Eleonore wants to prove that if a line divides two sides in a triangle proportionally, then it is parallel to the third side.
2 answers:
Please find image attached
Answer and explanation:
If (from the image attached) DE is a line segment that divides the sides AB and AC proportionally in ΔABC then we can prove that line segment DE is parallel to BC using the parallel transversal theorem. Based the parallel transversal theorem, the triangles ABC and ADE are similar therefore angles are congruent and line DE must be parallel to line BC
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Answer:
<em>(a) 8,204,716,800</em>
<em>(b) 5,985</em>
Step-by-step explanation:
<u>Combinations and Permutations</u>
Combinatorics is the part of the discrete mathematics that studies the enumeration of groups or sorting of a determined number of elements. The concept of combinations is tied to the different forms to group elements where the order of their arrangements is not important or does not differentiate from the very same set of elements picked in a different order.
The concept of combinations is tied to the differents forms to group elements where the order of their arrangements is not important or does not differentiate from the very same set of elements picked in different order.
On the other hand, permutations or variations are sets selected in a specific order and another set with the same element but in different order is considered a different set.
If we have n elements available to pick from in sets of m elements each, there can be C(n,m) different combinations, and it's given by
Similarly the number of permutations is given by
(a) I have n=21 songs to pick from and I want to choose m=8 of them where the order matters, so it's a permutation:
I can make more than 8 billion different setlists
(b) To choose m=4 songs from n=21 songs where the order does not matter, we compute the combination
I can make almost 6,000 sets of 4 songs