Answer:
1449/2691
Step-by-step explanation:
We must start from the fraction that is 7/13. Now, we know that it was simplified, with trial and error we can reach the result.
First, let's multiply both by 200:
7 * 200 = 1400
13 * 200 = 2600
1400 + 2600 = 4000
It means that we are missing 140, to reach the objective, that is, we are close, let's try 205 now:
7 * 205 = 1435
13 * 205 = 2665
1435 + 2665 = 4100
We get even closer, only 40 missing, let's try 207 below:
7 * 205 = 1449
13 * 205 = 2691
1449 + 2691 = 4140
We managed to get to the corresponding numbers, therefore the original fraction was 1449/2691
Answer:
The number 50 is a composite number because 50 can be divided by 1, by itself and at least by 2 and 5. So, it is possible to draw its prime tree. The prime factorization of 50 = 2•52.
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If cos B= 0.8926 ==> means arcos(0.8926) ===> B=26.7 or 26 dedree
Square both sides:
h^2 = 2t - 3
2t = h^2 + 3
t = (h^2 + 3)/2
The coefficient matrix is
![\begin{bmatrix}-1&-1&2\\3&2&-1\\4&4&-8\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D-1%26-1%262%5C%5C3%262%26-1%5C%5C4%264%26-8%5Cend%7Bbmatrix%7D)
Notice that the last row is -4 times the first row, so that the rows of the matrix are not independent. This means the determinant would be 0.
Just to confirm, we can compute the determinant via a Laplace expansion along the first row:
![\begin{vmatrix}-1&-1&2\\3&2&-1\\4&4&-8\end{vmatrix}=-\begin{vmatrix}2&-1\\4&-8\end{vmatrix}+\begin{vmatrix}3&-1\\4&-8\end{vmatrix}+2\begin{vmatrix}3&2\\4&4\end{vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bvmatrix%7D-1%26-1%262%5C%5C3%262%26-1%5C%5C4%264%26-8%5Cend%7Bvmatrix%7D%3D-%5Cbegin%7Bvmatrix%7D2%26-1%5C%5C4%26-8%5Cend%7Bvmatrix%7D%2B%5Cbegin%7Bvmatrix%7D3%26-1%5C%5C4%26-8%5Cend%7Bvmatrix%7D%2B2%5Cbegin%7Bvmatrix%7D3%262%5C%5C4%264%5Cend%7Bvmatrix%7D)
![=-(-16+4)+(-24+4)+2(12-8)=12-20+8=0](https://tex.z-dn.net/?f=%3D-%28-16%2B4%29%2B%28-24%2B4%29%2B2%2812-8%29%3D12-20%2B8%3D0)