Answer:
you pay 240 dollars a year
Step-by-step explanation:
y=20x
x is 12
20*12=
240
Answer:
45x - 9
step by step explanation:
hope this helps!
You just divide. 38÷12=3.166~ $3.17
Answer:
We have the equation
![c_1\left[\begin{array}{c}0\\0\\0\\1\end{array}\right] +c_2\left[\begin{array}{c}0\\0\\3\\1\end{array}\right] +c_3\left[\begin{array}{c}0\\4\\3\\1\end{array}\right] +c_4\left[\begin{array}{c}8\\4\\3\\1\end{array}\right] =\left[\begin{array}{c}0\\0\\0\\0\end{array}\right]](https://tex.z-dn.net/?f=c_1%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%2Bc_2%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%2Bc_3%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C4%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%2Bc_4%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%5C%5C4%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
Then, the augmented matrix of the system is
![\left[\begin{array}{cccc}0&0&0&8\\0&0&4&4\\0&3&3&3\\1&1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D0%260%260%268%5C%5C0%260%264%264%5C%5C0%263%263%263%5C%5C1%261%261%261%5Cend%7Barray%7D%5Cright%5D)
We exchange rows 1 and 4 and rows 2 and 3 and obtain the matrix:
![\left[\begin{array}{cccc}1&1&1&1\\0&3&3&3\\0&0&4&4\\0&0&0&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%261%261%5C%5C0%263%263%263%5C%5C0%260%264%264%5C%5C0%260%260%268%5Cend%7Barray%7D%5Cright%5D)
This matrix is in echelon form. Then, now we apply backward substitution:
1.
![8c_4=0\\c_4=0](https://tex.z-dn.net/?f=8c_4%3D0%5C%5Cc_4%3D0)
2.
![4c_3+4c_4=0\\4c_3+4*0=0\\c_3=0](https://tex.z-dn.net/?f=4c_3%2B4c_4%3D0%5C%5C4c_3%2B4%2A0%3D0%5C%5Cc_3%3D0)
3.
![3c_2+3c_3+3c_4=0\\3c_2+3*0+3*0=0\\c_2=0](https://tex.z-dn.net/?f=3c_2%2B3c_3%2B3c_4%3D0%5C%5C3c_2%2B3%2A0%2B3%2A0%3D0%5C%5Cc_2%3D0)
4.
![c_1+c_2+c_3+c_4=0\\c_1+0+0+0=0\\c_1=0](https://tex.z-dn.net/?f=c_1%2Bc_2%2Bc_3%2Bc_4%3D0%5C%5Cc_1%2B0%2B0%2B0%3D0%5C%5Cc_1%3D0)
Then the system has unique solution that is
and this imply that the vectors
are linear independent.