Answer:
Step-by-step explanation:
a)L=2w+4
b)P=2L+2w
sub L=2w+4,
P=2(2w+4)+2w
P=4w+8+2w
P=6w+8
c) 20=6w+8
12=6w
2=w
L=2(2)+4
=8
Hence,
L=8 and w=2
Answer:
324 44/69
Step-by-step explanation:
2000÷345=5 and 55/69
5 55/69 × 56 = 324 and 44/69
![\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ f(x)=Asin(Bx+C)+D \qquad \qquad f(x)=Acos(Bx+C)+D \\\\ f(x)=Atan(Bx+C)+D \qquad \qquad f(x)=Asec(Bx+C)+D \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } 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~~~~~~~~~~~~%5Ctextit%7Bfunction%20transformations%7D%20%5C%5C%5C%5C%5C%5C%20f%28x%29%3DAsin%28Bx%2BC%29%2BD%20%5Cqquad%20%5Cqquad%20f%28x%29%3DAcos%28Bx%2BC%29%2BD%20%5C%5C%5C%5C%20f%28x%29%3DAtan%28Bx%2BC%29%2BD%20%5Cqquad%20%5Cqquad%20f%28x%29%3DAsec%28Bx%2BC%29%2BD%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20stretches%20or%20shrinks%7D%5C%5C%20~~~~~~%5Ctextit%7Bhorizontally%20by%20amplitude%20%7D%20A%5Ccdot%20B%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20flips%20it%20upside-down%20if%20%7DA%5Ctextit%7B%20is%20negative%7D%5C%5C%20~~~~~~%5Ctextit%7Breflection%20over%20the%20x-axis%7D%20%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20flips%20it%20sideways%20if%20%7DB%5Ctextit%7B%20is%20negative%7D%5C%5C)
![\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}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Breflection%20over%20the%20y-axis%7D%20%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7B%20horizontal%20shift%20by%20%7D%5Cfrac%7BC%7D%7BB%7D%5C%5C%20~~~~~~if%5C%20%5Cfrac%7BC%7D%7BB%7D%5Ctextit%7B%20is%20negative%2C%20to%20the%20right%7D%5C%5C%5C%5C%20~~~~~~if%5C%20%5Cfrac%7BC%7D%7BB%7D%5Ctextit%7B%20is%20positive%2C%20to%20the%20left%7D%5C%5C%5C%5C%20%5Cbullet%20%5Ctextit%7Bvertical%20shift%20by%20%7DD%5C%5C%20~~~~~~if%5C%20D%5Ctextit%7B%20is%20negative%2C%20downwards%7D%5C%5C%5C%5C%20~~~~~~if%5C%20D%5Ctextit%7B%20is%20positive%2C%20upwards%7D)
![\bf \bullet \textit{function period}\\ ~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ ~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)](https://tex.z-dn.net/?f=%5Cbf%20%5Cbullet%20%5Ctextit%7Bfunction%20period%7D%5C%5C%20~~~~~~%5Cfrac%7B2%5Cpi%20%7D%7BB%7D%5C%20for%5C%20cos%28%5Ctheta%29%2C%5C%20sin%28%5Ctheta%29%2C%5C%20sec%28%5Ctheta%29%2C%5C%20csc%28%5Ctheta%29%5C%5C%5C%5C%20~~~~~~%5Cfrac%7B%5Cpi%20%7D%7BB%7D%5C%20for%5C%20tan%28%5Ctheta%29%2C%5C%20cot%28%5Ctheta%29)
now, with that template in mind
![\bf y = sin\left( x - \frac{3\pi }{2} \right)\implies y = \stackrel{A}{1}sin\left( \stackrel{B}{1}x \stackrel{C}{- \frac{3\pi }{2}} \right)+\stackrel{D}{0} \\\\\\ C = -\cfrac{3\pi }{2}\qquad \qquad \textit{\underline{horizontal shift} to the right of }\stackrel{3\pi }{2}\textit{ units}](https://tex.z-dn.net/?f=%5Cbf%20y%20%3D%20sin%5Cleft%28%20x%20-%20%5Cfrac%7B3%5Cpi%20%7D%7B2%7D%20%5Cright%29%5Cimplies%20y%20%3D%20%5Cstackrel%7BA%7D%7B1%7Dsin%5Cleft%28%20%5Cstackrel%7BB%7D%7B1%7Dx%20%5Cstackrel%7BC%7D%7B-%20%5Cfrac%7B3%5Cpi%20%7D%7B2%7D%7D%20%5Cright%29%2B%5Cstackrel%7BD%7D%7B0%7D%20%5C%5C%5C%5C%5C%5C%20C%20%3D%20-%5Ccfrac%7B3%5Cpi%20%7D%7B2%7D%5Cqquad%20%5Cqquad%20%5Ctextit%7B%5Cunderline%7Bhorizontal%20shift%7D%20to%20the%20right%20of%20%7D%5Cstackrel%7B3%5Cpi%20%7D%7B2%7D%5Ctextit%7B%20units%7D)
If you are trying to find the area of a rectangle the formula is length times width. So if 5 is your length and 3 is your width, or vice versa, you just multiply them.
5*3=15