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:
(x,y,z)=(5,1,-2) or (5,-2,1) or (1,5,-2) or (1,-2,5) or (-2,5,1) or (-2,1,5)
Step-by-step explanation:
700070.07 = 700000 + 70 + 0.07
700000 = 7*10^5
70 =7*10^1
0.07=7*10^-2
Answer: C. Equal to
Step-by-step explanation:
The standard deviation is written as:
Sx = √( ∑(xₙ - x)^2/(n-1))
Where xₙ are the values of the data set, n is the number of data points and x is the mean of the data set.
Now, if we add a constant c to all the terms in our data set we will have:
(i will use the ' to denote the transformed data)
xₙ' are now xₙ + c.
And the new mean will be:
x' = ( (x₁ + c) + (x₂ + c) + .... + (xₙ + c))/n = (c*n + (x₁ + x₂ + ..))/n = c + (x₁ + x₂ +...)/n
x' = c + x
Then the new standard deviation will be:
Sx' =√( ∑(xₙ' - x')^2/(n-1))
Sx' = √( ∑((xₙ+c) - (x +c))^2/(n-1)) = √( ∑(xₙ - x)^2/(n-1)) = Sx
So the standard deviation does not change.
The correct option is C.
Yes Manolo is correct because if g = 6 g × g would equal 36, since g = 6
