You can just use the tn formula to solve this tn= t1 + (n-1)d
4 + 5z = 5z + 4 is an identity and is true for all values of z.
The equation has, therefore, infinitely many solutions.
Answer:
The volume of the sphere is 288π in³
Step-by-step explanation:
To calculate the volume of a sphere we have to use the following formula:
V = volume
r = radius
V = ⁴⁄₃πr³
V = ⁴⁄₃ * π * (6in)³
V = π * ⁴⁄₃ * 216 in³
V = 288π in³
The volume of the sphere is 288π in³
Answer:
$69.99 or $50.08
Step-by-step explanation:
2 for 1 by dividing by 100: 80/100 =0.8 mulitply price by decimal rate
Answer:
(8,-3)
Step-by-step explanation:
The given parabola is
![y = - 3 {x}^{2} + 48x - 195](https://tex.z-dn.net/?f=y%20%3D%20%20-%203%20%7Bx%7D%5E%7B2%7D%20%20%2B%2048x%20%20-%20195)
We factor -3 from the first two terms to get:
![y = - 3( {x}^{2} - 16x) - 195](https://tex.z-dn.net/?f=y%20%3D%20%20-%203%28%20%7Bx%7D%5E%7B2%7D%20%20%20-%2016x%29%20%20-%20195)
Add and subtract the square of half the coefficient of x
![y = - 3( {x}^{2} - 16x + 64) + 3 \times 64- 195](https://tex.z-dn.net/?f=y%20%3D%20%20-%203%28%20%7Bx%7D%5E%7B2%7D%20%20%20-%2016x%20%2B%2064%29%20%20%20%2B%203%20%5Ctimes%2064-%20195)
![y = - 3 {(x - 8)}^{2} + 192 - 195](https://tex.z-dn.net/?f=y%20%3D%20%20-%203%20%7B%28x%20-%208%29%7D%5E%7B2%7D%20%20%2B%20192%20-%20195)
We simplify to get:
![y = - 3 {(x - 8)}^{2} - 3](https://tex.z-dn.net/?f=y%20%3D%20%20-%203%20%7B%28x%20-%208%29%7D%5E%7B2%7D%20%20-%203)
We compare this to y=a(x-h)²+k,
The vertex is (h,k)=(8,-3)