Final answer:
The expression -x^2+70x-600 represents a company's profit for selling x items. To find the number of items sold for which the company's profit is equal to $0, we set the expression equal to 0 and solve for x. The company's profit is equal to $0 for either selling 10 items or selling 60 items.
Step-by-step explanation:
The expression -x^2+70x-600 represents a company's profit for selling x items. To find the number of items sold for which the company's profit is equal to $0, we set the expression equal to 0 and solve for x. So, we have:
-x^2+70x-600 = 0
This is a quadratic equation. We can use the quadratic formula to solve for x. The quadratic formula is: x = (-b ± sqrt(b^2 - 4ac)) / (2a) where a, b, and c are the coefficients of the equation. In this case, a = -1, b = 70, and c = -600.
Substituting the values into the quadratic formula, we get:
x = (-70 ± sqrt(70^2 - 4(-1)(-600))) / (2(-1))
Simplifying the equation further, we have:
x = (-70 ± sqrt(4900 - 2400)) / (-2)
x = (-70 ± sqrt(2500)) / (-2)
x = (-70 ± 50) / (-2)
x = (-70 + 50) / (-2) or x = (-70 - 50) / (-2)
x = 20 / (-2) or x = -120 / (-2)
x = -10 or x = 60
Therefore, the company's profit is equal to $0 for either selling 10 items or selling 60 items.