a: \(\left\{{}\begin{matrix}2\left(x+y\right)+3\left(x-y\right)=4\\x+y+2\left(x-y\right)=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+2y+3x-3y=4\\x+y+2x-2y=5\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}5x-y=4\\3x-y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x-y-3x+y=4-5\\3x-y=5\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}2x=-1\\y=3x-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{2}\\y=3\cdot\dfrac{-1}{2}-5=-\dfrac{3}{2}-5=-\dfrac{13}{2}\end{matrix}\right.\)

b: \(\left\{{}\begin{matrix}\left(x+1\right)\left(y-1\right)=xy-1\\\left(x-3\right)\left(y+3\right)=xy-3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}xy-x+y-1=xy-1\\xy+3x-3y-9=xy-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x+y=0\\3x-3y=6\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x-y=0\\x-y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-y-x+y=0-2\\x-y=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}0y=-2\\x-y=0\end{matrix}\right.\Leftrightarrow\left(x;y\right)\in\varnothing\)

ΔABC=ΔDEF

=>\(\widehat{A}=\widehat{D}\)

=>\(\widehat{D}=55^0\)

ΔABC=ΔDEF

=>\(\widehat{B}=\widehat{E}\)

=>\(\widehat{B}=75^0\)

Xét ΔABC có \(\widehat{A}+\widehat{B}+\widehat{C}=180^0\)

=>\(\widehat{C}=180^0-55^0-75^0=50^0\)

=>\(\widehat{F}=\widehat{C}=50^0\)

1. protect

2. skillful

3. services

4. collected

5. community

6. development

7. voluntary

8. elderly

9. organization

10. donation

1 protect

2 skillful

3 services

4 collected

5 community

6 development

7 voluntary 

8 elderly

9 organization

10 donation

\(\dfrac{11}{3}+\left|x\right|=\dfrac{9}{4}\)

=>\(\left|x\right|=\dfrac{9}{4}-\dfrac{11}{3}=\dfrac{27}{12}-\dfrac{44}{12}=-\dfrac{17}{12}\)

mà \(\left|x\right|>=0\forall x\)

nên \(x\in\varnothing\)

66.2

3 hat => a hat

4 job => a job

5 OK

6 apple => an apple

7 party => a party

8 wonderful thing => a wonderful thing

9 island => an island

10 key => a key

11 OK

12 good idea => a good idea

13 car => a car

14 cup => a cup

15 OK

16 umbrella => an umbrella

66.3

2 a piece of wood

3 a glass of water

4 a bar of chocolate

5 a cup of tea

6 a piece of paper

7 a bowl of soup

8 a loaf of bread

9 a jar of honey

66.2

3 a hat

4 a job

5 ok

6 an apple

7 a party

8  a wonderful thing

9 an island

10 a key

11 ok

12 a good idea

13 a car

14 a cup 

14 ok

16 an umbrella

\(\left(\dfrac{1}{2}\right)^{x+2}=16^{4-2x}\)

=>\(2^{-x-2}=2^{4\left(4-2x\right)}\)

=>-x-2=4*(4-2x)

=>-x-2=16-8x

=>-x+8x=16+2

=>7x=18

=>\(x=\dfrac{18}{7}\)

a: \(\dfrac{x}{y}+\dfrac{y}{x}>=2\cdot\sqrt{\dfrac{x}{y}\cdot\dfrac{y}{x}}=2\)

b: \(\dfrac{1}{x}+\dfrac{1}{y}>=\dfrac{4}{x+y}\)

=>\(\dfrac{x+y}{xy}>=\dfrac{4}{x+y}\)

=>\(\left(x+y\right)^2>=4xy\)

=>\(x^2+2xy+y^2-4xy>=0\)

=>\(x^2-2xy+y^2>=0\)

=>\(\left(x-y\right)^2>=0\)(luôn đúng)

Bài 2:

a) \(\dfrac{-7}{-13}=\dfrac{7}{13}\) là số hưu tỉ dương

b) \(\dfrac{2}{-17}=-\dfrac{2}{17}\) là số hưu tỉ âm

c) \(-\dfrac{-6}{5}=\dfrac{6}{5}\) là số hưu tỉ dương

Bài 3:

a) \(-2\dfrac{1}{4}=-\left(2+\dfrac{1}{4}\right)=-\dfrac{9}{4}\)

b) \(6\dfrac{2}{3}=6+\dfrac{2}{3}=\dfrac{20}{3}\)

c) \(-3\dfrac{1}{4}=-\left(3+\dfrac{1}{4}\right)=-\dfrac{13}{4}\)

a: \(x^2+y^2>=2xy\)

=>\(x^2-2xy+y^2>=0\)

=>\(\left(x-y\right)^2>=0\)(luôn đúng)

b: \(x^2+4xy>=-4y^2\)

=>\(x^2+4xy+4y^2>=0\)

=>\(\left(x+2y\right)^2>=0\)(luôn đúng)

c: \(2\left(x^2+y^2\right)>=\left(x+y\right)^2\)

=>\(2x^2+2y^2-x^2-2xy-y^2>=0\)

=>\(x^2-2xy+y^2>=0\)

=>\(\left(x-y\right)^2>=0\)(luôn đúng)

câu b nhé bạn

câu b