Answer:
The separated values of x and y from the given equation is ![x=\frac{13-3y}{4}, y=1-\frac{4}{13}x](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B13-3y%7D%7B4%7D%2C%20y%3D1-%5Cfrac%7B4%7D%7B13%7Dx)
Step-by-step explanation:
Given equation is ![4 x+3y=13](https://tex.z-dn.net/?f=4%20x%2B3y%3D13)
Now to find the separated values of x and y with the given equation.
Now find the value of x and so we have to separate the value x from the given equation
![4x+3y=13](https://tex.z-dn.net/?f=4x%2B3y%3D13)
![4x=13=3y](https://tex.z-dn.net/?f=4x%3D13%3D3y)
![x=\frac{13-3y}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B13-3y%7D%7B4%7D)
Therfore ![x=\frac{13-3y}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B13-3y%7D%7B4%7D)
Now find the value of y and so we have to separate the value y from the given equation
![4x+13y=13](https://tex.z-dn.net/?f=4x%2B13y%3D13)
![13y=13-4x](https://tex.z-dn.net/?f=13y%3D13-4x)
![y=\frac{13-4x}{13}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B13-4x%7D%7B13%7D)
![y=\frac{13}{13}-\frac{4x}{13}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B13%7D%7B13%7D-%5Cfrac%7B4x%7D%7B13%7D)
![y=1-\frac{4}{13}](https://tex.z-dn.net/?f=y%3D1-%5Cfrac%7B4%7D%7B13%7D)
Therefore ![y=1\frac{4}{13}x](https://tex.z-dn.net/?f=y%3D1%5Cfrac%7B4%7D%7B13%7Dx)
The separated values of x and y from the given equation is
![x=\frac{13-3y}{4}, y=1-\frac{4}{13}x](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B13-3y%7D%7B4%7D%2C%20y%3D1-%5Cfrac%7B4%7D%7B13%7Dx)
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)
0.1 = 1/10
0.16 = 16/100 = 8/50 = 4/25
0.6 = 6/10 = 3/5
0/6 = 6/10 = 3/5
Answer: $106.8
Step-by-step explanation:
Given that the bond price is $100.75
With a 6% brokerage fee
Find the total cost to the nearest cent
First, we calculate the 6% brokerage fee= 6/100 × 100.75
= 0.06 x 100.75
= 6.045
Total cost therefore is the sum of brokerage fee and the cost of bond
= $6.045 + $100.75
= $106.795
To the nearest cent = $106.8