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.
3x - 4 + x^2 - 1 + 2x^2 - 15
3x^2 + 3x - 20
I wasn't sure if you wanted me to solve for x, but I did anyways.
x ≈ 1.86, or -2.86
A is the answer because its right according to the chart
Answer:
It will take 3.2 hours for 8 inches of snow to fall.
Step-by-step explanation:
You can solve this be going "backwards".
You have 2.5 inches of snow falling per hour for x hours until you get 8 inches of snow, which can be represented like this:
2.5x=8 From here you being to solve by isolating x on one side of the equation. You would divide both sides by 2.5 to do this
2.5x=8
/2.5 /2.5
8 divided by 2.5 is 3.2 and you then get
x=3.2
It takes 3.2 hours for 8 inches of snow to fall
Answer:
(300 + 50x)/(2 + x)
Step-by-step explanation:
Let the cost of teachers' edition books be t
Let the cost of students' edition books be s
So t = 150; s = 50
Then the total cost of 2 teachers' editions and x students' editions is 2t + sx = 2 × 150 + 50x = 300 + 50x.
The total number of books is 2 + x.
So the average cost per book is (300 + 50x)/(2 + x)
