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.
2.
3.
4.
Then the system has unique solution that is 
and this imply that the vectors 
are linear independent.
Equilateral triangle is a triangle with the 3 sides of the same length, and the 3 angles with the same measures/degree.
The formula to find the area of a triangle is base x height/2 , you do have the base (40), but you need the height. To find the height of an equilateral triangle you use the formula: side/2 x radical3, this way u'll find the height and therefor can calculate the area of the triangle.
Hope that helped :)
Let's simplify step-by-step.<span><span><span><span>8.9x</span>−5</span>−<span>6.8x</span></span>+8</span><span>=<span><span><span><span><span><span>8.9x</span>+</span>−5</span>+</span>−<span>6.8x</span></span>+<span>8
</span></span></span>Combine Like Terms:<span>=<span><span><span><span>8.9x</span>+<span>−5</span></span>+<span>−<span>6.8x</span></span></span>+8</span></span><span>=<span><span>(<span><span>8.9x</span>+<span>−<span>6.8x</span></span></span>)</span>+<span>(<span><span>−5</span>+8</span>)</span></span></span><span>=<span><span>2.1x</span>+<span>3
The simplified answer is </span></span></span><span><span>2.1x</span>+<span>3</span></span>
Well all the factors of 32 are 1 and 32, 2 and 16, 4 and 8.
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