<h2>
Answer:</h2>
<em>x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.</em>
<h2>
Explanation:</h2>
Here we have the function:
![f(x) = -x^2 + 50x - 264](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-x%5E2%20%2B%2050x%20-%20264)
that models the profit in dollars, where x is the number of memberships sold. In order to get the zeros we'll use the quadratic formula:
![\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ For: \\ \\ a=-1,\:b=50,\:c=-264:\quad x_{1,\:2}=\frac{-50\pm \sqrt{50^2-4\left(-1\right)\left(-264\right)}}{2\left(-1\right)} \\ \\ \\ x_{1}=\frac{-50+\sqrt{50^2-4\left(-1\right)\left(-264\right)}}{2\left(-1\right)}=\frac{-50+\sqrt{50^2-4\cdot \:1\cdot \:264}}{-2\cdot \:1}=\frac{-50+\sqrt{1444}}{-2\cdot \:1}=6 \\ \\ \\](https://tex.z-dn.net/?f=%5Cquad%20x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20%5C%5C%20%5C%5C%20For%3A%20%5C%5C%20%5C%5C%20a%3D-1%2C%5C%3Ab%3D50%2C%5C%3Ac%3D-264%3A%5Cquad%20x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-50%5Cpm%20%5Csqrt%7B50%5E2-4%5Cleft%28-1%5Cright%29%5Cleft%28-264%5Cright%29%7D%7D%7B2%5Cleft%28-1%5Cright%29%7D%20%5C%5C%20%5C%5C%20%5C%5C%20x_%7B1%7D%3D%5Cfrac%7B-50%2B%5Csqrt%7B50%5E2-4%5Cleft%28-1%5Cright%29%5Cleft%28-264%5Cright%29%7D%7D%7B2%5Cleft%28-1%5Cright%29%7D%3D%5Cfrac%7B-50%2B%5Csqrt%7B50%5E2-4%5Ccdot%20%5C%3A1%5Ccdot%20%5C%3A264%7D%7D%7B-2%5Ccdot%20%5C%3A1%7D%3D%5Cfrac%7B-50%2B%5Csqrt%7B1444%7D%7D%7B-2%5Ccdot%20%5C%3A1%7D%3D6%20%5C%5C%20%5C%5C%20%5C%5C)
![x_{2}=\frac{-50-\sqrt{50^2-4\left(-1\right)\left(-264\right)}}{2\left(-1\right)}=\frac{-50-\sqrt{50^2-4\cdot \:1\cdot \:264}}{-2\cdot \:1}=\frac{-50-\sqrt{1444}}{-2}=44](https://tex.z-dn.net/?f=x_%7B2%7D%3D%5Cfrac%7B-50-%5Csqrt%7B50%5E2-4%5Cleft%28-1%5Cright%29%5Cleft%28-264%5Cright%29%7D%7D%7B2%5Cleft%28-1%5Cright%29%7D%3D%5Cfrac%7B-50-%5Csqrt%7B50%5E2-4%5Ccdot%20%5C%3A1%5Ccdot%20%5C%3A264%7D%7D%7B-2%5Ccdot%20%5C%3A1%7D%3D%5Cfrac%7B-50-%5Csqrt%7B1444%7D%7D%7B-2%7D%3D44)
So the zeros are:
![x=6 \\ \\ x=44](https://tex.z-dn.net/?f=x%3D6%20%5C%5C%20%5C%5C%20x%3D44)
The zeros occurs when
, so we can conclude that at those points there is no any profit.
In conclusion:
<em>x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.</em>
Answer:
4) The square root of 25 is rational
5) pi is irrational
Step-by-step explanation:
To know if the answer is rational or irrational, check to see if they can be turned into a fraction.
The answer is 500 because when you multiply 500 times 10 you will get 5000