Answer:
Step-by-step explanation:
Because vertical angles are always equal, we want to solve 
.
We can add 10 to both sides to get 
.
We can subtract 
from both sides to get 
.
Lastly, we divide both sides by 20 to get 
.
So, 
and we're done!
The check is left as an exercise to the reader.
You can 14 rows of 5 chairs, which also means you can do 5 rows of 14. Or 7 rows of 10 or 10 rows of seven. That's all I'm getting that doesn't exceed the 20 row limit.
2/3 to 8 is the same ratio if we multiply both sides by 3/2 so:
2/3×3/2=1
8×3/2=12
So 1 to 12
Answer:
The answer is below
Step-by-step explanation:
The system of equations:
8x-9y+13z=11
-8x-5y+5z=15
3x+4y-8z=-10
The equations can be represented in matrix form as:
AX = B
X = A⁻¹B
Therefore:
![\left[\begin{array}{ccc}8&-9&13\\-8&-5&5\\3&4&-8\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}11\\15\\-10\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}8&-9&13\\-8&-5&5\\3&4&-8\end{array}\right] ^{-1}\left[\begin{array}{c}11\\15\\-10\end{array}\right]\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-9%2613%5C%5C-8%26-5%265%5C%5C3%264%26-8%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D11%5C%5C15%5C%5C-10%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26-9%2613%5C%5C-8%26-5%265%5C%5C3%264%26-8%5Cend%7Barray%7D%5Cright%5D%20%5E%7B-1%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D11%5C%5C15%5C%5C-10%5Cend%7Barray%7D%5Cright%5D%5C%5C)
![\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{19} &-\frac{1}{19}&\frac{1}{19}\\-\frac{49}{380}&-\frac{103}{380}&-\frac{36}{95} \\-\frac{17}{380}&-\frac{69}{380}&-\frac{28}{95} \end{array}\right] \left[\begin{array}{c}11\\15\\-10\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}-0.74\\-1.69\\0.13\end{array}\right] \\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B19%7D%20%26-%5Cfrac%7B1%7D%7B19%7D%26%5Cfrac%7B1%7D%7B19%7D%5C%5C-%5Cfrac%7B49%7D%7B380%7D%26-%5Cfrac%7B103%7D%7B380%7D%26-%5Cfrac%7B36%7D%7B95%7D%20%5C%5C-%5Cfrac%7B17%7D%7B380%7D%26-%5Cfrac%7B69%7D%7B380%7D%26-%5Cfrac%7B28%7D%7B95%7D%20%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D11%5C%5C15%5C%5C-10%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-0.74%5C%5C-1.69%5C%5C0.13%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Answer:
y=5x+7
Step-by-step explanation:
