The parabola will show the vertex in the format: y-k = (x-h)^2, where the vertex point
lies at (h, k).
![so \: for \: {x}^{2} + 2x - y + 3 = 0](https://tex.z-dn.net/?f=so%20%5C%3A%20for%20%5C%3A%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20-%20y%20%2B%203%20%3D%200)
let's first put it in "y =" standard format:
![y = {x}^{2} + 2x + 3](https://tex.z-dn.net/?f=y%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20%2B%203)
Since we cannot get a perfect square out of this, we complete the square: a=1, b=2, c=3
(b/2)^2 = (2/2)^2 = 1, so
![y = {(x +1)}^{2} ...\: is \: y = {x}^{2} + 2x + 1](https://tex.z-dn.net/?f=y%20%3D%20%20%7B%28x%20%2B1%29%7D%5E%7B2%7D%20...%5C%3A%20is%20%5C%3A%20y%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20%2B%201)
So there's +2 leftover, since 3-1=2; so:
![y = {(x + 1)}^{2} + 2](https://tex.z-dn.net/?f=y%20%3D%20%20%7B%28x%20%2B%201%29%7D%5E%7B2%7D%20%20%2B%202)
Now we'll subtract the 2 from both sides to show our vertex:
![y - 2 = {(x + 1)}^{2}](https://tex.z-dn.net/?f=y%20-%202%20%3D%20%20%7B%28x%20%2B%201%29%7D%5E%7B2%7D%20)
where our vertex (h, k) is at (-1, 2)
Answer:
y= 2x
Y = total earned. X= the number of cups sold.
Step-by-step explanation:
Answer:
<em>options: A,C,E </em>are correct.
Step-by-step explanation:
We have to find the expression equivalent to the expression:
![\dfrac{21^x}{3^x}](https://tex.z-dn.net/?f=%5Cdfrac%7B21%5Ex%7D%7B3%5Ex%7D)
we know that: ![21^x=(3\times7)^x\\\\21^x=3^x\times7^x](https://tex.z-dn.net/?f=21%5Ex%3D%283%5Ctimes7%29%5Ex%5C%5C%5C%5C21%5Ex%3D3%5Ex%5Ctimes7%5Ex)
Hence,
-----(1)
A)
(same as(1))
Hence, option A is correct.
B) 7 ; which is a different expression from (1)
Option B is incorrect.
C)
(Same as (1))
Option C is correct.
D)
which is a different expression from (1)
Hence, option D is incorrect.
E)
; which is same as (1)
Hence, Option E is correct.
F)
; which is not same as expression (1)
Hence, option F is incorrect.
Answer:
The expected volume of the box is 364 cubic inches.
Step-by-step explanation:
Since the die is fair, then P(X=k) = 1/6 for any k in {1,2,3,4,5,6}. Let Y represent the volume of the box in cubic inches. For how the box is formed, Y = X²*24. Thus, the value of Y depends directly on the value of X, and we have
- (When X = 1) Y = 1²*24 = 24, with probability 1/6 (the same than P(X=1)
- (When X = 2) Y = 2²*24 = 96, with probability 1/6 (the same than P(X=2)
- (When X = 3) Y = 3²*24 = 216, with probability 1/6 (the same than P(X=3)
- (When X = 4) Y = 4²*24 = 384, with probability 1/6 (the same than P(X=4)
- (When X = 5) Y = 5²*24 = 600, with probability 1/6 (the same than P(X=5)
- (When X = 6) Y = 6²*24 = 864, with probability 1/6 (the same than P(X=6)
As a consequence, the expected volume of the box in cubic inches is
E(Y) = 1/6 * 24 + 1/6*96 + 1/6*216+ 1/6*384+ 1/6*600+1/6*864 = 364