Answer:
Step-by-step explanation:
The attached diagram shows the given triangle labelled as triangle ABC. Line DE is parallel to line AB. It means that triangle DEC is similar to triangle ABC. Comparing the sides,
DC/DE = AC/AB
DC = 5
DE = 8
AC = 5 + x
AB = 10
Therefore,
5/8 = (5+x)/10
Cross multiplying
5 × 10 = 8(5 + x)
50 = 40 + 8x
8x = 50-40 = 10
x = 10/8 = 1.25
Similarly,
CE/DE = CB/AB
CE = 7
CB = 7 + y
DE = 8
AB = 10
Therefore
7/8 = (7+y)/10
Cross multiplying
7 × 10 = 8(7 + y)
70 = 56 + 8y
8y = 70 - 56 = 14
y = 14/8 = 1.75
Check the picture below.
so if y = 2, then 2y = 4, thus
![\textit{area of a segment of a circle}\\\\A=\cfrac{r^2}{2}\left(\cfrac{\pi \theta }{180}~~ - ~~sin(\theta ) \right)~~\begin{cases}r=radius\\\theta =\stackrel{degrees}{angle}\\[-0.5em]\hrulefill\\r=4\\\theta =60\end{cases}\\\\\\A=\cfrac{4^2}{2}\left(\cfrac{\pi (60) }{180}~~ - ~~sin(60^o ) \right)\implies A=8\left( \cfrac{\pi }{3}~~ - ~~\cfrac{\sqrt{3}}{2} \right)\\\\\\A=\cfrac{8\pi }{3}~~ - ~~4\sqrt{3}\implies A\approx 1.45](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20segment%20of%20a%20circle%7D%5C%5C%5C%5CA%3D%5Ccfrac%7Br%5E2%7D%7B2%7D%5Cleft%28%5Ccfrac%7B%5Cpi%20%5Ctheta%20%7D%7B180%7D~~%20-%20~~sin%28%5Ctheta%20%29%20%20%5Cright%29~~%5Cbegin%7Bcases%7Dr%3Dradius%5C%5C%5Ctheta%20%3D%5Cstackrel%7Bdegrees%7D%7Bangle%7D%5C%5C%5B-0.5em%5D%5Chrulefill%5C%5Cr%3D4%5C%5C%5Ctheta%20%3D60%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5CA%3D%5Ccfrac%7B4%5E2%7D%7B2%7D%5Cleft%28%5Ccfrac%7B%5Cpi%20%2860%29%20%7D%7B180%7D~~%20-%20~~sin%2860%5Eo%20%29%20%20%5Cright%29%5Cimplies%20A%3D8%5Cleft%28%20%5Ccfrac%7B%5Cpi%20%7D%7B3%7D~~%20-%20~~%5Ccfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%5Cright%29%5C%5C%5C%5C%5C%5CA%3D%5Ccfrac%7B8%5Cpi%20%7D%7B3%7D~~%20-%20~~4%5Csqrt%7B3%7D%5Cimplies%20A%5Capprox%201.45)
Answer:
The answer is 4.
Step-by-step explanation:
Change 4 2/3 to 4 4/6 to match 11/6.
Add 4 4/6 and 11/6 and get 4 15/6.
Subtract 4 15/6 by 15/6 and get 4.
4 is the answer.
I hope this helps.
Have a nice day!
Answer:
thats easy j
Step-by-step explanation:
<u>Area of Banner is 4 sq.ft.</u>
<u>Step-by-step explanation:</u>
Class made 20 smaller rectangles
dimension of each rectangle = 3/5 ft × 1/3 ft
Area f banner = 20 * ( area of 1 rectangle)
⇒ 20 * ( 3/5 * 1/3 )
⇒ 20 * 0.2
⇒ 4 sq.ft
<u>Area of Banner is 4 sq.ft.</u>
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