Which of the following correctly simplifies (9x^2+17x+13)−(2x^2+12x+11)?
7x^2+29x+24
9x^2+17x+13−2x^2−12x−11
7x^2+5x+2
12x^2+2
The correct simplification is:
(9x^2+17x+13) - (2x^2+12x+11) = (9x^2 - 2x^2) + (17x - 12x) + (13 - 11)
This simplifies to:
7x^2 + 5x + 2
So, the correct answer is:
7x^2+5x+2
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 given statements correctly interpret a part of the expression.
The correct interpretation of the expression 35x+55y is that Antoine spends $35.00 per pair of shoes (x) and $55.00 per jersey (y). The expression represents the total spending of Antoine on shoes and jerseys, but it does not provide information about the total spending for shoes alone.
To simplify the expression (9x^2+17x+13)−(2x^2+12x+11), we can distribute the negative sign to the terms inside the parentheses:
9x^2 + 17x + 13 - 2x^2 - 12x - 11
Next, combine like terms:
(9x^2 - 2x^2) + (17x - 12x) + (13 - 11)
This simplifies to:
7x^2 + 5x + 2
So, the correct simplification of the expression is 7x^2 + 5x + 2.