1. Correct. The reflection happens over segment AB and then you translate 6 units to the right and 3 units up. This will move point A to D, B to F, C to E, to have the triangles line up perfectly.
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2. Problem 1 already confirmed the triangles are congruent based on how they line up perfectly. Another way to prove this is to either use the SAS (side angle side) or LL (leg leg) theorem. With SAS, we need a pair of congruent sides and a pair of angles, with the angles between the two sides. The horizontal and vertical sides can be easily measured. The angles between the two sides are 90 degree angles. Because we have right triangles, we can use LL which is really just a special case of SAS.
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3. Segment EF is 5 units. You can use the pythagorean theorem with a = 3 and b = 4 to solve a^2+b^2 = c^2 to get c = 5. Or you can use the fact that BC = 5 is given to us, so EF must also be 5 as well. This is because of the idea that if two triangles are congruent, then their corresponding pieces must be the same as well.
Real world example: imagine having 2 houses that are perfect clones of each other. If this is the case, then surely their front doors would be identical copies as well. In this analogy, a house is a triangle, while the front door is the segment.
Answer + Explanation:
The Monty Hall problem is a famous problem in conditional probability and reasoning using Bayes' theorem.
How to explain the probability?
In the problem, you are on a game show, being asked to choose between three doors. Behind each door, there is either a car or a goat.
You choose a door. The host, Monty Hall, picks one of the other doors, which he knows has a goat behind it, and opens it, showing you the goat.
You know, by the rules of the game, that Monty will always reveal a goat. Monty then asks whether you would like to switch your choice of door to the other remaining door.
In conclusion, the solution is that switching will let you win twice as often as sticking with the original choice.
4m-5
- 6m-7+2n
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-2m+2+2n
D. Multiply the top equation by 2
That way, 3y(2) - 6y = 6y - 6y = 0
hope this helps
