Answer:
The answer is "
"
Step-by-step explanation:
Given:
![\bold{\frac{(m-n)}{m^2-n^2} + \frac{?}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0}\\\\](https://tex.z-dn.net/?f=%5Cbold%7B%5Cfrac%7B%28m-n%29%7D%7Bm%5E2-n%5E2%7D%20%2B%20%5Cfrac%7B%3F%7D%7B%28m-1%29%28m-2%29%7D%20-%20%5Cfrac%7B2m%7D%7Bm%5E2-n%5E2%7D%3D0%7D%5C%5C%5C%5C)
let, ? = x then,
![\Rightarrow \frac{(m-n)}{m^2-n^2} + \frac{x}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0\\\\\Rightarrow \frac{(m-n)}{m^2-n^2} - \frac{2m}{m^2-n^2}=- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{(m-n)-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{m-n-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-n-m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-(m+n)}{(m+n)(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-1}{(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B%28m-n%29%7D%7Bm%5E2-n%5E2%7D%20%2B%20%5Cfrac%7Bx%7D%7B%28m-1%29%28m-2%29%7D%20-%20%5Cfrac%7B2m%7D%7Bm%5E2-n%5E2%7D%3D0%5C%5C%5C%5C%5CRightarrow%20%5Cfrac%7B%28m-n%29%7D%7Bm%5E2-n%5E2%7D%20-%20%5Cfrac%7B2m%7D%7Bm%5E2-n%5E2%7D%3D-%20%5Cfrac%7Bx%7D%7B%28m-1%29%28m-2%29%7D%20%5C%5C%5C%5C%5CRightarrow%20%5Cfrac%7B%28m-n%29-2m%7D%7B%28m%5E2-n%5E2%29%7D%20%3D-%20%5Cfrac%7Bx%7D%7B%28m-1%29%28m-2%29%7D%20%5C%5C%5C%5C%5CRightarrow%20%5Cfrac%7Bm-n-2m%7D%7B%28m%5E2-n%5E2%29%7D%20%3D-%20%5Cfrac%7Bx%7D%7B%28m-1%29%28m-2%29%7D%20%5C%5C%5C%5C%5CRightarrow%20%5Cfrac%7B-n-m%7D%7B%28m%5E2-n%5E2%29%7D%20%3D-%20%5Cfrac%7Bx%7D%7B%28m-1%29%28m-2%29%7D%20%5C%5C%5C%5C%5CRightarrow%20%5Cfrac%7B-%28m%2Bn%29%7D%7B%28m%2Bn%29%28m-n%29%7D%20%3D-%20%5Cfrac%7Bx%7D%7B%28m-1%29%28m-2%29%7D%20%5C%5C%5C%5C%5CRightarrow%20%5Cfrac%7B-1%7D%7B%28m-n%29%7D%20%3D-%20%5Cfrac%7Bx%7D%7B%28m-1%29%28m-2%29%7D%20%5C%5C%5C%5C)
![\Rightarrow -((m-1)(m-2))=-x(m-n) \\\\\Rightarrow x= \frac{- (m-1)(m-2)}{- (m-n)} \\\\\Rightarrow \boxed{x= \frac{(m-1)(m-2)}{(m-n)}} \\](https://tex.z-dn.net/?f=%5CRightarrow%20-%28%28m-1%29%28m-2%29%29%3D-x%28m-n%29%20%5C%5C%5C%5C%5CRightarrow%20x%3D%20%5Cfrac%7B-%20%28m-1%29%28m-2%29%7D%7B-%20%28m-n%29%7D%20%5C%5C%5C%5C%5CRightarrow%20%5Cboxed%7Bx%3D%20%5Cfrac%7B%28m-1%29%28m-2%29%7D%7B%28m-n%29%7D%7D%20%5C%5C)
You would just do 4 x 7, which means there are 28 combinations.
Answer:
The sum of the first six terms is
![32-8+2-0.5+\frac{1}{8}-\frac{1}{32}=25.59](https://tex.z-dn.net/?f=32-8%2B2-0.5%2B%5Cfrac%7B1%7D%7B8%7D-%5Cfrac%7B1%7D%7B32%7D%3D25.59)
Step-by-step explanation:
Given series is 32-8+2-0.5+...
We may write ![{\{32,-8,2,-0.5,...}\}](https://tex.z-dn.net/?f=%7B%5C%7B32%2C-8%2C2%2C-0.5%2C...%7D%5C%7D)
Let ![a_{1}=32,a_{2}=-8,a_{3}=2,a_{4}=-05,...](https://tex.z-dn.net/?f=a_%7B1%7D%3D32%2Ca_%7B2%7D%3D-8%2Ca_%7B3%7D%3D2%2Ca_%7B4%7D%3D-05%2C...)
Common ratio ![r=\frac{a_{2}}{a_{1}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_%7B2%7D%7D%7Ba_%7B1%7D%7D)
![r=\frac{-8}{32}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-8%7D%7B32%7D)
![r=\frac{-1}{4}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-1%7D%7B4%7D)
![r=\frac{a_{3}}{a_{2}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_%7B3%7D%7D%7Ba_%7B2%7D%7D)
![r=\frac{2}{-8}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B2%7D%7B-8%7D)
![r=\frac{-1}{4}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-1%7D%7B4%7D)
Therefore the common ratio is ![r=\frac{-1}{4}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-1%7D%7B4%7D)
Therefore given sequence is of the form of Geometric sequence
The nth term of the geometric sequence is
![a_{n}=ar^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Dar%5E%7Bn-1%7D)
First to find the 5th and 6th term
That is substitute n=5 and n=6 ,a=32 and
in above equation we get
![a_{5}=32(\frac{-1}{4})^{5-1}](https://tex.z-dn.net/?f=a_%7B5%7D%3D32%28%5Cfrac%7B-1%7D%7B4%7D%29%5E%7B5-1%7D)
![a_{5}=32(\frac{-1}{4})^{4}](https://tex.z-dn.net/?f=a_%7B5%7D%3D32%28%5Cfrac%7B-1%7D%7B4%7D%29%5E%7B4%7D)
![a_{5}=32[(\frac{-1}{4})\times (\frac{-1}{4})\times (\frac{-1}{4})\times (\frac{-1}{4})]](https://tex.z-dn.net/?f=a_%7B5%7D%3D32%5B%28%5Cfrac%7B-1%7D%7B4%7D%29%5Ctimes%20%28%5Cfrac%7B-1%7D%7B4%7D%29%5Ctimes%20%28%5Cfrac%7B-1%7D%7B4%7D%29%5Ctimes%20%28%5Cfrac%7B-1%7D%7B4%7D%29%5D)
![=\frac{1}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B8%7D)
Therefore ![a_{5}=\frac{1}{8}](https://tex.z-dn.net/?f=a_%7B5%7D%3D%5Cfrac%7B1%7D%7B8%7D)
![a_{6}=32(\frac{-1}{4})^{6-1}](https://tex.z-dn.net/?f=a_%7B6%7D%3D32%28%5Cfrac%7B-1%7D%7B4%7D%29%5E%7B6-1%7D)
![a_{6}=32(\frac{-1}{4})^{5}](https://tex.z-dn.net/?f=a_%7B6%7D%3D32%28%5Cfrac%7B-1%7D%7B4%7D%29%5E%7B5%7D)
![a_{6}=32[(\frac{-1}{4})\times (\frac{-1}{4})\times (\frac{-1}{4})\times (\frac{-1}{4})\times (\frac{-1}{4})]](https://tex.z-dn.net/?f=a_%7B6%7D%3D32%5B%28%5Cfrac%7B-1%7D%7B4%7D%29%5Ctimes%20%28%5Cfrac%7B-1%7D%7B4%7D%29%5Ctimes%20%28%5Cfrac%7B-1%7D%7B4%7D%29%5Ctimes%20%28%5Cfrac%7B-1%7D%7B4%7D%29%5Ctimes%20%28%5Cfrac%7B-1%7D%7B4%7D%29%5D)
![=\frac{-1}{32}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-1%7D%7B32%7D)
Therefore ![a_{6}=-\frac{1}{32}](https://tex.z-dn.net/?f=a_%7B6%7D%3D-%5Cfrac%7B1%7D%7B32%7D)
Therefore the sum of the first six terms is
![32-8+2-0.5+\frac{1}{8}-\frac{1}{32}](https://tex.z-dn.net/?f=32-8%2B2-0.5%2B%5Cfrac%7B1%7D%7B8%7D-%5Cfrac%7B1%7D%7B32%7D)
![=25.5+\frac{3}{32}](https://tex.z-dn.net/?f=%3D25.5%2B%5Cfrac%7B3%7D%7B32%7D)
![=\frac{819}{32}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B819%7D%7B32%7D)
![=25.59](https://tex.z-dn.net/?f=%3D25.59)
Therefore the sum of the first six terms is
![32-8+2-0.5+\frac{1}{8}-\frac{1}{32}=25.59](https://tex.z-dn.net/?f=32-8%2B2-0.5%2B%5Cfrac%7B1%7D%7B8%7D-%5Cfrac%7B1%7D%7B32%7D%3D25.59)
Answer:
Sarah bought 3 first class tickets and 3 coach tickets.
Step by Step Explanation:
1030+1030+1030=3850
380+380+380=1140
3850+1140=4230
1) 6*10=60, 6*7=42/2=21, 21+60=81
2) 12*12=144, 12*12=144*3.14=452.16/2=226.08, 144+226.08=370.08
3) 14*5=70, 5*10=50, 70+50=120 (maybe)
4) 6*5=30/2=15, 4*3=12/2=6,15+6=21
5) 6*6=36*3.14=113.04/2=56.52, 5*5=25*3.14=78.5/2=39.25, 56.52+39.25=95.77
if right then give brainliest plz