Answer:
Third option.
Step-by-step explanation:
Some transformations for a function f(x), are:
If 
, the function is shifted down "k" units.
If 
, the function is shifted up "k" units.
If 
, and 
, the functio is stretch vertically by a factor of "b".
If 
, the function is reflected over the x-axis.
Therefore, knowing that the parent function 
was transformated by reflecting it over the x-axis, stretching vertically by a factor of 2 and shifting it down 3 units, we can determine that the following function represents the transformation:
Answer:
(You only need to give one solution)
Step-by-step explanation:
We have the following equation
First, we need to foil out the parenthesis
Now we can combine the like terms
Now, we need to factor this equation.
To factor this, we need to find a set of numbers that add together to get -3 and multiply to give us -4.
The pair of numbers that would do this would be 1 and -4.
This means that our factored form would be
As the first binomial is a difference of squares, it can be factored futher into
Now, we can get our solutions.
The first binomial will produce two complex (Not real) solutions.
So our solutions to this equation are
Answer:
![\displaystyle \boxed{8[x + 2][x^2 - 2x + 4]}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cboxed%7B8%5Bx%20%2B%202%5D%5Bx%5E2%20-%202x%20%2B%204%5D%7D)
Step-by-step explanation:
Use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] to figure this out:
![\displaystyle 8x^3 + 64 \\ 8[x^3 + 8] \\ \\ x + 2 = \sqrt[3]{x^3 + 8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%208x%5E3%20%2B%2064%20%5C%5C%208%5Bx%5E3%20%2B%208%5D%20%5C%5C%20%5C%5C%20x%20%2B%202%20%3D%20%5Csqrt%5B3%5D%7Bx%5E3%20%2B%208%7D)
Then, since the divisor\factor is in the form of <em>x - c</em>, use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
−2| 1 0 0 8
↓ −2 4 −8
___________
1 −2 4 0 → 
You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [x³ + 8]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², the −2x follows right behind it, then 4, giving you the other factor of 
, attaching this to the first two factors you started out your work on:
I am joyous to assist you anytime.
156 divided by 8 is 19.5 i think the answer is 19
Thirty-two and fifteen hundredths
