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Based on the properties of similar triangles, the two true statements are:
- ΔAXC ≅ ΔCXB.
- ΔACB ≅ ΔAXC.
In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the properties of similar triangles, we have the following points:
- ∠A in ΔAXC matches ∠A in ΔABC and ∠C in ΔCXB.
- ∠C in ΔAXC matches ∠B in ΔABC and ∠B in ΔCXB.
- ∠X in ΔAXC matches ∠C in ΔABC and ∠X in ΔCXB.
In this scenario, we can can logically deduce that the two true statements are:
- ΔAXC is congruent to ΔCXB (ΔAXC ≅ ΔCXB).
- ΔACB is congruent to ΔAXC (ΔACB ≅ ΔAXC).
Read more on similar triangles here: brainly.com/question/7411945
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Answer:
a) This is a permutation, there are 210 ways to do it
b) This is a permutation with 6 possibilities
c) This is a combination with a total of 1081575 possibilities
Step-by-step explanation:
a) Here the order does matter bacause it is not the same that they go to France in the weak trip than they go there for 2 days, as a result, this scenario is a permutation.
You need to pick 3 countries from a total of 7, but the order matters, so the total amount of ways to do this is
b) Here each permutation of 123 will give you a possible (and a different one from the others) lock-combination, so this is again a permutation.
The total amount of ways we have to do the selectio of the lock-combination is the total amount of permutations of a set of 3 elements, in other words, it is 3! = 6.
c) If you only cares about who advances to the finals, then the order doesnt matter here, you just want 8 people out of the 25 available. This is therefore a combination, and the total amount of possible cases are
.