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:
10, 11 , 16, 18 &19
Step-by-step explanation:
9514 1404 393
Answer:
A = 2000(1 +1)^(t/9)
$64,000
Step-by-step explanation:
The growth rate is 100% in 9 years, so the equation can be written ...
A = 2000(1 +1.00)^(t/9)
The amount in 45 years is ...
A = 2000(2^5) = 2000×32 = 64,000 . . . dollars
Answer:
Yes
Step-by-step explanation:
4 dozen cookies is 4*12 = 48.. Each cookies has 3 cookies. This requires 3*48 = 144. She has 4 jars of 40 each or 4*40 =160. So she has enough.
Lets say gallon is G
and the bin is B
X is the amount needed to fill the bin
1/2G +x = 2/3B
so if we cut 1/2 G in half it gives you 1/3 and that will fill the whole bin so
1/2G + 1/4G =B
so the answer is
3/4 of a gallon
