Answer:
That I have no idea what it is. sorry
Step-by-step explanation:
Answer:
7 of the angles measure 144 degrees each and one angle measures 72 degrees
Step-by-step explanation:
Let
x -----> represent the measures of the seven same-size angles,
x/2 ----> represent the measure of the one that is "two times smaller."
we know that
The sum of internal angles of a polygon can be calculated as:
![S=180^o(n-2)](https://tex.z-dn.net/?f=S%3D180%5Eo%28n-2%29)
where
n is the number of sides of the polygon
In this case
n=8 (octagon)
substitute
![S=180^o(8-2)=1,080^o](https://tex.z-dn.net/?f=S%3D180%5Eo%288-2%29%3D1%2C080%5Eo)
so
The linear equation that represent this problem is
![\frac{x}{2}+7x=1,080](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%2B7x%3D1%2C080)
solve for x
![\frac{15x}{2}=1,080\\\\15x=2,160\\\\x=144^o](https://tex.z-dn.net/?f=%5Cfrac%7B15x%7D%7B2%7D%3D1%2C080%5C%5C%5C%5C15x%3D2%2C160%5C%5C%5C%5Cx%3D144%5Eo)
so
![\frac{x}{2}=72^o](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%3D72%5Eo)
therefore
7 of the angles measure 144 degrees each and one angle measures 72 degrees
Observe that
![\sin\left(\dfrac\pi6-v\right)=\sin\dfrac\pi6\cos v-\cos\dfrac\pi6\sin v=\dfrac12\cos v-\dfrac{\sqrt3}2\sin v](https://tex.z-dn.net/?f=%5Csin%5Cleft%28%5Cdfrac%5Cpi6-v%5Cright%29%3D%5Csin%5Cdfrac%5Cpi6%5Ccos%20v-%5Ccos%5Cdfrac%5Cpi6%5Csin%20v%3D%5Cdfrac12%5Ccos%20v-%5Cdfrac%7B%5Csqrt3%7D2%5Csin%20v)
In the original equation, divide both sides by
:
![-\sqrt3\sin v+\cos v=\sqrt3\implies\dfrac12\cos v-\dfrac{\sqrt3}2\sin v=\dfrac{\sqrt3}2](https://tex.z-dn.net/?f=-%5Csqrt3%5Csin%20v%2B%5Ccos%20v%3D%5Csqrt3%5Cimplies%5Cdfrac12%5Ccos%20v-%5Cdfrac%7B%5Csqrt3%7D2%5Csin%20v%3D%5Cdfrac%7B%5Csqrt3%7D2)
![\implies\sin\left(\dfrac\pi6-v\right)=\dfrac{\sqrt3}2](https://tex.z-dn.net/?f=%5Cimplies%5Csin%5Cleft%28%5Cdfrac%5Cpi6-v%5Cright%29%3D%5Cdfrac%7B%5Csqrt3%7D2)
Next,
![\sin x=\dfrac{\sqrt3}2\implies x=\dfrac\pi3+2n\pi,x=\dfrac{2\pi}3+2n\pi](https://tex.z-dn.net/?f=%5Csin%20x%3D%5Cdfrac%7B%5Csqrt3%7D2%5Cimplies%20x%3D%5Cdfrac%5Cpi3%2B2n%5Cpi%2Cx%3D%5Cdfrac%7B2%5Cpi%7D3%2B2n%5Cpi)
where
is any integer. Then
![\sin\left(\dfrac\pi6-v\right)\implies v=-\dfrac\pi6-2n\pi,v=-\dfrac\pi2-2n\pi](https://tex.z-dn.net/?f=%5Csin%5Cleft%28%5Cdfrac%5Cpi6-v%5Cright%29%5Cimplies%20v%3D-%5Cdfrac%5Cpi6-2n%5Cpi%2Cv%3D-%5Cdfrac%5Cpi2-2n%5Cpi)
Fix
to ensure
, so that
![v=-\dfrac\pi6,v=-\dfrac\pi2](https://tex.z-dn.net/?f=v%3D-%5Cdfrac%5Cpi6%2Cv%3D-%5Cdfrac%5Cpi2)
What pattern are you talk about
Answer: For a) the Factor is (x+2) (x+1)
Step-by-step explanation: Because (x+2) multiplied by (x+1) gives you x2 + 3x +2.
I don't know your language so I don't know if that was the question or what the other questions were asking, but that's the best I can do