![\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis}](https://tex.z-dn.net/?f=%5Cbf%20~%5Chspace%7B10em%7D%5Ctextit%7Bfunction%20transformations%7D%20%5C%5C%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%20f%28x%29%3D%20A%28%20Bx%2B%20C%29%5E2%2B%20D%20%5C%5C%5C%5C%20f%28x%29%3D%20A%5Csqrt%7B%20Bx%2B%20C%7D%2B%20D%20%5C%5C%5C%5C%20f%28x%29%3D%20A%28%5Cmathbb%7BR%7D%29%5E%7B%20Bx%2B%20C%7D%2B%20D%20%5Cend%7Barray%7D%5Cqquad%20%5Cqquad%20%5Cbegin%7Barray%7D%7Bllll%7D%20f%28x%29%3D%5Ccfrac%7B1%7D%7BA%28Bx%2BC%29%7D%2BD%20%5C%5C%5C%5C%5C%5C%20f%28x%29%3D%20A%20sin%5Cleft%28%20B%20x%2B%20C%20%5Cright%29%2B%20D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20stretches%20or%20shrinks%20horizontally%20by%20%7D%20A%5Ccdot%20B%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20flips%20it%20upside-down%20if%20%7D%20A%5Ctextit%7B%20is%20negative%7D%5C%5C%20~~~~~~%5Ctextit%7Breflection%20over%20the%20x-axis%7D)
with that template in mind, let's see
down by 5 units, D = -5
to the left by 4 units, C = +4
Triangle A
hypotenuse: 3y + x
leg: y - x
Triangle B
hypotenuse: y + 5
leg: x + 5
Congruency => 3y + x = y + 5 and y - x = x + 5
Solve the system
3y + x = y + 5 -> 2y + x = 5
y - x = x + 5 -> y - 2x = 5
2y + x = 5
-2y + 4x = -10
5x = -5
x = -1
y = (5 -(-1)) / 2 = 6/2 = 3
Verify:
hypotenuses
3y + x = 9 - 1 = 8
y + 5 = 3 + 5 = 8
Legs:
y - x = 3 -(-1) = 3 + 1 = 4
x + 5 = -1 + 5 = 4.
Then both hypotenuses and both legs are congruent.
Answer: x = -1 and y = 3
Answer:
1/2
Step-by-step explanation:
3/8 + 2/8 is 5/8, 1/2 is equal to 4/8, so 5/8 is only 1/8 away from 1/2 while 5/8 is also 3/8 away from 1 or 8/8 therefore, it is closer to 1/2
Answer:
JL = 78
Step-by-step explanation:
The shorter segment is a midline, so is half the length of the longer one.
2(5x-16) = 4x +34
5x -16 = 2x +17 . . . . . divide by 2
3x = 33 . . . . . . . . . . add 16-2x
x = 11 . . . . . . . . . . divide by 3
Then segment JL is ...
JL = 4x +34 = 4(11) +34 = 44+34
JL = 78
