To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expression 7.5x – 100, where x represents the number of items sold. The company’s operation costs are modeled by the expression 79.86 + 5.8x. How many items does the company need to sell to make a profit? The inequality that will determine the number of items that need to be sold to make a profit is
.

The solution to the inequality is
.

The company must sell at least
items to make a profit.

Inequality: 7.5x – 100 > 79.86 + 5.8x

Solution: x>106

The company must sell at least  106 items to make a profit.

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

Revenue: 7.5x – 100

Costs: 79.86 + 5.8x

To make a profit, a company’s revenue must be greater than its operating costs.

So:

7.5x – 100 > 79.86 + 5.8x

Solving for x (number of items sold)

7.5x-5.8x>79.86+100

1.7x >179.86

x>179.86/1.7

x> 105.8

x>106

The company must sell at least 106 items to make a profit.

Feel free to ask for more if needed or if you did not understand something.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1