Answer:
x = -2![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
Step-by-step explanation:
First we have to distinguish the numbers with x from the "normal" numbers.
2x and 6x are numbers with x.
3 and 0 are "normal" numbers.
Now we have to seperate them on different sides of the equal sign.
To do this, we can subtract 3 from the left side and then add it to 0 on the left side.
Therefore, the equation will now be 2x + 6x = -3.
Now we can add 2x and 6x together, making it 8x.
The equation will now be 8x = -3.
To find the product of x, we need to divide both sides together.
So 8 divided by -3 will make -2
.
Therefore, x is -2
.
Hope my explination makes sense :)
Answer:
![(g\cdot f) = -3x^2-3](https://tex.z-dn.net/?f=%28g%5Ccdot%20f%29%20%3D%20%20-3x%5E2-3)
Step-by-step explanation:
![f(x) = x^2 + 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20%2B%201)
![g(x) = -3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-3)
The problem state to multiply the function
and
so the symbol seems to be incorrect.
We actually want to calculate
![g(x) f(x) =gf(x) = (-3) \cdot (x^2+1)= -3x^2-3](https://tex.z-dn.net/?f=g%28x%29%20%20f%28x%29%20%3Dgf%28x%29%20%3D%20%20%28-3%29%20%20%5Ccdot%20%28x%5E2%2B1%29%3D%20-3x%5E2-3)
Note
![g\circ f(x)=g(f(x))=g(x^2+1)=-3](https://tex.z-dn.net/?f=g%5Ccirc%20f%28x%29%3Dg%28f%28x%29%29%3Dg%28x%5E2%2B1%29%3D-3)
Answer:
Step-by-step explanation:
12 x + 4 y = 42 .............1
16 x + 8 y = 64 .............2
Eliminate y
multiply (1)by -2
Multiply (2) by 1
-24 x -8 y = -84
16 x 8 y = 64
Add the two equations
-8 x = -20
Answer:
2 and 1
Step-by-step explanation:
adjacent means next t, and angles 2 and 1 are next to each other
Answer:
![f(x)=\frac{1}{4}x^2](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B4%7Dx%5E2)
Step-by-step explanation:
Recall the vertex form of a quadratic equation:
![f(x)=a(x-h)^2+k](https://tex.z-dn.net/?f=f%28x%29%3Da%28x-h%29%5E2%2Bk)
Where (h,k) is the vertex.
We are told that the vertex is (0,0). Therefore:
![f(x)=a(x-0)^2+(0)](https://tex.z-dn.net/?f=f%28x%29%3Da%28x-0%29%5E2%2B%280%29)
Simplify:
![f(x)=ax^2](https://tex.z-dn.net/?f=f%28x%29%3Dax%5E2)
So, to finish the equation, we need to find a.
We know that a point is (2,1). Thus, substitute 1 for f(x) and 2 for x:
![1=a(2)^2](https://tex.z-dn.net/?f=1%3Da%282%29%5E2)
Square:
![1=4a](https://tex.z-dn.net/?f=1%3D4a)
Divide both sides by 4:
![a=\frac{1}{4}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B1%7D%7B4%7D)
So, our a value is 1/4.
And we can thus complete our equation:
![f(x)=\frac{1}{4}x^2](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B4%7Dx%5E2)
And we are done :)