Answer:
The absolute value graph below does not flip.
Step-by-step explanation:
New graphs are made when transformed from their parents graphs. The parent graph for an absolute value graph is f(x) = |x|.
The equation used for a new graph transformed from the parent graph is in the form f(x) = a |k(x - d)| + c.
"a" shows vertical stretch (a>1) or vertical compression (0<a<1), and <u>flip across the x-axis if "a" is negative</u>.
"k" shows horizontal stretch (0<k<1) or horizontal compression (k>1), and <u>flip across the y-axis if "k" is negative</u>.
"d" shows horizontal shifts left (positive number) or right (negative number).
"c" shows vertical shifts up (positive) or down (negative).
The function f(x)=2|x-9|+3 has these transformations from the parent graph:
a = 2; Vertical stretch by a factor of 2
k = 1; No change
d = 9; Horizontal shift right 9 units
c = 3; Vertical shift up 3 units
Since neither "a" nor "k" was negative, there were no flips, <u>also known as reflections</u>.
The answer is believed to be around 1500
![\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=a+5\\ w=a-2\\ A=60 \end{cases}\implies 60=(a+5)(a-2) \\\\\\ 60=\stackrel{F~O~I~L}{a^2+3a-10}\implies 0=a^2+3a-70 \\\\\\ 0=(a+10)(a-7)\implies a= \begin{cases} -10\\\\ 7 ~~ \textit{\LARGE \checkmark} \end{cases}](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20rectangle%7D%5C%5C%5C%5C%20A%3DLw%20~~%20%5Cbegin%7Bcases%7D%20L%3Dlength%5C%5C%20w%3Dwidth%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20L%3Da%2B5%5C%5C%20w%3Da-2%5C%5C%20A%3D60%20%5Cend%7Bcases%7D%5Cimplies%2060%3D%28a%2B5%29%28a-2%29%20%5C%5C%5C%5C%5C%5C%2060%3D%5Cstackrel%7BF~O~I~L%7D%7Ba%5E2%2B3a-10%7D%5Cimplies%200%3Da%5E2%2B3a-70%20%5C%5C%5C%5C%5C%5C%200%3D%28a%2B10%29%28a-7%29%5Cimplies%20a%3D%20%5Cbegin%7Bcases%7D%20-10%5C%5C%5C%5C%207%20~~%20%5Ctextit%7B%5CLARGE%20%5Ccheckmark%7D%20%5Cend%7Bcases%7D)
notice, we didn't use the negative value, valid though as it is, because in this case "a" can't be negative.
Answer:
Step-by-step explanation:
We can simplify this equation down until we have x isolated.
If we add 17 to both sides:
Now we can divide both sides by 3:
So .
Hope this helped!
