Let
x: number of regular basketball
y: number of long-distance basket
We have the following system of equations:
2x + 3y = 96
x + y = 45
Solving the system we have
y = 45-x
2x + 3 (45-x) = 96
2x +135 -3x = 96
-x = 96 -135
x = 39
Then,
y = 45-x
y = 45-39
y = 6
answer
were made
regular baskets = 39
long-distance baskets = 6
Answer:
The greater number is 12
the smaller number is 10
I found the answer just by multiplying the 6:5 by 2 and checked to see the lcm and it was 60 so here you go
Answer:
42
Step-by-step explanation:
15.54 divided by 0.37 equals 42
Answer:
![- \frac{8}{\pi}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B%5Cpi%7D%20)
Step-by-step explanation:
Use slope formula.
Rise over run.
Or
y over x.
![\frac{ {y}^{2} - y {}^{1} }{ {x}^{2} - x {}^{1} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7By%7D%5E%7B2%7D%20%20-%20y%20%7B%7D%5E%7B1%7D%20%7D%7B%20%7Bx%7D%5E%7B2%7D%20-%20x%20%7B%7D%5E%7B1%7D%20%20%7D%20)
Over changes in x value would be - 3/4 pi.
Plug in seepage intervals for x to find y.
![6 \cos(2(\pi) - 4](https://tex.z-dn.net/?f=6%20%5Ccos%282%28%5Cpi%29%20%20-%204)
In the regular function,
![\cos(\pi) = 1](https://tex.z-dn.net/?f=%20%5Ccos%28%5Cpi%29%20%20%3D%201)
Since our period is 2, it would stay the same since 1x2=2
Since our amplitude is 6, our y value now is 6.
Since our vertical shift is -4, our y value is 2.
So
![6 \cos(2(\pi)) - 4 = 2](https://tex.z-dn.net/?f=6%20%5Ccos%282%28%5Cpi%29%29%20%20-%204%20%3D%202)
![{x}^{2} = \pi \: \: \: \: {y}^{2} = 2](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%20%5Cpi%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%7By%7D%5E%7B2%7D%20%20%3D%202)
Let do the other point,
![\cos( \frac{\pi}{4} ) = \frac{ \sqrt{2} }{2}](https://tex.z-dn.net/?f=%20%5Ccos%28%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%29%20%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B2%7D%20)
Our period is 2 so
![\frac{ {\pi} }{4} \times \frac{2}{1} = \frac{\pi}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B%5Cpi%7D%20%7D%7B4%7D%20%20%5Ctimes%20%20%5Cfrac%7B2%7D%7B1%7D%20%20%3D%20%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20)
![\cos( \frac{\pi}{2} ) = 0](https://tex.z-dn.net/?f=%20%5Ccos%28%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%29%20%20%3D%200)
Multiply this by 6.
It stays 0 then subtract 4 we get
![6 \cos(2( \frac{\pi}{4} )) - 4 = - 4](https://tex.z-dn.net/?f=6%20%5Ccos%282%28%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%29%29%20%20-%204%20%3D%20%20-%204)
Use the earlier formula, slope
![\frac{2 + 4}{ - \frac{3\pi}{4} } = - \frac{8}{\pi}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%20%20%2B%204%7D%7B%20-%20%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%20%7D%20%20%3D%20%20-%20%20%5Cfrac%7B8%7D%7B%5Cpi%7D%20)
Answer:
The 9th term for given sequence is 16.777
Therefore the 9th term is
.
Step-by-step explanation:
Given first three terms of a sequence are 100,80,64,...
Given
,
,
,...
Given sequence is of the form of Geometric sequence
Therefore it can be written as ![{\{a,ar,ar^2,...}\}](https://tex.z-dn.net/?f=%7B%5C%7Ba%2Car%2Car%5E2%2C...%7D%5C%7D)
therefore a=100 , ar=80 ,
,...
To find 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{80}{100}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B80%7D%7B100%7D)
![r=\frac{4}{5}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B5%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{64}{80}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B64%7D%7B80%7D)
![r=\frac{4}{5}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B5%7D)
Therefore ![r=\frac{4}{5}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B5%7D)
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)
To find the 9th tem for the given geometric sequence is
![a_{n}=ar^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Dar%5E%7Bn-1%7D)
put n=9, a=100 and ![r=\frac{4}{5}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B5%7D)
![a_{9}=100(\frac{4}{5})^{9-1}](https://tex.z-dn.net/?f=a_%7B9%7D%3D100%28%5Cfrac%7B4%7D%7B5%7D%29%5E%7B9-1%7D)
![=100(\frac{4}{5})^{8}](https://tex.z-dn.net/?f=%3D100%28%5Cfrac%7B4%7D%7B5%7D%29%5E%7B8%7D)
![=100(\frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5})](https://tex.z-dn.net/?f=%3D100%28%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%29)
![=100(\frac{256\times 256}{625\times 625})](https://tex.z-dn.net/?f=%3D100%28%5Cfrac%7B256%5Ctimes%20256%7D%7B625%5Ctimes%20625%7D%29)
![=100(\frac{65536}{390625})](https://tex.z-dn.net/?f=%3D100%28%5Cfrac%7B65536%7D%7B390625%7D%29)
![=100(0.16777})](https://tex.z-dn.net/?f=%3D100%280.16777%7D%29)
![=16.777](https://tex.z-dn.net/?f=%3D16.777)
Therefore ![a_{9}=16.777](https://tex.z-dn.net/?f=a_%7B9%7D%3D16.777)
The 9th term is 16.777