Answer:
ab - b^2
Step-by-step explanation:
The area of the large rectangle is
A = l*w
=a*b
The area of the unshaded region is
A = b*b = b^2
The area of the shaded region is the area of the rectangle minus the area of the unshaded region
ab - b^2
Answer:
![A:B=-8n:-27n\\\\=8:27](https://tex.z-dn.net/?f=A%3AB%3D-8n%3A-27n%5C%5C%5C%5C%3D8%3A27)
Step-by-step explanation:
Let the A be the amount Alice initially has and B be Bob's initial amount.
#Alice receives $n from Bob:
![4(A+n)=B-n\ \ \ \ \ \ \ \ \ i](https://tex.z-dn.net/?f=4%28A%2Bn%29%3DB-n%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%5C%20i)
#Alice gives n to Bob:
![3(A-n)=B+n\ \ \ \ \ \ \ \ \ \ ii](https://tex.z-dn.net/?f=3%28A-n%29%3DB%2Bn%5C%20%5C%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%20%5C%20%5C%20%5C%20ii)
#We simultaneously solve the two expressions:
![4(A+n)=B-n\\\\3(A-n)=B+n\\\\=>from \ i\\4A+4n+n=B\\\\4A+5n=B\\\\\# substitute \ in \ ii\\\\3A-3n=4A+5n+n\\\\A=-8n\\\\B=4A+5n=4(-8n)+5n=-27n](https://tex.z-dn.net/?f=4%28A%2Bn%29%3DB-n%5C%5C%5C%5C3%28A-n%29%3DB%2Bn%5C%5C%5C%5C%3D%3Efrom%20%5C%20i%5C%5C4A%2B4n%2Bn%3DB%5C%5C%5C%5C4A%2B5n%3DB%5C%5C%5C%5C%5C%23%20substitute%20%5C%20in%20%5C%20ii%5C%5C%5C%5C3A-3n%3D4A%2B5n%2Bn%5C%5C%5C%5CA%3D-8n%5C%5C%5C%5CB%3D4A%2B5n%3D4%28-8n%29%2B5n%3D-27n)
The initial amounts of Alice is -8n and Bob's is -27n
#We find the ratio of Alice:Bob:-
![A:B=-8n:-27n\\\\=8:27](https://tex.z-dn.net/?f=A%3AB%3D-8n%3A-27n%5C%5C%5C%5C%3D8%3A27)
Hence the ration of Alice to Bob is 8:27
Answer: 4,1 read carefully
Step-by-step explanation:
The answer is C. Here you go.