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: Recall the profit formula

Profit \(P(x)\) is given by \(P(x)=\text{Revenue}-\text{Cost}\).
Given \(\text{Cost}=500000 + 2x\) and \(\text{Revenue}=30x-0.00005x^{2}\).
So, \(P(x)=(30x - 0.00005x^{2})-(500000 + 2x)\).

Step2: Simplify the polynomial

$$
LATEXBLOCK0
$$

Step3: Evaluate for \(x = 300000\)

Substitute \(x = 300000\) into \(P(x)\):

$$
LATEXBLOCK1
$$

Answer:

The polynomial expression for profit is \(P(x)=-0.00005x^{2}+28x - 500000\) and when \(x = 300000\), the profit is \(3400000\) dollars.