Step-by-step explanation:
Given f(x) = 2x³ + 9x² + 7x – 6
Also given that -3 is a root, which means (x+3) is a factor of f(x).
In order to find the other factors, we need to divide f(x) by (x-3)
or (2x³ + 9x² + 7x – 6) / (x-3)
you can either use long division or synthetic division to perform this division, either way, you will end up with :
(2x³ + 9x² + 7x – 6) / (x-3) = (2x² + 3x -2) which is also a factor of f(x)
Hence f(x) can be expressed
f(x) = 2x³ + 9x² + 7x – 6 = (x-3)(2x² + 3x -2)
We notice that for (2x² + 3x -2) you can further factor this using quadratic factoring (or your choice of method to solve quadratic equations).
By factoring, (2x² + 3x -2) = (2x-1) (x+2)
hence f(x) = (x-3)(2x² + 3x -2) = (x-3)(2x-1)(x+2)
Answer:
66cm²
Step-by-step explanation:
Okay so lets start by breaking this down and writing a smiple equation to find the area.
We know that the N's are the same size. To make it easier we can turn them to a square/rectangle. I think it would be easist to move the bottem N's to the top. (look at the pic attached to see what i mean)
Lets start by finding the area of the top rectangle. We need to divide 8 by 2 to find the height.
a = b * h
a = 12 * 4 = 48(area of top rectangle)
a(of m) = 4.5 * 4 = 18
area of the whole thing:
a = 48 + 18 = 66
To get G^-1 all we need to do is flip the points around Example for (5,3) make it (3,5)
Here are the points in inverse (3,5); (3,2); (4,6)
To tell if a group of point can be a function we need to 1st look at the x values. If all the x values are different, then it is a function (the x's are not all different)
If there are x values that are the same, they MUST have the same y value.
look at the points (3,5) and (3,2) those have the same x but they go to different y values so it is not a function.
You can think about it like this. Can you go to more than 1 place at the EXACT same time? Obvious answer is no. Can you have multiple people go to the same room? Sure that is possible. Same with functions. An x value can ONLY go to 1 y value, and many different x values can go to the same y value.
x=3/2-1/4
8x+2y=12
move the variable to the right side and change the sign.
8x=12-2y
divide both sides of the equation by 8
x=3/2-1/4y
the final solution is
x=3/2-1/4y
