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.
The area of a rectangle is given by:
A = (w) * (l)
Where,
w: width
l: long
Substituting values we have:
(54x ^ 9y ^ 8) = (w) * (6x ^ 3y ^ 4)
Clearing w we have:
w = (54x ^ 9y ^ 8) / (6x ^ 3y ^ 4)
Rewriting:
w = (9 * x ^ 6y ^ 4)
Answer:
the length of the rectangle is:
w = (9 * x ^ 6y ^ 4)
So h is 3x
b is x
3x plus x equal 972
4x = 972
243 is base
243 times 3 is 729
Answer:
4c + 4c + 16c + 90 = 360
Add the like terms
24c + 90 = 360
Subtract 90 when taking it to the other side of the equal
24c = 270
Divide 270 by 24 to get ur answer.
c = 11.25
Answer:
Value of the car is decreasing by 13.9% each year.
Step-by-step explanation:
This equation tells us V(t) is the value of the car after a certain time in years, $21,000 is the initial value of the car. What we need to focus on is on the 0.861 part of this equation. This means that the price of the car is worth 0.861 or 86.1% of what it was worth the year prior, this means that the price of the car is decreasing over time. By how much is it decreasing? Well if we consider 1 to mean 100% (since 100 / 100 =1) then we have 100%-86.1%=13.9%. This means that the value of the car is decreasing 13.9% each year.
