The standard form of a quadratic equation is
, while the vertex form is:
, where (h, k) is the vertex of the parabola.
What we want is to write
as
First, we note that all the three terms have a factor of 3, so we factorize it and write:
.
Second, we notice that
are the terms produced by
, without the 9. So we can write:
, and substituting in
we have:
![\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11]](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20y%3D3%28x%5E2-6x-2%29%3D3%5B%28x-3%29%5E2-9-2%5D%3D3%5B%28x-3%29%5E2-11%5D)
.
Finally, distributing 3 over the two terms in the brackets we have:
![y=3[x-3]^2-33](https://tex.z-dn.net/?f=y%3D3%5Bx-3%5D%5E2-33)
.
Answer:
Answer:
Henry is short of gravel
Step-by-step explanation:
Here, we are to identify which of the ingredients Henry is short of.
To identify this ingredient, what is needed to be done is to share the 180kg of concrete appropriately to get which of the material does not meet its ratio and thus allowing us know which is insufficient.
The total ratio is 1 + 4 + 7 = 12
For cement, we have ;
1/12 * 180 = 15 kg
For sand, we have
4/12 * 180 = 60kg
For gravel, we have
7/12 * 180 = 105 kg
From the values in the question, we can see that all the values we have are greater what is shared in the ratio except in the case of gravel. So we can confidently say he is short of gravel
Answer:
The one time fee of $25 is the ibdependent variable.
Step-by-step explanation:
Answer:
Part A) The proportional equation is 
Part B) 8 hours of training
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form 
or 
Let
c -----> the cost to hire a dog
h ----> the amount of time in hours
The linear equation is equal to
Sue spent $660 on 12 hours of obedience training for her dog Muffin
Find the value of k (constant of proportionality)
substitute the values
therefore
The linear equation is
For 
Find the value of h
substitute in the equation and solve for h
