Direct variation has the form y=kx. Given a point we can solve for the constant k.
y=kx, when y=9 and x=-3 becomes:
9=-3k
k=-3 so the constant of variation is negative 3

We have been given a Quadratic equation, where we have to find the real values of x ~
So, let's proceed with middle term splitting method :




Now, we have two conditions here~
Either (x + 6) = 0

or (x - 1) = 0

Three points on the graph of the function f(x)f(x) are \{(0, 4), (1, 6), (2, 8)\}{(0,4),(1,6),(2,8)}. Which equation represents
Blababa [14]
Answer:
y = 2x + 4
Step-by-step explanation:
Slope: (6-4)/(1-0) = 2
y = 2x + 4
12.56 = 2(3.14) square root (L/32)
12.56 = 6.28 square root (L/32)
square root (L/32) = 2
L/ 32 = 2^2
L/ 32 = 4
L = 4 (32)
L = 128
Answer:
We verified that ![a^3+b^3+c^3-3abc=\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%2Bc%5E3-3abc%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
Hence proved
Step-by-step explanation:
Given equation is ![a^3+b^3+c^3-3abc=\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%2Bc%5E3-3abc%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
We have to prove that ![a^3+b^3+c^3-3abc=\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%2Bc%5E3-3abc%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
That is to prove that LHS=RHS
Now taking RHS
![\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
(using
)
(adding the like terms)
![=\frac{a+b+c}{2}[2a^2+2b^2+2c^2-2ab-2bc-2ac]](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B2a%5E2%2B2b%5E2%2B2c%5E2-2ab-2bc-2ac%5D)
![=\frac{a+b+c}{2}\times 2[a^2+b^2+c^2-ab-bc-ac]](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5Ctimes%202%5Ba%5E2%2Bb%5E2%2Bc%5E2-ab-bc-ac%5D)
![=a+b+c[a^2+b^2+c^2-ab-bc-ac]](https://tex.z-dn.net/?f=%3Da%2Bb%2Bc%5Ba%5E2%2Bb%5E2%2Bc%5E2-ab-bc-ac%5D)
Now multiply the each term to another each term in the factor
![=a^3+ab^2+ac^2-a^2b-abc-a^2c+ba62+b^3+bc^2-ab^2-b^2c-abc+ca^2+cb^2+c^3-abc-bc^2-ac^2]](https://tex.z-dn.net/?f=%3Da%5E3%2Bab%5E2%2Bac%5E2-a%5E2b-abc-a%5E2c%2Bba62%2Bb%5E3%2Bbc%5E2-ab%5E2-b%5E2c-abc%2Bca%5E2%2Bcb%5E2%2Bc%5E3-abc-bc%5E2-ac%5E2%5D)
(adding the like terms and other terms getting cancelled)
=LHS
Therefore LHS=RHS
Therefore ![a^3+b^3+c^3-3abc=\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%2Bc%5E3-3abc%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
Hence proved.