Kool Klothes has determined that the revenue function for selling x thousand pairs of shorts is R(x) = -5x^2 + 21x. The cost functiom C(x) = 2x + 10 is the cost of producing the shorts.

A) How many pairs of shorts must the company sell in order to break even. Do i use the quadratic formula... when i do im not getting the right answer

I get 0.469 but i don't think it is right

Break even is a point where the costs is equal to your profits.

Thus, we just equate the two functions:
R(x) = C(x)
-5x^2 + 21x = 2x + 10
-5x^2 + 21x - 2x - 10 = 0
-5x^2 + 19x - 10 = 0
5x^2 - 19x + 10 = 0
Use the quadratic formula:
x = ( -b +/- sqrt(b^2 - 4ac) ) / 2a
You should get
x = 3.16886
x = 0.6311

Get the smaller, x = 0.6311. since it's asking for the number of pairs of shorts, we multiply the value of x by 1000 (because x is in thousands of pairs units), and also note that the number of pair of shorts should be an integer.

not also sure about this, but hope this helps~ `u`

To find the break-even point, we need to set the revenue function equal to the cost function and solve for x.

So, we have:
R(x) = C(x)
-5x^2 + 21x = 2x + 10

To solve this equation, let's move all the terms to one side to form a quadratic equation:
-5x^2 + 21x - 2x - 10 = 0

Combine like terms:
-5x^2 + 19x - 10 = 0

To solve this quadratic equation, we can use the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = -5, b = 19, and c = -10. Plugging these values into the quadratic formula:

x = (-19 ± √(19^2 - 4(-5)(-10))) / (2 * -5)

Simplifying further:

x = (-19 ± √(361 - 200)) / -10
x = (-19 ± √(161)) / -10

Here, we encounter a problem. The square root of 161 is irrational (approximately 12.69), which means there are no real solutions for x. This implies that the company will not break even based on the given revenue and cost functions.

It is possible that there may be some other constraints or conditions missing that would allow us to find a break-even point, but based solely on the given information, we cannot find a break-even point.

To find the number of pairs of shorts that the company must sell in order to break even, we need to set the revenue function equal to the cost function and solve for x.

The revenue function is R(x) = -5x^2 + 21x.
The cost function is C(x) = 2x + 10.

To break even, the company's revenue should be equal to its cost, so we can set R(x) equal to C(x):

-5x^2 + 21x = 2x + 10

Now, let's rearrange this equation to bring all terms to one side to form a quadratic equation:

-5x^2 + 19x - 10 = 0

To solve this equation, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Applying this formula to our equation, we have:

x = (-(19) ± √((19)^2 - 4(-5)(-10))) / (2(-5))

Simplifying further:

x = (-19 ± √(361 - 200)) / (-10)
x = (-19 ± √161) / (-10)

Now we have two possible solutions for x. Let's compute both:

x1 = (-19 + √161) / (-10)
x2 = (-19 - √161) / (-10)

These are the values we get using the quadratic formula. If you are not getting the correct answer, please double-check your calculations and make sure you entered the equation correctly.