Essay question: show all work. Suzie’s flower shop estimates that supplies costs for one month will be given by the polynomial 5x2 + x – 4. She estimates that utilities costs for one month is given by 8x – 7. Find and simplify an expression that would estimate Suzie’s total costs for one month.
C = (5X^2 + X -4) + (8X - 7),
Combine like-trms:
C = 5X^2 + 9X - 11.
To find an expression that estimates Suzie's total costs for one month, we need to add the supplies costs and the utilities costs together.
The supplies costs are given by the polynomial 5x^2 + x - 4.
The utilities costs are given by the expression 8x - 7.
To estimate the total costs, we add these two expressions:
Total costs = (5x^2 + x - 4) + (8x - 7)
To simplify this expression, we combine like terms.
First, let's combine the x^2 term with the x term. There is only one x^2 term, so we can simply write it as 5x^2. The x term is x + 8x, which gives us 9x.
Our expression now becomes:
Total costs = 5x^2 + 9x - 4 - 7
Next, let's combine the constants (-4 and -7):
Total costs = 5x^2 + 9x - 11
So, the simplified expression that estimates Suzie's total costs for one month is 5x^2 + 9x - 11.