Question

1. math on the spot suppose the cost in dollars of producing x model kits is given by the polynomial 500,000 + 2x and the revenue generated from sales is given by the polynomial 30x - 0.00005x². find a polynomial expression for the profit from making and selling x model kits. then evaluate the expression for x = 300,000
2. critique reasoning to solve the problem shown at the right. marla wrote the following solution:

(4 - 3x + 2x²) + (x³ - 7x + 5)
2x² - 3x + 4
+ x³ - 7x + 5
3x³ - 10x + 9
explain the error in marlas reasoning. then correct the error and finish solving the problem.

1. suppose f(x) = 4x³ + 3x² - 12x - 32, h(x) = 4x⁴ - 3x² + 2x - 19, and (f + g)(x) = h(x). what is g(x)?

a g(x) = -4x⁴ + 4x³ + 6x² - 14x - 13
b g(x) = 4x⁴ - 4x³ - 6x² + 14x + 13
c g(x) = 4x⁴ + 4x² - 10x - 51
d g(x) = -4x⁴ - 4x² + 10x + 51

1. the sides of a triangle are represented by the expressions 5 - 4x², 32x - 5x², and x² - 5. what is the perimeter of the triangle?

a -8x² + 32x
b 2x² + 32x
c -8x² + 32x + 10
d 2x² + 32x + 10

Explanation:

Step1: Combine like terms

$$\begin{align*} (4 - 3x + 2x^{2})+(x^{3}-7x + 5)&=x^{3}+2x^{2}+(-3x-7x)+(4 + 5)\\ \end{align*}$$

Step2: Simplify the expression

$$\begin{align*} x^{3}+2x^{2}+(-3x-7x)+(4 + 5)&=x^{3}+2x^{2}-10x + 9 \end{align*}$$

Answer:

Marla made an error in combining the \(x^{2}\) terms. The correct answer is \(x^{3}+2x^{2}-10x + 9\)