Answer:
<MBK because of the isosceles triangle theorem. If two sides of a triangle are congruent, it is isosceles, so the angles opposite them are also congruent.
Step-by-step explanation:
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.
Hello Bubbleshi !
The first step you need to do is get everything in like terms.
- 1/6 and - 7 /4
Look at the denominator (number on the bottom)
6 and 4 go into 12, so lets check that out.
-1/6 , how can we get 12 from the denominator? Multiply it by 2.
So you multiply both the numerator (number on the top) and the denominator.
-1/6 becomes -2/12.
With -7/4, you want to get the 4 as a 12 (like terms!) so once again you multiply it by 3, and multiply the numerator as well.
-7/4 becomes -21/12.
-2/12 + (-21/12) is your final form of the problem.
You add -2 and -21 in the numerator, which is -23.
So its -23/12 which is your final answer.
Let me know if you need any more help!
Answer: I believe it's 5 I am not sure
Step-by-step explanation:
Let c represent the original amount that this guy had saved up.
He spent 25% of this amount, or 0.25c, on the printer.
To progress further, we have to know how much the printer cost.
Supposing that the printer cost $100 (which we do not know as a fact), this would be equal to 0.25c.
Thus, his savings originally amounted to c = $100/0.25 = $400.
