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:
C = 75.
Step-by-step explanation:
Set up our eq:
600 x
___ = ___
80 100
Cross multiply:
6 x 10 = 60 (add two zero's) = 6000
now, 80 * x. 80x
Now we divide:
6000
_____
80
C = 75
Answer:
The total amount without tax is $141.57
Step-by-step explanation:
Since the coupon is 10% off, they would only have to pay 90% of what they would before (this is before tax). To find out the total after the coupon you would find 90% of 157.30. (This is the longer but better explainable/showable way)
157.30 / 100 = 1.573 (this is 1%)
1.573 * 90 = 141.57
Therefore the answer is $141.57
