Answer:
y = 26 when x = 2
Step-by-step explanation:
Y varies directly with X
y= kx
39 = 3k
k = 13
y = 13x
y(2)= 13(2) = 26
Answer:
its mean
Step-by-step explanation:
I promise :)
Answer:
[Vertex form]
Step-by-step explanation:
Given function:
![Y=-\frac{1}{3}x^2-4x-5](https://tex.z-dn.net/?f=Y%3D-%5Cfrac%7B1%7D%7B3%7Dx%5E2-4x-5)
We need to find the vertex form which is.,
![y=a(x-h)^2+k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E2%2Bk)
where
represents the co-ordinates of vertex.
We apply completing square method to do so.
We have
![Y=-\frac{1}{3}x^2-4x-5](https://tex.z-dn.net/?f=Y%3D-%5Cfrac%7B1%7D%7B3%7Dx%5E2-4x-5)
First of all we make sure that the leading co-efficient is =1.
In order to make the leading co-efficient is =1, we multiply each term with -3.
![-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5](https://tex.z-dn.net/?f=-3%5Ctimes%20Y%3D-3%5Ctimes%5Cfrac%7B1%7D%7B3%7Dx%5E2-%28-3%29%5Ctimes4x-%28-3%29%5Ctimes%205)
![-3Y=x^2+12x+15](https://tex.z-dn.net/?f=-3Y%3Dx%5E2%2B12x%2B15)
Isolating
and
terms on one side.
Subtracting both sides by 15.
![-3Y-15=x^2+12x-15-15](https://tex.z-dn.net/?f=-3Y-15%3Dx%5E2%2B12x-15-15)
![-3Y-15=x^2+12x](https://tex.z-dn.net/?f=-3Y-15%3Dx%5E2%2B12x)
In order to make the right side a perfect square trinomial, we will take half of the co-efficient of
term, square it and add it both sides side.
square of half of the co-efficient of
term = ![(\frac{1}{2}\times 12)^2=(6)^2=36](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%5Ctimes%2012%29%5E2%3D%286%29%5E2%3D36)
Adding 36 to both sides.
![-3Y-15+36=x^2+12x+36](https://tex.z-dn.net/?f=-3Y-15%2B36%3Dx%5E2%2B12x%2B36)
![-3Y+21=x^2+12x+36](https://tex.z-dn.net/?f=-3Y%2B21%3Dx%5E2%2B12x%2B36)
Since
is a perfect square of
, so, we can write as:
![-3Y+21=(x+6)^2](https://tex.z-dn.net/?f=-3Y%2B21%3D%28x%2B6%29%5E2)
Subtracting 21 to both sides:
![-3Y+21-21=(x+6)^2-21](https://tex.z-dn.net/?f=-3Y%2B21-21%3D%28x%2B6%29%5E2-21)
![-3Y=(x+6)^2-21](https://tex.z-dn.net/?f=-3Y%3D%28x%2B6%29%5E2-21)
Dividing both sides by -3.
![\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}](https://tex.z-dn.net/?f=%5Cfrac%7B-3Y%7D%7B-3%7D%3D%5Cfrac%7B%28x%2B6%29%5E2%7D%7B-3%7D-%5Cfrac%7B21%7D%7B-3%7D)
[Vertex form]
6n−20=−2n+4(1−3n)
Simplify both sides of the equation.
−6n−20=−2n+4(1−3n)
−6n+−20=−2n+(4)(1)+(4)(−3n)(Distribute)
−6n+−20=−2n+4+−12n
−6n−20=(−2n+−12n)+(4)(Combine Like Terms)
−6n−20=−14n+4
−6n−20=−14n+4
Add 14n to both sides.
−6n−20+14n=−14n+4+14n
8n−20=4
Add 20 to both sides.
8n−20+20=4+20
8n=24
Divide both sides by 8.
8n/8 = 24/8
n=3
Answer:
p/q = -5/25
multiply-25/5 × -5/25 You'll get the answer as 1.