juan lists the price for a shirt at his store. the equation shown represents the profit, in dollars, that he…

juan lists the price for a shirt at his store. the equation shown represents the profit, in dollars, that he makes, where x is the price that juan lists for the shirt. -10x² + 580x - 6720 = p. what is one possible price, in dollars, that will result in zero profit?

juan lists the price for a shirt at his store. the equation shown represents the profit, in dollars, that he makes, where x is the price that juan lists for the shirt. -10x² + 580x - 6720 = p. what is one possible price, in dollars, that will result in zero profit?

Answer

Explanation:

Step1: Set profit $P$ to 0

$-10x^{2}+580x - 6720=0$

Step2: Divide by -10

$x^{2}-58x + 672 = 0$

Step3: Factor the quadratic equation

We need to find two numbers that multiply to 672 and add up to 58. The numbers are 14 and 44. So, $(x - 14)(x - 44)=0$

Step4: Solve for $x$

Using the zero - product property, if $(x - 14)(x - 44)=0$, then $x-14 = 0$ or $x - 44=0$. So $x = 14$ or $x=44$.

Answer:

14 or 44