Check the picture below.
now, let's notice the larger "yellow" semicircle, it has a gap, the gap on the right is of a semicircle with a diameter of 10, BUT it also has a descender on the left, a part that's hanging out, that part is also a semicircle.
so if we use the descending semicircle to fill up the gap on the right, we'll end up with a filled up larger semicircle, whose diameter is 20, and whose radius is 10 cm.
![\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=10 \end{cases}\implies A=\pi 10^2\implies A=100\pi \\\\\\ \stackrel{\textit{half of that for a semicircle}}{A=\cfrac{100\pi }{2}}\implies A=50\pi \implies \stackrel{\pi =3.142}{A=157.1}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20circle%7D%5C%5C%5C%5C%20A%3D%5Cpi%20r%5E2~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D10%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Cpi%2010%5E2%5Cimplies%20A%3D100%5Cpi%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bhalf%20of%20that%20for%20a%20semicircle%7D%7D%7BA%3D%5Ccfrac%7B100%5Cpi%20%7D%7B2%7D%7D%5Cimplies%20A%3D50%5Cpi%20%5Cimplies%20%5Cstackrel%7B%5Cpi%20%3D3.142%7D%7BA%3D157.1%7D)
Answer:
x = - 4
Step-by-step explanation:
Given
8x - 3 = 5(2x + 1) ← distribute
8x - 3 = 10x + 5 ( subtract 10x from both sides )
- 2x - 3 = 5 ( add 3 to both sides )
- 2x = 8 ( divide both sides by - 2 )
x = - 4
Y=-2x+7 That is the equation written in y=mx+b formula
Answer:
23 and 14
Step-by-step explanation:
The sum of x and y is 37. In other words, x plus y equals 37 and can be written as equation A:
x + y = 37
The difference between x and y is 9. In other words, x minus y equals 9 and can be written as equation B:
x - y = 9
Now solve equation B for x to get the revised equation B:
x - y = 9
x = 9 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 37
9 + y + y = 37
9 + 2y = 37
2y = 28
y = 14
Now we know y is 14. Which means that we can substitute y for 14 in equation A and solve for x:
x + y = 37
x + 14 = 37
X = 23
Summary: The sum of two numbers is 37 and their difference is 9. What are the two numbers? Answer: 23 and 14 as proven here:
Sum: 23 + 14 = 37
Difference: 23 - 14 = 9
Step 1.) Set up the equation
28 %
---- = ------
40 100
Step 2.) Multiply the cross products
2800 = 40x
-------- ------
40 40
70% = x
