We are given the following function:
![f(x)=x^2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2)
We are asked to do the following tranformations:
1. Shift down 5 units and left 77 units.
First, to shift a function down a number "n" of units we follow the next rule:
![h(x)=f(x)-n](https://tex.z-dn.net/?f=h%28x%29%3Df%28x%29-n)
And, to shift a function "m" units to the left we use the following rule:
![h(x)=f(x+m)](https://tex.z-dn.net/?f=h%28x%29%3Df%28x%2Bm%29)
Applying both rules simultaneously we get:
![h(x)=(x+77)^2-5](https://tex.z-dn.net/?f=h%28x%29%3D%28x%2B77%29%5E2-5)
2. Reflect about the y-axis.
The rule to reflect a function about the y-axis is the following:
![r(x)=h(-x)](https://tex.z-dn.net/?f=r%28x%29%3Dh%28-x%29)
The means that we will change "x" for "-x" in the function we are going to reflect. Applying the rule we get:
![r(x)=(-x+77)^2-5](https://tex.z-dn.net/?f=r%28x%29%3D%28-x%2B77%29%5E2-5)
3. Compress vertically by a factor of 2.
To compress a function vertically by a factor "m" we multiply the entire function by 1/m, like this:
![g(x)=\frac{1}{m}r(x)](https://tex.z-dn.net/?f=g%28x%29%3D%5Cfrac%7B1%7D%7Bm%7Dr%28x%29)
Applying the rule we get:
![g(x)=\frac{1}{2}((-x+77)^2-5)](https://tex.z-dn.net/?f=g%28x%29%3D%5Cfrac%7B1%7D%7B2%7D%28%28-x%2B77%29%5E2-5%29)
And thus we get to the final function.
Answer:
<h2>x = 2, y = 4</h2>
Step-by-step explanation:
![\left\{\begin{array}{ccc}x+\frac{3}{4}y=5&\text{multiply both sides by 4}\\x-\frac{1}{2}y=0&\text{multiply both sides by 6}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}4x+3y=20\\6x-3y=0\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad10x=20\qquad\text{divide both sides by 10}\\.\qquad\dfrac{10x}{10}=\dfrac{20}{10}\\.\qquad\boxed{x=2}\\\\\\\text{Put it to the first equation:}\\\\4(2)+3y=20\\8+3y=20\qquad\text{subtract 8 from both sides}\\8-8+3y=20-8\\3y=12\qquad\text{divide both sides by 3}\\\boxed{y=4}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dx%2B%5Cfrac%7B3%7D%7B4%7Dy%3D5%26%5Ctext%7Bmultiply%20both%20sides%20by%204%7D%5C%5Cx-%5Cfrac%7B1%7D%7B2%7Dy%3D0%26%5Ctext%7Bmultiply%20both%20sides%20by%206%7D%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Cunderline%7B%2B%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D4x%2B3y%3D20%5C%5C6x-3y%3D0%5Cend%7Barray%7D%5Cright%7D%5Cqquad%5Ctext%7Badd%20both%20sides%20of%20the%20equations%7D%5C%5C.%5Cqquad10x%3D20%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%2010%7D%5C%5C.%5Cqquad%5Cdfrac%7B10x%7D%7B10%7D%3D%5Cdfrac%7B20%7D%7B10%7D%5C%5C.%5Cqquad%5Cboxed%7Bx%3D2%7D%5C%5C%5C%5C%5C%5C%5Ctext%7BPut%20it%20to%20the%20first%20equation%3A%7D%5C%5C%5C%5C4%282%29%2B3y%3D20%5C%5C8%2B3y%3D20%5Cqquad%5Ctext%7Bsubtract%208%20from%20both%20sides%7D%5C%5C8-8%2B3y%3D20-8%5C%5C3y%3D12%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5Cboxed%7By%3D4%7D)
Supplementary angles.
Supplementary angles are two angles that add up to 180 degrees.
Answer:
Appeal to reason is a fallacy is True
2x+8y in factor form is 2(x+4y)