Question

Mario has a business selling muffins. let x be the price of a muffin. then, the profit p for mario’s business is given by P(x)= -100x²+350x-150. choose the inequality that shows the business will make a positive profit.

Answer 1

The business will make a positive profit within certain intervals defined by the x values in the profit function.

Step-by-step explanation:

To determine the inequality that shows the business will make a positive profit, we need to find the range of x values for which the profit function P(x) is greater than zero. Given that P(x) = -100x² + 350x - 150, we need to find the values of x that satisfy the inequality P(x) > 0.

To do this, we can graph the parabolic function P(x) and identify the intervals where the graph is above the x-axis. The points where the graph intersects the x-axis represent the break-even points.

By performing a quadratic factorization, we can determine that the profit function can be written as P(x) = -100(x - 1)(x - 1.5).

Since the coefficient of the x² term is negative, the graph of the parabola opens downward. Therefore, the regions between the break-even points (x = 1 and x = 1.5) represent the intervals where the business will make a positive profit.