We know that
<span>Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.
In this problem to prove circle 1 and circle 2 are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.
</span>we have that
<span>Circle 1 is centered at (4,3) and has a radius of 5 centimeters
</span><span> Circle 2 is centered at (6,-2) and has a radius of 15 centimeters
</span>
step 1
<span>Move the center of the circle 1 onto the center of the circle 2
</span>the transformation has the following rule
(x,y)--------> (x+2,y-5)
so
(4,3)------> (4+2,3-5)-----> (6,-2)
so
center circle 1 is now equal to center circle 2
<span>The circles are now concentric (they have the same center)
</span>
step 2
A dilation is needed to increase the size of circle 1<span> to coincide with circle 2
</span>
scale factor=radius circle 2/radius circle 1-----> 15/5----> 3
radius circle 1 will be=5*scale factor-----> 5*3-----> 15 cm
radius circle 1 is now equal to radius circle 2
A translation, followed by a dilation<span> will map one circle onto the other, thus proving that the circles are similar</span>
Answer:
The area of the window is of 840 square inches.
Step-by-step explanation:
To find the area of an trapezoid, we need to add the sum of the bases, multiply by the height, and then divide by 2.
Matematically:
![A = \frac{(b_{1} + b_{2})*h}{2}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B%28b_%7B1%7D%20%2B%20b_%7B2%7D%29%2Ah%7D%7B2%7D)
In which
and
are the bases and h is the height.
In this question:
![b_{1} = 30, b_{2} = 40, h = 24](https://tex.z-dn.net/?f=b_%7B1%7D%20%3D%2030%2C%20b_%7B2%7D%20%3D%2040%2C%20h%20%3D%2024)
All the measures in inches, so the area is in square inches.
![A = \frac{(30 + 40)*24}{2} = 840](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B%2830%20%2B%2040%29%2A24%7D%7B2%7D%20%3D%20840)
The area of the window is of 840 square inches.
Answer:
Step-by-step explanation:
Anthony-t
Charlie-t(3)-2
Answer:
x = 24, y = 21
Step-by-step explanation:
x + y = 45
x - y = 3
Add them together
2x = 48
x = 24
24 + y = 45
y = 21
Answer:
1.5, 3.4, 1.2
Step-by-step explanation: