We know that<span>
<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.
we have that</span>
<span> Circle 1 is centered at (5,8) and has a
radius of 8 centimeters
Circle 2 is centered at (1,-2) and has a radius of 4 centimeters
</span>
step 1
<span>Move the center of the circle 1 onto the
center of the circle 2
the transformation has the following rule</span>
(x,y)--------> (x-4,y-10)
so
(5,8)------> (5-4,8-10)-----> (1,-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
<span>A dilation is needed to decrease the size of
circle 1 to coincide with circle 2
</span>
scale factor=radius circle 2/radius circle
1-----> 4/8----> 0.5
radius circle 1 will be=8*scale factor-----> 8*0.5-----> 4 cm
radius circle 1 is now equal
to radius circle 2
<span>A
translation, followed by a dilation will map one circle onto the other,
thus proving that the circles are similar
the answer is
</span></span>The circles are similar because you can translate Circle 1 using the transformation rule (x-4,y-10) and then dilate it using a scale factor of (0.5)
For the first question, find the mean, first quartile, minimum, maximum, and third quartile, and then graph on the x-axis (a number line). Then, create a line through the median, first, and third quartile. Lastly, connect the median, first and third quartile to make a box. Google images for more details.
Using the Fundamental Counting Theorem, it is found that:
The 2 people can arrange themselves in 40 ways.
<h3>What is the Fundamental Counting Theorem?</h3>
It is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
With one people in the aisle and one in the normal seats, the parameters are:
n1 = 4, n2 = 7
With both in the aisle, the parameters is:
n1 = 4, n2 = 3
Hence the number of ways is:
N = 4 x 7 + 4 x 3 = 28 + 12 = 40.
More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866
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Answer:
6
Step-by-step explanation:
4 = 24 / 6
They are the opposite of each other. Like if one function has the point (1,3) the inverse function with have the point (3,1)