associative Property of Multiplication.

An equivalent expression to (a⋅b)⋅c using the Associative Property of Multiplication is a⋅(b⋅c).

Which expression is equivalent to -3x-5?

(-4x-6)+(2+5x)
(x-7)+(2-4x)
-1+(x-4x)+6
-1+3x-(2x+6)

An equivalent expression to -3x - 5 is -1 + (x - 4x) + 6.