Y=4/3x+2 have a great day
Answer:
<h2>
![\bold{a_n=2\cdot(-2)^{n-1}}\\\\or\\\\\bold{a_n=(-1)^{n-1}\cdot2^{n}}](https://tex.z-dn.net/?f=%5Cbold%7Ba_n%3D2%5Ccdot%28-2%29%5E%7Bn-1%7D%7D%5C%5C%5C%5Cor%5C%5C%5C%5C%5Cbold%7Ba_n%3D%28-1%29%5E%7Bn-1%7D%5Ccdot2%5E%7Bn%7D%7D)
</h2>
Step-by-step explanation:
-4÷2 = -2
8÷(-4) = -2
-16÷8 = -2
So this is a geometric sequence with the first term of 2 and a common ratio of -2
the nth term of a geometric sequence: ![a_n=a_1\cdot r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1%5Ccdot%20r%5E%7Bn-1%7D)
Therefore:
![a_n=2\cdot(-2)^{n-1}\\\\a_n=2\cdot(-1\cdot2)^{n-1}=2\cdot(-1)^{n-1}\cdot2^{n-1}=(-1)^{n-1}\cdot2^{n-1+1}\\\\a_n=(-1)^{n-1}\cdot2^{n}](https://tex.z-dn.net/?f=a_n%3D2%5Ccdot%28-2%29%5E%7Bn-1%7D%5C%5C%5C%5Ca_n%3D2%5Ccdot%28-1%5Ccdot2%29%5E%7Bn-1%7D%3D2%5Ccdot%28-1%29%5E%7Bn-1%7D%5Ccdot2%5E%7Bn-1%7D%3D%28-1%29%5E%7Bn-1%7D%5Ccdot2%5E%7Bn-1%2B1%7D%5C%5C%5C%5Ca_n%3D%28-1%29%5E%7Bn-1%7D%5Ccdot2%5E%7Bn%7D)
Answer:
6:9,2:3
Step-by-step explanation:
sorry I Only knew this much
Answer:
is there multiple choice? just wondering
Step-by-step explanation:
Answer:
--- Length
--- Width
Step-by-step explanation:
Given
Let: ![L = Length; W = Width](https://tex.z-dn.net/?f=L%20%3D%20Length%3B%20W%20%3D%20Width)
![Area = 27m^2](https://tex.z-dn.net/?f=Area%20%3D%2027m%5E2)
![L = 2W- 3m](https://tex.z-dn.net/?f=L%20%3D%202W-%203m)
Required
Find the dimensions of the rectangle
Area (A) is calculated as:
![A = L * W](https://tex.z-dn.net/?f=A%20%20%3D%20L%20%2A%20W)
This gives:
![27 = (2W - 3) * W](https://tex.z-dn.net/?f=27%20%3D%20%282W%20-%203%29%20%2A%20W)
Open bracket
![27 = 2W^2 - 3W](https://tex.z-dn.net/?f=27%20%3D%202W%5E2%20-%203W)
Express as a quadratic function
![2W^2 - 3W - 27 = 0](https://tex.z-dn.net/?f=2W%5E2%20-%203W%20-%2027%20%3D%200)
Expand
![2W^2 + 6W - 9W - 27 = 0](https://tex.z-dn.net/?f=2W%5E2%20%2B%206W%20-%209W%20-%2027%20%3D%200)
Factorize:
![2W(W + 3) - 9(W + 3) = 0](https://tex.z-dn.net/?f=2W%28W%20%2B%203%29%20-%209%28W%20%2B%203%29%20%3D%200)
![(2W - 9)(W + 3) = 0](https://tex.z-dn.net/?f=%282W%20-%209%29%28W%20%2B%203%29%20%3D%200)
This gives:
![2W - 9 = 0\ or\ W + 3 = 0](https://tex.z-dn.net/?f=2W%20-%209%20%3D%200%5C%20or%5C%20W%20%2B%203%20%3D%200)
![2W = 9 \ or\ W = -3](https://tex.z-dn.net/?f=2W%20%3D%209%20%5C%20or%5C%20W%20%3D%20-3)
Width can not be negative.
So:
![2W = 9](https://tex.z-dn.net/?f=2W%20%3D%209)
![W = 4.5](https://tex.z-dn.net/?f=W%20%3D%204.5)
Recall that:
![L = 2W- 3m](https://tex.z-dn.net/?f=L%20%3D%202W-%203m)
![L = 2 * 4.5 - 3](https://tex.z-dn.net/?f=L%20%3D%202%20%2A%204.5%20-%203)
![L = 6](https://tex.z-dn.net/?f=L%20%3D%206)