For this case we have the following diagonals:
AE = 40
ST = x + 5
The intersection of the diagonals occurs when:
AE = ST
Therefore, matching we have:
40 = x + 5
Clearing x we have:
x = 40-5
x = 35
Answer:
The value of x is:
x = 35
42% of 100 is 42 so 42% of is half of the first answer, therefore the answer is 21.
There are 80 questions
if 20%=16 Q
then 100÷20=5
therefore 5×16=80 questions on the test
Answer:
![REF= \left[\begin{array}{ccc}5&-1&1\\0&\frac{-7}{5} &\frac{-18}{5}\end{array}\right]](https://tex.z-dn.net/?f=REF%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%26%5Cfrac%7B-7%7D%7B5%7D%20%26%5Cfrac%7B-18%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D)
![RREF=\left[\begin{array}{ccc}1&0&\frac{5}{7} \\0&1&\frac{18}{7}\end{array}\right]](https://tex.z-dn.net/?f=RREF%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26%5Cfrac%7B5%7D%7B7%7D%20%5C%5C0%261%26%5Cfrac%7B18%7D%7B7%7D%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The augmented matrix of the system is: ![\left[\begin{array}{ccc}5&-1&1\\3&-2&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C3%26-2%26-3%5Cend%7Barray%7D%5Cright%5D)
First we find the stepped form of A (REF):
1. We subtract 3/5 from row 1 to row 2 (R2-
R1) and get the matrix
![\left[\begin{array}{ccc}5&-1&1\\0&\frac{-7}{5} &\frac{-18}{5}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%261%5C%5C0%26%5Cfrac%7B-7%7D%7B5%7D%20%26%5Cfrac%7B-18%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D)
Note that this matrix is in echelon form.
Now we find the reduced row echelon form of the augmented matrix (RREF)
2. From the previous matrix, we multiply the first row by 1/5 and the second row by -5/7 and obtain the matrix:
![\left[\begin{array}{ccc}1&\frac{-1}{5} &\frac{1}{5} \\0&1&\frac{18}{7}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cfrac%7B-1%7D%7B5%7D%20%26%5Cfrac%7B1%7D%7B5%7D%20%5C%5C0%261%26%5Cfrac%7B18%7D%7B7%7D%5Cend%7Barray%7D%5Cright%5D)
3. From the previous matrix, to row 1 we add 1/5 of row 2 (R1 +
R2) and we obtain the matrix
![\left[\begin{array}{ccc}1&0&\frac{5}{7} \\0&1&\frac{18}{7}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26%5Cfrac%7B5%7D%7B7%7D%20%5C%5C0%261%26%5Cfrac%7B18%7D%7B7%7D%5Cend%7Barray%7D%5Cright%5D)
which is the reduced row echelon form of the augmented matrix.