Basically, you have two circles. You are asked to take circle 1 and "move it" so that it is on top of circle 2. This process of moving is called a translation and can be thought of as sliding. You do this by ensuring that the two have the same center. So, starting at (-4,5) how do you have to move to end up at (2,1)?
To do this we need to move right 6 as the x-coordinate goes from -4 to 2. We also need to move down 4 as the y-coordinate goes from 5 to 1. So we add 6 to the x-coordinate and subtract 4 from the y-coordinate. The transformation rule is (x+6, y-4).
Once you do this the circles have the same center. Next you wish to dilate circle 1 so it ends up being the same size at circle 2. That means you stretch it out in such a way that it keeps its shape. Circle 1 has a radius of 2 centimeters and circle 2 has a radius of 6 centimeters. That is 3x bigger. So we dilate by a factor of 3.
Translations and dilations (along with reflections and rotations) belong to a group known as transformations.
You use lots and lots of math.
Answer:
8, 16, 64
Step-by-step explanation:
8 = 2^3 . . . a perfect cube
16 = 4^2 . . . a perfect square
32 = 2^5 . . . neither a cube nor a square
64 = 2^6 = 4^3 = 8^2 . . . both a perfect cube and a perfect square
128 = 2^7 . . . neither a cube nor a square
Answer:
...........the answer is 7?!
