the solid is made up of 2 regular octagons, 8 sides, joined up by 8 rectangles, one on each side towards the other octagonal face.
from the figure, we can see that the apothem is 5 for the octagons, and since each side is 3 cm long, the perimeter of one octagon is 3*8 = 24.
the standing up sides are simply rectangles of 8x3.
if we can just get the area of all those ten figures, and sum them up, that'd be the area of the solid.
![\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ a=5\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(5)(24)\implies \stackrel{\textit{just for one octagon}}{A=60} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{two octagon's area}}{2(60)}~~+~~\stackrel{\textit{eight rectangle's area}}{8(3\cdot 8)}\implies 120+192\implies 312](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20regular%20polygon%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B2%7Dap~~%20%5Cbegin%7Bcases%7D%20a%3Dapothem%5C%5C%20p%3Dperimeter%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a%3D5%5C%5C%20p%3D24%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B2%7D%285%29%2824%29%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bjust%20for%20one%20octagon%7D%7D%7BA%3D60%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Btwo%20octagon%27s%20area%7D%7D%7B2%2860%29%7D~~%2B~~%5Cstackrel%7B%5Ctextit%7Beight%20rectangle%27s%20area%7D%7D%7B8%283%5Ccdot%208%29%7D%5Cimplies%20120%2B192%5Cimplies%20312)
Answer:
(a) 
(b) 
Step-by-step explanation:
It is given that 
.
(a)
![[\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Csin%20x%3D%5Csin%20y%5CRightarrow%20x%3Dn%5Cpi%2B%28-1%29%5Eny%5D)
(b)
![[\because \sin x=\dfrac{1}{\csc x}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Csin%20x%3D%5Cdfrac%7B1%7D%7B%5Ccsc%20x%7D%5D)
Therefore, .
The correct answer is option 1: g(x) = f(x +3). It represents a horizontal transformation of 3 units to the left.
Answer:
A
Step-by-step explanation:
because the answer is A
Answer:
2x-10+x+x+10=180, or 4x=180
Step-by-step explanation:
So since the total is 180, you add them all up like an equation.
So,
2x-10+x+x+10
Combine like terms
4x=180
x=45
Then plug it back in to the equations.
x=45
(2x-10)=80
(x+10)=55
