Quick Fix Inc. repairs bikes. Their revenue, in dollars, can be modeled by the equation y = 400 + 220x, where x is the number of
hours spent repairing bikes. Their overhead cost, in dollars, can be modeled by the equation y=20x2+160 , where x is the number of hours spent repairing bikes. After how many hours does the company break even?
Note: The phrase break even refers to the value where the two functions are equivalent.
The break even point is that where the total cost is equal to the total revenue. To determine the number of hours in which Quick Fix Inc. will have a breakeven, we have to equate the two equations and solve for the value of x, 400 + 220 x = 20x² + 160 The values of x from the equation are 12 and -1. Since, we do not have a negative for the number of hours, our answer is 12 hours.
The a point is refrected through the line y = x, the new point is found by interchanging the x and y-cordinate of the original point. i.e. if the original point is (a, b) and is refrected through the line y = x, the new point will be (b, a).
