Given, arc QR is congruent to arc LN and arc OP is congruent to arc VW.
And the expressions for each arc in the diagram also given as:
Arc QR = 2x - y, arc LN = 11 , arc OP= 10 and arc VW=5x+y.
Hence, we will get the system of equations as following:
Arc QR = Arc LN
2x - y = 11 ...(1)
Arc OP = Arc VW
5x + y = 10 ...(2)
We need to find the value of x. So, we can add the equations to eliminate y so that we can solve the equations for x. Therefore,
2x+5x = 11 + 10
7x = 21
Divide each sides by 7.
So, x= 3
Answer:
6x + 8y
Step-by-step explanation:
Distribute 2:
Note: This means to multiply 2 with the numbers inside the parentheses.
2 * 3x = 6x
2 * 4y = 8y
Our answer would be 6x +8y
Answer
(a)
![A^{-1} = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix}](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7B3493%7D%20%20%5Cbegin%7Bpmatrix%7D%20210%20%26%26%20-59%20%26%26%20-12%20%5C%5C%2084%20%26%26%20176%20%26%26%2095%20%5C%5C%2077%20%26%26%20-5%20%26%26%20295%20%5Cend%7Bpmatrix%7D)
(b)
![A^{-1} b = \begin{pmatrix} \frac{500}{7} \\\\ \frac{2400}{7} \\\\ \frac{2700}{7} \end{pmatrix}](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20b%20%3D%20%5Cbegin%7Bpmatrix%7D%20%5Cfrac%7B500%7D%7B7%7D%20%5C%5C%5C%5C%20%5Cfrac%7B2400%7D%7B7%7D%20%5C%5C%5C%5C%20%5Cfrac%7B2700%7D%7B7%7D%20%5Cend%7Bpmatrix%7D)
Step-by-step explanation:
Remember that when you want to solve a problem like this, you express the equation as following
![Ax = b](https://tex.z-dn.net/?f=Ax%20%3D%20b)
So, if you know the inverse of
then
![x = A^{-1} b](https://tex.z-dn.net/?f=x%20%3D%20A%5E%7B-1%7D%20b)
For this case
![A = \begin{pmatrix} 15 && 5 && -1 \\ -5 && 18 && -6 \\ -4 && -1 && 12 \end{pmatrix}](https://tex.z-dn.net/?f=A%20%3D%20%5Cbegin%7Bpmatrix%7D%2015%20%26%26%20%205%20%26%26%20-1%20%5C%5C%20-5%20%26%26%2018%20%26%26%20-6%20%5C%5C%20-4%20%26%26%20-1%20%26%26%2012%20%20%5Cend%7Bpmatrix%7D)
Now for this case the inverse of A would be
![A^{-1} = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix}](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7B3493%7D%20%20%5Cbegin%7Bpmatrix%7D%20210%20%26%26%20-59%20%26%26%20-12%20%5C%5C%2084%20%26%26%20176%20%26%26%2095%20%5C%5C%2077%20%26%26%20-5%20%26%26%20295%20%5Cend%7Bpmatrix%7D)
Then when you multiply with the vector solution
![A^{-1} b = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix} * \begin{pmatrix} 2400 \\ 3500 \\ 4000 \end{pmatrix} = \frac{1}{3493} \begin{pmatrix} 249500 \\ 1197600 \\ 1347300 \end{pmatrix}\\\\\\= \begin{pmatrix} \frac{500}{7} \\\\ \frac{2400}{7} \\\\ \frac{2700}{7} \end{pmatrix}](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20b%20%3D%20%20%5Cfrac%7B1%7D%7B3493%7D%20%20%5Cbegin%7Bpmatrix%7D%20210%20%26%26%20-59%20%26%26%20-12%20%5C%5C%2084%20%26%26%20176%20%26%26%2095%20%5C%5C%2077%20%26%26%20-5%20%26%26%20295%20%5Cend%7Bpmatrix%7D%20%2A%20%5Cbegin%7Bpmatrix%7D%202400%20%5C%5C%203500%20%5C%5C%204000%20%5Cend%7Bpmatrix%7D%20%3D%20%5Cfrac%7B1%7D%7B3493%7D%20%20%5Cbegin%7Bpmatrix%7D%20249500%20%5C%5C%201197600%20%5C%5C%201347300%20%5Cend%7Bpmatrix%7D%5C%5C%5C%5C%5C%5C%3D%20%5Cbegin%7Bpmatrix%7D%20%5Cfrac%7B500%7D%7B7%7D%20%5C%5C%5C%5C%20%5Cfrac%7B2400%7D%7B7%7D%20%5C%5C%5C%5C%20%5Cfrac%7B2700%7D%7B7%7D%20%5Cend%7Bpmatrix%7D)
So from that information you can conclude that the solution to the system of equations is x = 500/7 y = 2400/7 and z = 2700/7
Answer:
d.all of the above
Step-by-step explanation:
System of equations with no solution means that lines are parallel to each other,don have any common point.
Note that two lines are parallel if their slopes are equal and they have different y-intercepts.
So all the alternatives are true.