Hello can you please help me posted picture of question
1 answer:
This is a problem of permutation. In mathematics, the permutation relates to the fact of arranging all the member of a set into order. So, the k permutations of n are the different ordered arrangements of a k element subset of a n set. In the problem above k = 9 are the elements which are all the numerals available. On the other hand, n set is equal to 4. So, the formula of such k-permutations of n is given by:
Solving for k = 9 and n = 4:
Solving for k = 9 and n = 4:
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As the exercise says, the triangles are similar. So, we can set up proportions between correspondent sides.
In order to solve for x we can set up the proportion between the horizontal and vertical sides:
Solving this proportion for x implies
Now you can solve for m and p using the pythagorean theorem, because both triangles are right:
Then, we know that the hypothenuse of the big triangle is m+p, so we have
which implies