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)
Answer:
17x and 3x
Step-by-step explanation:
like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.
Answer:
5%
Step-by-step explanation:
Look at the values from high school athletes (the first row of numbers) to the values of college student athletes (the second row). Since we are only looking for male percentages, ignore the women's basketball
Take any of the college values, and divide it by the high school values. After this, multiply by 100 to get a percentage
Example, 56500 ÷ 983600 = 0.05
0.05 * 100 = 5%
You will get 5% for all males sports in this table
Answer:
the Associative Property
Step-by-step explanation:
Notice that the ORDER doesn't change -- a, b, c on both sides. But the GROUPING changes.
Example:
3 + (4 + 5) = (3 + 4) + 5
3 + 9 = 7 + 5
12 = 12
Subtraction does NOT behave this way!
8 - (7 - 1) = 8 - 6 = 2
(8 - 7) - 1 = 1 - 1 = 0
It matters who you associate with! :-)
