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.
Answer:
nope
Step-by-step explanation:
<h3><u>The length is equal to 25.</u></h3><h3><u>The width is equal to 15.</u></h3>
l = 2w - 5
2l + 2w = 80
We have a value for l, so we can plug it into the second equation to solve for w.
2(2w - 5) + 2w = 80
Distributive property.
4w - 10 + 2w = 80
Combine like terms.
6w - 10 = 80
Add 10 to both sides.
6w = 90
Divide both sides by 6.
w = 15
Now that we have a value for w, we can plug it into the original equation to solve for l.
l = 2(15) - 5
l = 30 - 5
l = 25
Answer:
{2, 4}.
Step-by-step explanation:
A = {1, 2, 3, 4, 5} and B = {2, 4}.
A ∩ B?
This means intersection or what is in common
A ∩ B = {2, 4}.
