Assuming these are the angles for the inside of the triangle:
c=2
Step-by-step:
108+42+15c=180
150+15c=180
15c=30
c=2
Answer:
B: 60
Step-by-step explanation:
f(x)= 5x+10, if x=10
f(10)=5(10)+10
5(10)+10=60
f(10)=60
Note: √a * √a = a
√a * √b = √ab
(√2 + √10)² = (√2 + √10)(√2 + √10)
= √2(√2 + √10) + √10(√2 + √10)
= √2*√2 + √2*√10 + √10*√2 + √10*√10
= 2 + √20 + √20 + 10
= (2 + 10) + (√20 + √20)
= 12 + 2√20
√20 = √(4 *5) = √4 * √5 = 2√5
= 12 + 2√20 = 12 + 2(2√5)
= 12 + 4√5
Answer:
![A(1)=9](https://tex.z-dn.net/?f=A%281%29%3D9)
![A(2)=4](https://tex.z-dn.net/?f=A%282%29%3D4)
![A(3)=-1](https://tex.z-dn.net/?f=A%283%29%3D-1)
Arithmetic sequence
Step-by-step explanation:
We are given that
A(1)=9
We have to find first three terms and identify the sequence is geometric or arithmetic.
Substitute n=1
Then, we get
![A(2)=A(1)-5=9-5=4](https://tex.z-dn.net/?f=A%282%29%3DA%281%29-5%3D9-5%3D4)
For n=2
![A(3)=A(2)-5=4-5=-1](https://tex.z-dn.net/?f=A%283%29%3DA%282%29-5%3D4-5%3D-1)
For n=3
![A(4)=-1-5=-6](https://tex.z-dn.net/?f=A%284%29%3D-1-5%3D-6)
![d_1=A_2-A_1=4-9=-5](https://tex.z-dn.net/?f=d_1%3DA_2-A_1%3D4-9%3D-5)
![d_2=A_3-A_2=-1-4=-5](https://tex.z-dn.net/?f=d_2%3DA_3-A_2%3D-1-4%3D-5)
![d_3=A_4-A_3=-6+1=-5](https://tex.z-dn.net/?f=d_3%3DA_4-A_3%3D-6%2B1%3D-5)
![d_1=d_2=d_3=-5](https://tex.z-dn.net/?f=d_1%3Dd_2%3Dd_3%3D-5)
When the difference of consecutive terms are constant then the sequence is arithmetic sequence.
Therefore, given sequence is arithmetic sequence.
![\bf \textit{sum of interior angles in a regular polygon} \\\\\\ n\theta=180(n-2)\qquad \begin{cases} n=\textit{number of sides}\\ \theta=\textit{angle in degrees} \end{cases} \\\\\\ \textit{notice, your two polygons, are just two regular octagons}\\ \textit{OCTAgons, thus OCTA = 8, 8 sides, thus} \\\\\\ n\theta=180(n-2)\qquad n=8\implies 8\theta=180(8-2) \\\\\\ \theta=\cfrac{180\cdot 6}{8}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bsum%20of%20interior%20angles%20in%20a%20regular%20polygon%7D%0A%5C%5C%5C%5C%5C%5C%0An%5Ctheta%3D180%28n-2%29%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0An%3D%5Ctextit%7Bnumber%20of%20sides%7D%5C%5C%0A%5Ctheta%3D%5Ctextit%7Bangle%20in%20degrees%7D%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Bnotice%2C%20your%20two%20polygons%2C%20are%20just%20two%20regular%20octagons%7D%5C%5C%0A%5Ctextit%7BOCTAgons%2C%20thus%20OCTA%20%3D%208%2C%208%20sides%2C%20thus%7D%0A%5C%5C%5C%5C%5C%5C%0An%5Ctheta%3D180%28n-2%29%5Cqquad%20n%3D8%5Cimplies%208%5Ctheta%3D180%288-2%29%0A%5C%5C%5C%5C%5C%5C%0A%5Ctheta%3D%5Ccfrac%7B180%5Ccdot%206%7D%7B8%7D)
so... that's how much an internal angle is
now, subtract that from 180 and you get the angle outside, in the picture
subtract that outside angle twice from 180, and you get angle "2"
because angle 2 is in the same triangle as those two outside angles, and all internal angles in a triangle is 180, thus 180 - (those two angles) is angle "2"