Answer:
The interval notation for the domain is ![[\frac{23}{3},\infty ]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B23%7D%7B3%7D%2C%5Cinfty%20%20%5D)
.
Step-by-step explanation:
Consider the provided information.
It is given that 
We need to find the value of 
.
Put the value of g(x) in .
....(1)
Now, put x=x-7 in 
From equation 1.
The domain of the function is the set of input values for which a function is defined.
Here, the value of 
should be greater or equal to 0 as the square root of a negative number is not real.
Domain= 
The value of x is all real number greater than 
.
Hence, the interval notation for the domain is .
I added the diagram of the question.
<u><em>Answer:</em></u>h = 60°
<u><em>Explanation:</em></u>We are given that lines k and l are parallel lines.
This means that angles 120° and h are <u>supplementary angles</u>.
This means that their measures <u>add up to 180°</u>
<u>Therefore:</u>
180° = 120° + h
h = 180° - 120°
h = 60°
Hope this helps :)
![\bf \textit{zeros at } \begin{cases} x = -3\implies &x+3=0\\ x = -1\implies &x+1=0\\ x = 4\implies &x-4=0 \end{cases}\qquad \implies (x+3)(x+1)(x-4)=\stackrel{y}{0} \\\\\\ (x^2+4x+3)(x-4)=0\implies x^3~~\begin{matrix}+ 4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+3x~~\begin{matrix} -4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-16x-12=0 \\\\\\ x^3-13x-12=0](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bzeros%20at%20%7D%20%5Cbegin%7Bcases%7D%20x%20%3D%20-3%5Cimplies%20%26x%2B3%3D0%5C%5C%20x%20%3D%20-1%5Cimplies%20%26x%2B1%3D0%5C%5C%20x%20%3D%204%5Cimplies%20%26x-4%3D0%20%5Cend%7Bcases%7D%5Cqquad%20%5Cimplies%20%28x%2B3%29%28x%2B1%29%28x-4%29%3D%5Cstackrel%7By%7D%7B0%7D%20%5C%5C%5C%5C%5C%5C%20%28x%5E2%2B4x%2B3%29%28x-4%29%3D0%5Cimplies%20x%5E3~~%5Cbegin%7Bmatrix%7D%2B%204x%5E2%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%2B3x~~%5Cbegin%7Bmatrix%7D%20-4x%5E2%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~-16x-12%3D0%20%5C%5C%5C%5C%5C%5C%20x%5E3-13x-12%3D0)
we know that f(-2) = 24, namely when x = -2, y = 24, let's see if that's true
darn!! no dice.... hmmmm wait a second.... 4 * 6 = 24, if we could just use a common factor of 4 on the function, that common factor times 6 will give us 24, let's check.
![\bf 4(x^3-13x-12)=y\implies \stackrel{x = -2}{4[~~(-2)^3-13(-2)-12~~]}=y \\\\\\ 4[~~-8+26-22~~]=y\implies 4[6]=y\implies 24=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 4x^3-52x-48=y~\hfill](https://tex.z-dn.net/?f=%5Cbf%204%28x%5E3-13x-12%29%3Dy%5Cimplies%20%5Cstackrel%7Bx%20%3D%20-2%7D%7B4%5B~~%28-2%29%5E3-13%28-2%29-12~~%5D%7D%3Dy%20%5C%5C%5C%5C%5C%5C%204%5B~~-8%2B26-22~~%5D%3Dy%5Cimplies%204%5B6%5D%3Dy%5Cimplies%2024%3Dy%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%204x%5E3-52x-48%3Dy~%5Chfill)
Answer:
y = x -7
Step-by-step explanation:
y2 - y1 / x2 - x1
-5 - (-2) / 2 - 5
-3/-3
1
y = x + b
-2 = 5 + b
-7 = b
y = -7
y = x -7
