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.
None of the statements correctly interprets a part of the expression.
In the given expression 35x + 55y, the term 35x represents the cost for the pairs of shoes, not a single pair. Therefore, the correct interpretation would be:
Antoine spends $35.00 for each pair of shoes, not per pair of shoes.
Consider the expression (16-12)^2+5(8+2^2)/5^3-(1+4)^2 What is the simplified numerator?
76
4^2+60
54
100
To simplify the numerator, we start by simplifying the terms within the parentheses:
(16-12)^2 + 5(8+2^2) / 5^3 - (1+4)^2
Inside the first parentheses, we have 16 - 12, which equals 4:
4^2 + 5(8+2^2) / 5^3 - (1+4)^2
Inside the second parentheses, we have 8 + 2^2. We calculate the exponent first:
2^2 = 4
Then we add 8 and 4, which gives us 12:
4^2 + 5(12) / 5^3 - (1+4)^2
Now we can simplify the exponent in the third parentheses:
(1+4)^2 = 5^2 = 25
So the expression becomes:
4^2 + 5(12) / 5^3 - 25
Next, we calculate the exponent of 4:
4^2 = 16
Now we have:
16 + 5(12) / 5^3 - 25
Next, let's calculate the multiplication:
5(12) = 60
Now we have:
16 + 60 / 5^3 - 25
Next, let's calculate the exponent of 5:
5^3 = 125
Now we have:
16 + 60 / 125 - 25
Now we perform the division:
60 / 125 = 0.48
So the expression becomes:
16 + 0.48 - 25
Finally, we perform the addition and subtraction:
16 + 0.48 - 25 = -8.52
Therefore, the simplified numerator is -8.52.
that didn't help
I apologize for the confusion in my previous response. Let's simplify the numerator step by step:
First, let's simplify the terms within the parentheses:
(16 - 12)^2 + 5(8 + 2^2) / 5^3 - (1 + 4)^2
Inside the first parentheses, 16 - 12 equals 4.
Now we simplify the second parentheses:
(4)^2 + 5(8 + 2^2) / 5^3 - (1 + 4)^2
Inside the second parentheses, 2^2 equals 4.
So the expression becomes:
(4)^2 + 5(8 + 4) / 5^3 - (1 + 16)
Next, let's simplify the exponents:
4^2 equals 16 and 5^3 equals 125.
Now the expression is:
16 + 5(8 + 4) / 125 - (1 + 16)
Next, let's simplify the multiplication inside the parentheses:
5(8 + 4) equals 5(12) equals 60.
Now the expression is:
16 + 60 / 125 - (1 + 16)
Next, let's simplify the addition inside the parentheses:
1 + 16 equals 17.
Now the expression is:
16 + 60 / 125 - 17
Next, let's calculate the division:
60 / 125 equals 0.48.
Now the expression is:
16 + 0.48 - 17
Finally, let's perform the addition and subtraction:
16 + 0.48 equals 16.48.
16.48 - 17 equals -0.52.
Therefore, the simplified numerator is -0.52.
didnt help
I apologize for the confusion caused in my previous response. Let's simplify the numerator step by step:
First, let's simplify the terms within the parentheses:
(16-12)^2 + 5(8+2^2) / 5^3 - (1+4)^2
Inside the first parentheses, we have 16 - 12, which equals 4.
Now let's simplify the second parentheses:
(4)^2 + 5(8 + 2^2) / 5^3 - (1 + 4)^2
Inside the second parentheses, 2^2 = 4.
So the expression becomes:
(4)^2 + 5(8 + 4) / 5^3 - (1 + 4)^2
Next, let's calculate the exponent inside the third parentheses:
(1 + 4)^2 = 5^2 = 25
Now the expression is:
(4)^2 + 5(8 + 4) / 5^3 - 25
Next, let's simplify the exponent:
(4)^2 = 16
Now the expression is:
16 + 5(8 + 4) / 5^3 - 25
Next, let's simplify the multiplication inside the parentheses:
5(8 + 4) equals 5(12) equals 60.
Now the expression is:
16 + 60 / 5^3 - 25
Next, let's calculate the exponent:
5^3 = 125
Now the expression is:
16 + 60 / 125 - 25
Next, let's perform the division:
60 / 125 equals 0.48.
Now the expression is:
16 + 0.48 - 25
Finally, let's perform the addition and subtraction:
16 + 0.48 equals 16.48.
16.48 - 25 equals -8.52.
Therefore, the simplified numerator is -8.52.
use the Commutative Property of Multiplication to rewrite the algebraic expression: k^17⋅z^33
Using the Commutative Property of Multiplication, we can rewrite the algebraic expression as:
z^33⋅k^17
The given expression for Antoine's total spending is 35x + 55y, where x represents the number of pairs of shoes and y represents the number of jerseys. Let's break it down to understand its interpretation better.
The coefficient of x in the expression is 35, and since x represents the number of pairs of shoes Antoine buys, the coefficient 35 indicates how much Antoine spends per pair of shoes. Thus, Statement #1 correctly interprets a part of the expression by stating that Antoine spends $35.00 per pair of shoes. Therefore, Statement #1 is correct.
The coefficient of y in the expression is 55, and since y represents the number of jerseys Antoine buys, the coefficient 55 indicates how much Antoine spends per jersey. Therefore, Statement #2, which states that Antoine spends $55.00 per pair of shoes, is incorrect.
Lastly, the expression 35x represents the total amount Antoine spends on shoes alone, without considering the jerseys. It shows that the cost of the shoes is dependent on the number of pairs he buys. Therefore, Statement #3, which states that Antoine spends $35.00 in total for shoes, is incorrect.
In summary, only Statement #1 correctly interprets a part of the given expression.