Question

Martin is saving money to buy a new phone that costs $1,000 by selling trees. His net pay is modeled by the function p(x) = x^2 - 20x - 196p(x)=x^2 −20x−196, where xx represents the number of sales. How many sales does Martin need to make to earn $1,000?

Options:
A. 25 sales
B. 30 sales
C. 35 sales
D. 40 sales

Answer 1

After solving the quadratic equation 1000 = x^2 - 20x - 196, Martin needs to make 36 sales to earn $1,000. The given options are incorrect.

Step-by-step explanation:

The student is tasked with finding the number of sales Martin needs to make to earn $1,000 from the given function p(x) = x2 - 20x - 196. This is a simple algebraic problem where we need to solve the equation for x when p(x) is set to $1,000.

Setting the function equal to $1,000, we get the equation 1000 = x2 - 20x - 196. From here, we need to solve the quadratic equation for x. First, we bring all terms to one side: x2 - 20x - 1196 = 0. This equation factors to (x - 36)(x + 16) = 0, which gives us two possible solutions for x: 36 and -16.

Since the number of sales cannot be negative, Martin needs to make 36 sales to earn $1,000. None of the given options (A-D) are correct, so there might be an error in the options provided.