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Answer:
Ratio of circumferences: 
Ratio of radii:
Ratio of areas: 
Step-by-step explanation:
Hi there!
We are given:
- The circumference of Circle K is 
- The circumference of Circle L is 
Therefore, the ratio of their circumferences would be:
⇒ when simplified
The formula for circumference is 
, where <em>r</em> is the radius. To find the ratio of the circles' radii, we must identify their radii through their given circumferences.
If the circumference of Circle K is , or 
, then its radius is 
.
If the circumference of Circle L is , then its radius is 
, which is 2.
Therefore the ratio their radii would be:
⇒ 
⇒ when simplified
The formula for area is:
First, let's find the area of Circle K:
Now, let's find the area of Circle L:
Therefore, the ratio of their areas would be:
⇒ 
⇒ 
⇒ when simplified
I hope this helps!
Problem 4
a)
MR = AG is a true statement because MARG is an isosceles trapezoid. The diagonals of any isosceles trapezoid are always the same length.
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b)
MA = GR is false. Parallel sides in a trapezoid are never congruent (otherwise you'll have a parallelogram).
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c)
MR and AG do NOT bisect each other. The diagonals bisect each other only if you had a parallelogram.
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Problem 5
a)
LC = AJ (nonparallel sides of isosceles trapezoid are always the same length)
x^2 = 25
x = sqrt(25)
<h3>x = 5</h3>
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b)
LU = 25
UC = 25 because point U cuts LC in half
LC = LU+UC = 25+25 = 50
AJ = LC = 50 (nonparallel sides of isosceles trapezoid are always the same length)
AS = (1/2)*AJ
AS = (1/2)*50
<h3>AS = 25</h3>
-------------------------
c)
angle LCA = 71
angle CAJ = 71 (base angles of isosceles trapezoid are always congruent)
(angleAJL)+(angleCAJ) = 180
(angleAJL)+(71) = 180
angle AJL = 180-71
<h3>angle AJL = 109 </h3>
Answer: X = 8.67
Step-by-step explanation:
