Answer: 1, 2, 3, 4, 6, 12
Calculation/Explanation:
Common factors are factors that both the numbers, in this case, 60 and 72, have in common. The factors listed above are all factors shared by 60 and 72.
Answer:
a) t=5
5+5+5=15
b) x=11
11-8=3
or you can add 3 to both sides and x=11
c) w=3
7(3) = 21
21+3=24
or subtract 3 from both sides to get 7w=21
then divide by 7 on both sides to get w=3
![\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ % templates f(x)= A( Bx+ C)+ D \\\\ ~~~~y= A( Bx+ C)+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \\\\ f(x)= A sin\left( B x+ C \right)+ D \\\\ --------------------](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bfunction%20transformations%7D%0A%5C%5C%5C%5C%5C%5C%0A%25%20templates%0Af%28x%29%3D%20%20A%28%20%20Bx%2B%20%20C%29%2B%20%20D%0A%5C%5C%5C%5C%0A~~~~y%3D%20%20A%28%20%20Bx%2B%20%20C%29%2B%20%20D%0A%5C%5C%5C%5C%0Af%28x%29%3D%20%20A%5Csqrt%7B%20%20Bx%2B%20%20C%7D%2B%20%20D%0A%5C%5C%5C%5C%0Af%28x%29%3D%20%20A%28%5Cmathbb%7BR%7D%29%5E%7B%20%20Bx%2B%20%20C%7D%2B%20%20D%0A%5C%5C%5C%5C%0Af%28x%29%3D%20%20A%20sin%5Cleft%28%20B%20x%2B%20%20C%20%20%5Cright%29%2B%20%20D%0A%5C%5C%5C%5C%0A--------------------)
![\bf \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} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbullet%20%5Ctextit%7B%20stretches%20or%20shrinks%20horizontally%20by%20%20%7D%20%20%20A%5Ccdot%20%20%20B%5C%5C%5C%5C%0A%5Cbullet%20%5Ctextit%7B%20flips%20it%20upside-down%20if%20%7D%20%20A%5Ctextit%7B%20is%20negative%7D%5C%5C%0A~~~~~~%5Ctextit%7Breflection%20over%20the%20x-axis%7D%0A%5C%5C%5C%5C%0A%5Cbullet%20%5Ctextit%7B%20flips%20it%20sideways%20if%20%7D%20%20B%5Ctextit%7B%20is%20negative%7D)
![\bf ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Breflection%20over%20the%20y-axis%7D%0A%5C%5C%5C%5C%0A%5Cbullet%20%5Ctextit%7B%20horizontal%20shift%20by%20%7D%5Cfrac%7B%20%20C%7D%7B%20%20B%7D%5C%5C%0A~~~~~~if%5C%20%5Cfrac%7B%20%20C%7D%7B%20%20B%7D%5Ctextit%7B%20is%20negative%2C%20to%20the%20right%7D%5C%5C%5C%5C%0A~~~~~~if%5C%20%5Cfrac%7B%20%20C%7D%7B%20%20B%7D%5Ctextit%7B%20is%20positive%2C%20to%20the%20left%7D%5C%5C%5C%5C%0A%5Cbullet%20%5Ctextit%7B%20vertical%20shift%20by%20%7D%20%20D%5C%5C%0A~~~~~~if%5C%20%20%20D%5Ctextit%7B%20is%20negative%2C%20downwards%7D%5C%5C%5C%5C%0A~~~~~~if%5C%20%20%20D%5Ctextit%7B%20is%20positive%2C%20upwards%7D%5C%5C%5C%5C%0A%5Cbullet%20%5Ctextit%7B%20period%20of%20%7D%5Cfrac%7B2%5Cpi%20%7D%7B%20%20B%7D)
and with that template in mind,
notice from a parent function of f(x) = x³,
a derived function with f(x+5) = (x + 5)³
has a C component of 5, C = 5, which means is the as the parent, just shifted to the left by 5 units.