40. A triangle is placed inside of a circle of radius 3x. The base of the
1 answer:
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Answer:
Given: In triangle ABC and triangle DBE where DE is parallel to AC.
In ΔABC and ΔDBE
[Given]
As we know, a line that cuts across two or more parallel lines. In the given figure, the line AB is a transversal.
Line segment AB is transversal that intersects two parallel lines. [Conclusion from statement 1.]
Corresponding angles theorem: two parallel lines are cut by a transversal, then the corresponding angles are congruent.
then;
and
Reflexive property of equality states that if angles in geometric figures can be congruent to themselves.
by Reflexive property of equality:
By AAA (Angle Angle Angle) similarity postulates states that all three pairs of corresponding angles are the same then, the triangles are similar
therefore, by AAA similarity postulates theorem
Similar triangles are triangles with equal corresponding angles and proportionate side.
then, we have;
[By definition of similar triangles]
therefore, the missing statement and the reasons are
Statement Reason
3. Corresponding angles theorem
and
5. AAA similarity postulates
6. BD over BA Definition of similar triangle
Answer:
<h2>There are 3,921,225 ways to select the winners.</h2>Step-by-step explanation:
This problem is about combinations with no repetitions, because the same person can't win four times. It's a combinaction because the order of winning doesn't really matter.
Combinations without repetitions are defined as
Where and
.
Replacing values, we have
Therefore, there are 3,921,225 ways to select the winners.
Additionally, as you can imagine, the probability of winning is extremely low, it would be 3,921,225 to 1.