Answer:
45 quarters
Step-by-step explanation:
1. Think of this as the ration equation 9/3=x/15 where x is the number of quarters to play 15 levels
2. To solve the ratio, you need to cross multiply, and then divide
3. Multiply 9 times 15 (135)
4. Divide that number by 3 (45), and that's your answer!
Answer:
Hyperbola:
![x^2-y^2-8x+6y-1=0](https://tex.z-dn.net/?f=x%5E2-y%5E2-8x%2B6y-1%3D0)
Step-by-step explanation:
the given hyperbola has equation:
![x^2-y^2=8](https://tex.z-dn.net/?f=x%5E2-y%5E2%3D8)
This is an equation of a hyperbola centered at the origin.
This hyperbola is translated so its center is now at T(4,3)
![(x-4)^2-(y-3)^2=8](https://tex.z-dn.net/?f=%28x-4%29%5E2-%28y-3%29%5E2%3D8)
We expand to get:
![x^2-8x+16-(y^2-6y+9)=8](https://tex.z-dn.net/?f=x%5E2-8x%2B16-%28y%5E2-6y%2B9%29%3D8)
![x^2-8x+16-y^2+6y-9=8](https://tex.z-dn.net/?f=x%5E2-8x%2B16-y%5E2%2B6y-9%3D8)
![x^2-8x-y^2+6y+7=8](https://tex.z-dn.net/?f=x%5E2-8x-y%5E2%2B6y%2B7%3D8)
![x^2-8x-y^2+6y+7-8=0](https://tex.z-dn.net/?f=x%5E2-8x-y%5E2%2B6y%2B7-8%3D0)
![x^2-y^2-8x+6y-1=0](https://tex.z-dn.net/?f=x%5E2-y%5E2-8x%2B6y-1%3D0)
Sn = n/2 (a1+an)
= 8/2 (3-38)
= 4 (-35)
= -140
<span>A = {odd numbers between 0 and 100}
</span><span>A = {1, 3, 5, 7,...., 95, 97, 99}
B = </span><span>{numbers between 50 and 150 that are evenly divisible by 5}
B = {50, 55, 60, 65, ..., 140, 145, 150}
The notation </span><span>A ∩ B means the set of items that are in set A and also in set B. In terms of venn diagrams, it's the overlapping region between circle A and circle B
In this case, the following values are found in both set A and set B
{55, 65, 75, 85, 95}
So that's why
</span>A ∩ B = <span>{55, 65, 75, 85, 95}
which is the final answer</span>
Answer:
![w=\frac{30-5z}{4}](https://tex.z-dn.net/?f=w%3D%5Cfrac%7B30-5z%7D%7B4%7D)
Step-by-step explanation:
![4w+5z=30\\\\4w+5z-5z=30-5z\\\\4w=30-5z\\\\\frac{4w=30-5z}{4}\\\\\boxed{w=\frac{30-5z}{4}}](https://tex.z-dn.net/?f=4w%2B5z%3D30%5C%5C%5C%5C4w%2B5z-5z%3D30-5z%5C%5C%5C%5C4w%3D30-5z%5C%5C%5C%5C%5Cfrac%7B4w%3D30-5z%7D%7B4%7D%5C%5C%5C%5C%5Cboxed%7Bw%3D%5Cfrac%7B30-5z%7D%7B4%7D%7D)
Hope this helps.