A car dealership manager has determined that the profit, in thousands of dollars, of the dealership can be determined by the expression LaTeX: x^2-4xL a T e X : x 2 − 4 x, where LaTeX: xL a T e X : x is the number of cars sold. A different manager states that the profit of the dealership can be determined by the function LaTeX: 5xL a T e X : 5 x. What number of cars sold makes the equation LaTeX: x^2-4x=5xL a T e X : x 2 − 4 x = 5 x true? Select all that apply.
Answer:
x = 0 ; x = 9
Explanation:
Given that:
Manager 1 's profit function:
x² - 4x ; x = number of cars sold
Manager 2's profit function:
5x ; x = number of cars sold
Nunbers That makes the equation:
x² - 4x = 5x true
x² - 4x = 5x
Subtract 5x from both sides to make right hand side =. 0
X² - 4x - 5x = 5x - 5x
x² - 9x = 0
Using factorization to equate separate the x values.
x(x - 9) = 0
x = 0 or (x - 9) = 0
Hence,
x = 0 ; or
x - 9 = 0 ; x = 9
x = 0 OR x = 9
Number of cars sold which makes both managers have the same profit from the functions are either 0 or 9