Answer:
1. corresponding angles
2. same side interior angles
m-5 = 71 degrees
m-7 = 109 degrees
Step-by-step explanation:
3.
m-1= 71 degrees
m-4=71 degrees
71 + 71 = 142 degrees
360 - 142 = 218
218 / 2 = 109 degrees.
m-2 = 109 degrees
m-3 = 109 degrees
Answer:
AB and MN
∠B and ∠N
CB and LN
Step-by-step explanation:
edg
Answer: Thanks!
Step-by-step explanation:
<span>Simplifying
(c + 3) + -2c + -1(1 + -3c) = 2
Reorder the terms:
(3 + c) + -2c + -1(1 + -3c) = 2
Remove parenthesis around (3 + c)
3 + c + -2c + -1(1 + -3c) = 2
3 + c + -2c + (1 * -1 + -3c * -1) = 2
3 + c + -2c + (-1 + 3c) = 2
Reorder the terms:
3 + -1 + c + -2c + 3c = 2
Combine like terms: 3 + -1 = 2
2 + c + -2c + 3c = 2
Combine like terms: c + -2c = -1c
2 + -1c + 3c = 2
Combine like terms: -1c + 3c = 2c
2 + 2c = 2
Add '-2' to each side of the equation.
2 + -2 + 2c = 2 + -2
Combine like terms: 2 + -2 = 0
0 + 2c = 2 + -2
2c = 2 + -2
Combine like terms: 2 + -2 = 0
2c = 0
Solving
2c = 0
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Divide each side by '2'.
c = 0
Simplifying answer c = 0</span>
Answer:
The set of solutions is ![\{\left[\begin{array}{c}a\\b\\x\\y\\z\end{array}\right] = \left[\begin{array}{c}-26+503y+543z\\-37+655y+724z\\-4+80y+90z\\y\\z\end{array}\right] : \text{y, z are real numbers}\}](https://tex.z-dn.net/?f=%5C%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da%5C%5Cb%5C%5Cx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-26%2B503y%2B543z%5C%5C-37%2B655y%2B724z%5C%5C-4%2B80y%2B90z%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3A%20%5Ctext%7By%2C%20z%20are%20real%20numbers%7D%5C%7D)
Step-by-step explanation:
The matrix associated to the problem is ![A=\left[\begin{array}{ccccc}1&-1&2&-8&1\\2&-1&-4&1&-2\\-4&1&4&-3&-1\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%26-1%262%26-8%261%5C%5C2%26-1%26-4%261%26-2%5C%5C-4%261%264%26-3%26-1%5Cend%7Barray%7D%5Cright%5D)
and the vector of independent terms is (3,1,-1)^t. Then the matrix equation form of the system is Ax=b.
The vector equation form is ![a\left[\begin{array}{c}1\\2\\-4\end{array}\right]+b\left[\begin{array}{c}-1\\-1\\1\end{array}\right] + x\left[\begin{array}{c}2\\-4\\4\end{array}\right]+y\left[\begin{array}{c}-8\\1\\-3\end{array}\right] + z\left[\begin{array}{c}1\\-2\\-1\end{array}\right]=\left[\begin{array}{c}3\\1\\-1\end{array}\right]](https://tex.z-dn.net/?f=a%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C2%5C%5C-4%5Cend%7Barray%7D%5Cright%5D%2Bb%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%5C%5C-1%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%2B%20x%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C-4%5C%5C4%5Cend%7Barray%7D%5Cright%5D%2By%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-8%5C%5C1%5C%5C-3%5Cend%7Barray%7D%5Cright%5D%20%2B%20z%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C-2%5C%5C-1%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%5C%5C1%5C%5C-1%5Cend%7Barray%7D%5Cright%5D)
.
Now we solve the system.
The aumented matrix of the system is ![\left[\begin{array}{cccccc}1&-1&2&-8&1&3\\2&-1&-4&1&-2&1\\-4&1&4&-3&-1&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccccc%7D1%26-1%262%26-8%261%263%5C%5C2%26-1%26-4%261%26-2%261%5C%5C-4%261%264%26-3%26-1%26-1%5Cend%7Barray%7D%5Cright%5D)
.
Applying rows operations we obtain a echelon form of the matrix, that is ![\left[\begin{array}{cccccc}1&-1&2&-8&1&3\\0&1&-8&-15&-4&-5\\0&0&1&-80&-9&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccccc%7D1%26-1%262%26-8%261%263%5C%5C0%261%26-8%26-15%26-4%26-5%5C%5C0%260%261%26-80%26-9%26-4%5Cend%7Barray%7D%5Cright%5D)
Now we solve for the unknown variables:
- x-80y-90z=-4 then x=-4+80y+90z
- b-8x-15y-4z=-5, b-8(-4+80y+90z)-15y-4z=-5 then b=-37+655y+724z.
- a-b+2x-8y+z=3, a-(-37+655y+724z)+2(-4+80y+90z)-8y+z=3, then a=-26+503y+543z
Since the system has two free variables then has infinite solutions.
The set of solutions is
