for this case we have the following equation:
![2x + 5 = -x + 1](https://tex.z-dn.net/?f=2x%20%2B%205%20%3D%20-x%20%2B%201)
To resolve:
We add x to both sides of the equation:
![2x + x + 5 = -x + 1 + x](https://tex.z-dn.net/?f=2x%20%2B%20x%20%2B%205%20%3D%20-x%20%2B%201%20%2B%20x)
![3x + 5 = 1](https://tex.z-dn.net/?f=3x%20%2B%205%20%3D%201)
We subtract 5 on both sides of the equation:
![3x + 5-5 = 1-5\\3x = -4](https://tex.z-dn.net/?f=3x%20%2B%205-5%20%3D%201-5%5C%5C3x%20%3D%20-4)
We divide between 3 on both sides of the equation:
![x = - \frac {4} {3}](https://tex.z-dn.net/?f=x%20%3D%20-%20%5Cfrac%20%7B4%7D%20%7B3%7D)
Answer:
We add x to both sides of the equation
a) The linear function that models the amount of water after t minutes is given by:
![V(t) = 200 + 12t](https://tex.z-dn.net/?f=V%28t%29%20%3D%20200%20%2B%2012t)
b) It takes 92 minutes to completely fill the pond.
Item a:
- Initially, the pond contains 200 gal of water, that is, the linear function has a y-intercept of 200.
- Filled at a rate of 12 gallons per minute, thus the linear function has a slope of 12.
Then, the function is:
![V(t) = 200 + 12t](https://tex.z-dn.net/?f=V%28t%29%20%3D%20200%20%2B%2012t)
Item b:
It takes t minutes to fill the pond, t is found for which:
![V(t) = 1304](https://tex.z-dn.net/?f=V%28t%29%20%3D%201304)
Then
![200 + 12t = 1304](https://tex.z-dn.net/?f=200%20%2B%2012t%20%3D%201304)
![12t = 1104](https://tex.z-dn.net/?f=12t%20%3D%201104)
![t = \frac{1104}{12}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B1104%7D%7B12%7D)
![t = 92](https://tex.z-dn.net/?f=t%20%3D%2092)
It takes 92 minutes to completely fill the pond.
A similar problem is given at brainly.com/question/16302622
15 + 17r - 4r - 9 = 9
6 + 13r = 9
13r = -3
r = -3/13
:)
Answer with explanation:
The System of equations which we have to solve by Gauss Jordan Method:
![1.\rightarrow 2x_{1}-6x_{2}-2x_{3}=14, 2.\rightarrow 3x_{1}+4x_{2}-7x_{3}= 16, 3.\rightarrow 3x_{1}-6x_{2}+9x_{3}=21](https://tex.z-dn.net/?f=1.%5Crightarrow%202x_%7B1%7D-6x_%7B2%7D-2x_%7B3%7D%3D14%2C%202.%5Crightarrow%203x_%7B1%7D%2B4x_%7B2%7D-7x_%7B3%7D%3D%2016%2C%203.%5Crightarrow%203x_%7B1%7D-6x_%7B2%7D%2B9x_%7B3%7D%3D21)
Writing it in the form of Augmented Matrix=3 Rows and 4 Columns:
![\left[\begin{array}{cccc}2&-6&-2&14\\3&4&-7&16\\3&-6&9&21\end{array}\right]\\\\R_{1}=\frac{R_{1}}{2},R_{3}=\frac{R_{3}}{3}\\\\ \left[\begin{array}{cccc}1&-3&-1&7\\3&4&-7&16\\1&-2&3&7\end{array}\right]\\\\R_{3}\rightarrow R_{3}-R_{1}\\\\\left[\begin{array}{cccc}1&-3&-1&7\\3&4&-7&16\\0&1&4&0\end{array}\right]\\\\R_{2}\rightarrow R_{2}-3R_{1}\\\\\left[\begin{array}{cccc}1&-3&-1&7\\0&13&-4&-5\\0&1&4&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D2%26-6%26-2%2614%5C%5C3%264%26-7%2616%5C%5C3%26-6%269%2621%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5CR_%7B1%7D%3D%5Cfrac%7BR_%7B1%7D%7D%7B2%7D%2CR_%7B3%7D%3D%5Cfrac%7BR_%7B3%7D%7D%7B3%7D%5C%5C%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-3%26-1%267%5C%5C3%264%26-7%2616%5C%5C1%26-2%263%267%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5CR_%7B3%7D%5Crightarrow%20R_%7B3%7D-R_%7B1%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-3%26-1%267%5C%5C3%264%26-7%2616%5C%5C0%261%264%260%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5CR_%7B2%7D%5Crightarrow%20R_%7B2%7D-3R_%7B1%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-3%26-1%267%5C%5C0%2613%26-4%26-5%5C%5C0%261%264%260%5Cend%7Barray%7D%5Cright%5D)
![R_{3}\rightarrow R_{2}+R_{3}\\\\\left[\begin{array}{cccc}1&-3&-1&7\\0&13&-4&-5\\0&14&0&-5\end{array}\right]\\\\\rightarrow14 x_{2}= -5\\\\x_{2}=\frac{-5}{14}\\\\\rightarrow 13 x_{2}-4x_{3}=-5\\\\ \frac{-65}{14}-4 x_{3}=-5\\\\-4x_{3}=-5+\frac{65}{14}\\\\x_{3}=\frac{5}{56}\\\\x_{1}-3x_{2}-x_{3}=7\\\\x_{1}+\frac{15}{14}-\frac{5}{56}=7\\\\x_{1}+\frac{55}{56}=7\\\\x_{1}=7-\frac{55}{56}\\\\x_{1}=\frac{337}{56}](https://tex.z-dn.net/?f=R_%7B3%7D%5Crightarrow%20R_%7B2%7D%2BR_%7B3%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-3%26-1%267%5C%5C0%2613%26-4%26-5%5C%5C0%2614%260%26-5%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Crightarrow14%20x_%7B2%7D%3D%20-5%5C%5C%5C%5Cx_%7B2%7D%3D%5Cfrac%7B-5%7D%7B14%7D%5C%5C%5C%5C%5Crightarrow%2013%20x_%7B2%7D-4x_%7B3%7D%3D-5%5C%5C%5C%5C%20%5Cfrac%7B-65%7D%7B14%7D-4%20x_%7B3%7D%3D-5%5C%5C%5C%5C-4x_%7B3%7D%3D-5%2B%5Cfrac%7B65%7D%7B14%7D%5C%5C%5C%5Cx_%7B3%7D%3D%5Cfrac%7B5%7D%7B56%7D%5C%5C%5C%5Cx_%7B1%7D-3x_%7B2%7D-x_%7B3%7D%3D7%5C%5C%5C%5Cx_%7B1%7D%2B%5Cfrac%7B15%7D%7B14%7D-%5Cfrac%7B5%7D%7B56%7D%3D7%5C%5C%5C%5Cx_%7B1%7D%2B%5Cfrac%7B55%7D%7B56%7D%3D7%5C%5C%5C%5Cx_%7B1%7D%3D7-%5Cfrac%7B55%7D%7B56%7D%5C%5C%5C%5Cx_%7B1%7D%3D%5Cfrac%7B337%7D%7B56%7D)
Solution set
![=(\frac{337}{56},\frac{-5}{14},\frac{5}{56})](https://tex.z-dn.net/?f=%3D%28%5Cfrac%7B337%7D%7B56%7D%2C%5Cfrac%7B-5%7D%7B14%7D%2C%5Cfrac%7B5%7D%7B56%7D%29)