What is the scale factor of triangle ABC to triangle DEF?

Mathematics

1 answer:

8_murik_8 [283]3 years ago

5 0

Answer:

Second option, scale factor is 2.5

Step-by-step explanation:

We see that ∠B ≅ ∠E and ∠C ≅ ∠F, therefore, ΔABC ~ ΔDEF by the AA Similarity for Triangles Theorem which states that if two pairs of corresponding angles are congruent in two triangles, then those two triangles are similar. To find the scale factor, all we have to do is DF / AC = 5/2 or 2.5.

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suppose we want to choose 5 letters, without replacement, from 13 distinct letters. (a) how many ways can this be done, if the o

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A. The number of possible ways can this be done, if the order of the choices is not taken into consideration is 1, 287 ways

B. The number of possible ways can this be done, if the order of the choices is taken into consideration is 154,440 ways

<h3>What is meant by permutation and combination?</h3>

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.

A. We want to select 5 objects from a total 13, without considering the order in which they are chosen.

The correct way to do this exists by utilizing the combination formula since order exists not considered;

Therefore, we have ; 13 C 5 read as 13 combination 5;

Let the equation of combination be n C r = n!/(n-r)!r!

substituting the values in the above equation, we get

13!/(13-8)!8! = 13!/5!8! = 1,287 ways

B. By considering order, we shall be using the permutation formula;

Let the equation of permutation be n P r = n!/(n-r)!

substituting the values in the above equation, we get

13 P 5 = 13!/(13-5)!

= 13!/(13-5)! = 13!/8! = 154,440 ways

To learn more about permutation and combination refer to: