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.
The percent change is 75%
Here's the math:
First, we need to find out how many more 63 is than 36. We can do that by subtracting.
63 - 36 = 27
We could write an expression like this: 36 + 27 = 63.
The reason we wrote it like that was because we started off with 36, so writing it like that, we already know that the percent change will be less than 100% since 36 is 100%.
Now we need to find what percent of 36, 27 is since we started off with 3. To do that we divide 36 ÷ 27 and we get .75. Now that we have a decimal, to change it to a percent, we just multiply my 100 and we get 75. So 27 is 75% of 36.
Since it is 75% of 36 and is added to 36 to get 63, 75% is our percent change!
Thank you for your question! I hope this helped! Have an amazing day! :D
Amanda could’ve ate 1/4 and Lauren could’ve ate 3/4. I hope this helps!
To represent 5 steps forward as an integer, you would write 5 or +5. Forward is a positive movement.
11 steps backward would be -11 because moving backwards would be the opposite of moving forward (+).
Answer:
y=x+2
Step-by-step explanation:
Since 1 up, 1 down, 1 left, and 1 right would all cancel out so you would still get y=x+2