Answer:
![S_{10}=-55](https://tex.z-dn.net/?f=S_%7B10%7D%3D-55)
Step-by-step explanation:
The given series is
![(-1)+(-2)+(-3)+...+(-10)](https://tex.z-dn.net/?f=%28-1%29%2B%28-2%29%2B%28-3%29%2B...%2B%28-10%29)
The first term of this arithmetic sequence is
the last term is ![l=-10](https://tex.z-dn.net/?f=l%3D-10)
The sum of the first n-terms is given by
![S_n=\frac{n}{2}(a_1+l)](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%28a_1%2Bl%29)
The first 10 terms is
![S_{10}=\frac{10}{2}(-1+-10)](https://tex.z-dn.net/?f=S_%7B10%7D%3D%5Cfrac%7B10%7D%7B2%7D%28-1%2B-10%29)
![S_{10}=5(-11)](https://tex.z-dn.net/?f=S_%7B10%7D%3D5%28-11%29)
![S_{10}=-55](https://tex.z-dn.net/?f=S_%7B10%7D%3D-55)
Answer:
Slope = ∆y/∆x
slope = ( -5_1 ) / ( 3_-3 )
slope = -6 / 6
slope = -1
Answer:
x = ![\frac{8}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B3%7D)
![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
Step-by-step explanation:
in a 30-60-90 triangle the ratio of the side lengths is 1 : 2 : ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
to find the length of short leg, x, you can create this proportion:
x / 8 = 1 / ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
cross-multiply to get:
x = 8
x = 8 / ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
rationalize the denominator by multiplying numerator and denominator by ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
x = ![\frac{8}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B3%7D)
![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
Step-by-step explanation:
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Your answer for your problem is 137.802