Answer:
x = 32, ∠A = 132
Step-by-step explanation:
A and B are equal. Set both equations equal to each other.
5x - 18 = 3x + 42
Add 18 to both sides and subtract 3x from both sides.
2x = 60
Divide both sides by 2.
x = 30
Now plug x back in to solve for angle A.
5(30) - 18 = 132
Answer:
179+368+452 jeez that is hard
Answer:
<em>5</em><em> </em><em>is </em><em>correct</em><em> </em><em>answer</em>
Step-by-step explanation:
I hope it helps you
The first term in the series is 336. The second term is obtained by subtracting 4 from the first term; subtract 4 from that to get the third term; and so on. Then the <em>n</em>-th term in the series is
336 - 4 (<em>n</em> - 1)
or
340 - 4<em>n</em>
The last term in this series is 4, so we solve for <em>n</em> :
340 - 4<em>n</em> = 4
336 = 4<em>n</em>
<em>n</em> = 336/4 = 84
The sum of the series is then
![\displaystyle\sum_{n=1}^{84}(340-4n) = 340\sum_{n=1}^{84}1 - 4 \sum_{n=1}^{84}n](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5E%7B84%7D%28340-4n%29%20%3D%20340%5Csum_%7Bn%3D1%7D%5E%7B84%7D1%20-%204%20%5Csum_%7Bn%3D1%7D%5E%7B84%7Dn)
Recall that
![\displaystyle \sum_{n=1}^{N} 1 = N](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum_%7Bn%3D1%7D%5E%7BN%7D%201%20%3D%20N)
![\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum_%7Bn%3D1%7D%5EN%20n%20%3D%20%5Cfrac%7BN%28N%2B1%29%7D2)
Then the sum we want is
![\displaystyle\sum_{n=1}^{84}(340-4n) = 340\times84 - 4\times\frac{84\times85}2 = \boxed{14,280}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5E%7B84%7D%28340-4n%29%20%3D%20340%5Ctimes84%20-%204%5Ctimes%5Cfrac%7B84%5Ctimes85%7D2%20%3D%20%5Cboxed%7B14%2C280%7D)