(1)
we are given
U is the midpoint of RS
and we have
so, we can use formula
we can plug values
............Answer
(2)
V is the midpoint of ST
so, we get
now, we can plug values
divide both sides by 2
.........Answer
(3)
now, we can find y
W is the midpoint of TR
so, we get
we can plug value
divide both sides by 3
(4)
we can see that
triangles URW and RST are similar
so, their sides ratios must be equal
so, we get
we can plug values
...........Answer
(5)
we can see that
triangles SUV and RST are similar
so, their sides ratios must be equal
so, we get
now, we can plug values
.............Answer
1. First, you must apply the formula
for calculate the sum of the interior angles of a regular polygon, which is
shown below:
(n-2) × 180°
"n" is the number of sides of the polygon (n=5).
2. Then, the sum of the interior angles of the pentagon, is:
(5-2)x180°=540°
3. The problem says that the measure of each of the other interior angles is equal to the sum of the measures of the two acute angles and now you know that the sum of all the angles is 540°, then, you have:
α+α+2α+2α+2α=540°
8α=540°
α=540°/8
α=67.5°
4. Finally, the larger angle is:
2α=2(67.5°)=135°
5. Therefore, the answer is: 135°
The function of the trapezoid area is:
A(x)=(B+b)*h/2
Where B and b are the bases and h is the height.
With the given data: h=10 B and b =7 and x (it may vary which one is bigger)
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So that function becomes:
A(x)=(7+x)*10/2
A(x)=(7+x)*5
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So if you want the inverse function, you have to operate to find x:
A(x)/5=7+x
A(x)/5-7=x
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So the new function is:
x(A)=A/5-7
The mixed number is 4 5/12.
