Answer:
<u>Option A </u>is your answer
Step-by-step explanation:
hope it helps you
have a great day
Answer:
2 and 5
Step-by-step explanation:
Answer: 30%
Percentage Increase = (Final amount - Initial amount) / Initial amount x 100
![\frac{65 - 50}{50} \times 100](https://tex.z-dn.net/?f=%20%5Cfrac%7B65%20-%2050%7D%7B50%7D%20%20%5Ctimes%20100)
![\frac{15}{50} \times 100](https://tex.z-dn.net/?f=%20%5Cfrac%7B15%7D%7B50%7D%20%20%5Ctimes%20100)
=30%
If you plot these points on a coordinate plane, you see that both vertices and foci lie on the y axis. This means that you have a vertical hyperbola, and the equation looks like this:
![\frac{(y-k) ^{2} }{ a^{2} } - \frac{(x-h) ^{2} }{ b^{2} } =1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28y-k%29%20%5E%7B2%7D%20%7D%7B%20a%5E%7B2%7D%20%7D%20-%20%5Cfrac%7B%28x-h%29%20%5E%7B2%7D%20%7D%7B%20b%5E%7B2%7D%20%7D%20%3D1)
where h and k are the center. When you look at your graph, the origin is dead center between the vertices. (0, 0) is our h and k. Now we need a, b, and c. a is the distance between the center and the vertices, so our a = 4, and c is the distance between the center and the foci, so our c = 5. Use these in Pythagorean's Theorem to solve for b:
![(4) ^{2}+ b^{2}=(5) ^{2}](https://tex.z-dn.net/?f=%284%29%20%5E%7B2%7D%2B%20b%5E%7B2%7D%3D%285%29%20%5E%7B2%7D%20%20%20)
and
![16+ b^{2} =25](https://tex.z-dn.net/?f=16%2B%20b%5E%7B2%7D%20%3D25)
and b = 3. So we have all we need to do is replace all the variables. Our equation then would be this one:
![\frac{(y-0) ^{2} }{16} - \frac{(x-0) ^{2} }{9} =1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28y-0%29%20%5E%7B2%7D%20%7D%7B16%7D%20-%20%5Cfrac%7B%28x-0%29%20%5E%7B2%7D%20%7D%7B9%7D%20%3D1)
or, simplified,