Answer:
380
Step-by-step explanation:
280 coffe machine
15 bag multiple for 40= 600 - 15%= 540
540+280=820
1200-820=380
9514 1404 393
Answer:
see attached
Step-by-step explanation:
We don't know the drivers' names or when or where they started. We have made the assumption that the second equation pertains to Kylie.
Each line is plotted with the appropriate slope and y-intercept. The slope is the coefficient of x, and represents the "rise" for each unit of "run" to the right.
Answer:
Infinite number of solutions.
Step-by-step explanation:
We are given system of equations
![5x+4y+5z=-1](https://tex.z-dn.net/?f=%205x%2B4y%2B5z%3D-1)
![x+y+2z=1](https://tex.z-dn.net/?f=x%2By%2B2z%3D1)
![2x+y-z=-3](https://tex.z-dn.net/?f=2x%2By-z%3D-3)
Firs we find determinant of system of equations
Let a matrix A=
and B=![\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%5C%5C1%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
![\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}](https://tex.z-dn.net/?f=%5Cmid%20A%5Cmid%3D%5Cbegin%7Bvmatrix%7D5%264%265%5C%5C1%261%262%5C%5C2%261%26-1%5Cend%7Bvmatrix%7D)
![\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0](https://tex.z-dn.net/?f=%5Cmid%20A%5Cmid%3D5%28-1-2%29-4%28-1-4%29%2B5%281-2%29%3D-15%2B20-5%3D0)
Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.
We are finding rank of matrix
Apply
and ![R_3\rightarrow R_3-2R_2](https://tex.z-dn.net/?f=%20R_3%5Crightarrow%20R_3-2R_2)
:![\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%5C%5C1%5C%5C-5%5Cend%7Barray%7D%5Cright%5D)
Apply![R_2\rightarrow R_2-R_1](https://tex.z-dn.net/?f=%20R_2%5Crightarrow%20R_2-R_1)
:![\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%5C%5C6%5C%5C-5%5Cend%7Barray%7D%5Cright%5D)
Apply ![R_3\rightarrow R_3+R_2](https://tex.z-dn.net/?f=%20R_3%5Crightarrow%20R_3%2BR_2)
:![\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%5C%5C6%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
Apply
and ![R_2\rightarrow R_2-R_3](https://tex.z-dn.net/?f=%20R_2%5Crightarrow%20R_2-R_3)
:![\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%5C%5C%5Cfrac%7B13%7D%7B2%7D%5C%5C-%5Cfrac%7B1%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
Apply ![R_1\rightarrow R_1-R_3](https://tex.z-dn.net/?f=R_1%5Crightarrow%20R_1-R_3)
:![\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-%5Cfrac%7B9%7D%7B2%7D%5C%5C%5Cfrac%7B13%7D%7B2%7D%5C%5C-%5Cfrac%7B1%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.
Therefore, rank of matrix is equal to rank of B.
Y’all need to find out on the graft but it was 0.5 will be on the last line