\(a,A=\dfrac{x+1}{x-2}=\dfrac{x-2+3}{x-2}=1+\dfrac{3}{x-2}\)

Để A nguyên thì: 3 ⋮ x - 2

=> x - 2 ∈ Ư(3) = {1; -1; 3; -3} 

=> x ∈ {3; 1; 5; -1} 

\(b,B=\dfrac{2x-1}{x+5}=\dfrac{\left(2x+10\right)-11}{x+5}=\dfrac{2\left(x+5\right)-11}{x+5}=2-\dfrac{11}{x+5}\)

Để B nguyên thì 11 ⋮ x + 5

=> x + 5 ∈ Ư(11) = {1; -1; 11; -11}

=> x ∈ {-4; -6; 6; -16} 

\(c,C=\dfrac{10x-9}{2x-3}=\dfrac{\left(10x-15\right)+6}{2x-3}=\dfrac{5\left(2x-3\right)+6}{2x-3}=5+\dfrac{6}{2x-3}\)

Để C nguyên thì 6 ⋮ 2x - 3

=> 2x - 3 ∈ Ư(6) = {1; -1; 2; -2; 3; -3; 6; -6}

Mà: 2x - 3 luôn lẻ

=> 2x - 3 ∈ {1; -1; 3; -3}

=> 2x ∈ {4; 2; 6; 0}

=> x ∈ {2; 1; 3; 0} 

\(a,1,7-\dfrac{5}{9}+\dfrac{3}{10}\\ =\left(\dfrac{17}{10}+\dfrac{3}{10}\right)-\dfrac{5}{9}\\ =2-\dfrac{5}{9}\\ =\dfrac{13}{9}\\ b,-5,2+\left(-\dfrac{2}{9}\right)-\left(-4,2\right)\\ =\left(-5,2+4,2\right)+\dfrac{-2}{9}\\ =-1+\dfrac{-2}{9}\\ =-\dfrac{11}{9}\\ c,2,53-\dfrac{4}{11}+2,47-\dfrac{7}{11}\\ =\left(2,53+2,47\right)+\left(\dfrac{-4}{11}+\dfrac{-7}{11}\right)\\ =5-\dfrac{11}{11}\\ =5-1\\ =4\\ d,-\dfrac{-19}{13}+0,7+\dfrac{7}{13}-\dfrac{17}{10}\\ =\left(\dfrac{7}{10}-\dfrac{17}{10}\right)+\left(\dfrac{19}{13}+\dfrac{7}{13}\right)\\ =-\dfrac{10}{10}+\dfrac{13}{13}\\ =-1+1\\ =0\)

\(e,-\left(-3,498\right)+\dfrac{5}{13}+1,502-\dfrac{18}{13}\\ =3,498+\left(\dfrac{5}{13}-\dfrac{18}{13}\right)+1,502\\ =\left(3,498+1,502\right)+\dfrac{-13}{13}\\ =5-1\\ =4\\ f,4,2+\left(\dfrac{-9}{15}\right)-\left(-5,8\right)\\ =\left(4,2+5,8\right)+\left(\dfrac{-3}{5}\right)\\ =10+\left(\dfrac{-3}{5}\right)\\ =\dfrac{47}{5}\\ g,-\dfrac{5}{9}-0,385+\left(\dfrac{-4}{9}\right)+1,385\\ =\left(-0,385+1,385\right)+\left(\dfrac{-5}{9}+\dfrac{-4}{9}\right)\\ =1-1\\ =0\\ h,3,75-\dfrac{5}{9}+\left(\dfrac{-3}{4}\right)\\ =\left(3,75-0,75\right)-\dfrac{5}{9}\\ =3-\dfrac{5}{9}\\ =\dfrac{22}{9}\)

Ta có: \(\widehat{xOm}=\dfrac{\widehat{xOb}}{2}\)

\(\widehat{yOn}=\dfrac{\widehat{yOa}}{2}\)

mà \(\widehat{xOb}=\widehat{yOa}\)(hai góc đối đỉnh)

nên \(\widehat{xOm}=\widehat{yOn}\)

mà \(\widehat{xOm}+\widehat{mOy}=180^0\)(hai góc kề bù)

nên \(\widehat{yOm}+\widehat{yOn}=180^0\)

=>Om và On là hai tia đối nhau

a: Ta có: Ox\(\perp\)Oy

Ox\(\perp\)Az

Do đó: Oy//Az

b: Om không song song với Am nha bạn

1.More expensive

2.The tallest

3.The biggest

4.Best

5.Intelligent as

6.as beautiful

7.(chưa rõ đề bài)

8.the worse

1. more expensive

2. the tallest 

3. the biggest

4. the best 

5. intelligent as 

6. as beautiful 

7. không có dữ liệu 

8. the worst

\(BC=\sqrt{AB^2+AC^2}=\sqrt{3^2+4^2}=5\left(cm\right)\)

\(=>S_{xq}=\left(AB+AC+BC\right)\cdot CF=\left(3+4+5\right)\cdot7=84\left(cm^2\right)\) 

Diện tích hai mặt đáy là: \(2S_đ=2\cdot\dfrac{1}{2}\cdot AB\cdot AC=2\cdot\dfrac{1}{2}\cdot3\cdot4=12\left(cm^2\right)\)

Diện tích toàn phần: \(S_{tp}=2S_đ+S_{xq}=84+12=96\left(cm^2\right)\) 

Thể tích của hình lăng trụ là:

\(V=CF\cdot S_đ=7\cdot\dfrac{12}{2}=42\left(cm^3\right)\)

ΔABC vuông tại A

=>\(BC^2=AB^2+AC^2\)

=>\(BC=\sqrt{3^2+4^2}=5\left(cm\right)\)

Chu vi đáy là 3+4+5=12(cm)

Diện tích xung quanh là:

\(S_{xq}=12\cdot7=84\left(cm^2\right)\)

Diện tích đáy là: \(S_{đáy}=\dfrac{1}{2}\cdot3\cdot4=6\left(cm^2\right)\)

Diện tích toàn phần là: \(S_{tp}=S_{xq}+2\cdot S_{đáy}=84+2\cdot6=96\left(cm^2\right)\)

Thể tích là: \(V=S_{đáy}\cdot7=6\cdot7=42\left(cm^3\right)\)

3: Ta có: Om là phân giác của góc xOz

=>\(\widehat{mOz}=\dfrac{\widehat{xOz}}{2}\)

On là phân giác của góc yOz

=>\(\widehat{nOz}=\dfrac{\widehat{yOz}}{2}\)

\(\widehat{mOn}=\widehat{mOz}+\widehat{nOz}=\dfrac{1}{2}\left(\widehat{xOz}+\widehat{yOz}\right)\)

\(=\dfrac{1}{2}\cdot180^0=90^0\)

4: Om là phân giác của góc xOz

=>\(\widehat{zOm}=\dfrac{\widehat{xOz}}{2}\)

On là phân giác của góc yOz

=>\(\widehat{zOn}=\dfrac{\widehat{yOz}}{2}\)

\(\widehat{mOn}=\widehat{mOz}+\widehat{nOz}=\dfrac{1}{2}\left(\widehat{xOz}+\widehat{yOz}\right)\)

\(=\dfrac{1}{2}\cdot180^0=90^0\)

`(2x+3)^2 =` \(\dfrac{9}{121}\)

`=> (2x + 3)^2 =` \(\left(\dfrac{3}{11}\right)^2\)

=> \(\left[{}\begin{matrix}2x+3=\dfrac{3}{11}\\2x+3=-\dfrac{3}{11}\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}2x=\dfrac{3}{11}-3\\2x=-\dfrac{3}{11}-3\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}2x=\dfrac{3}{11}-\dfrac{33}{11}\\2x=-\dfrac{3}{11}-\dfrac{33}{11}\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}2x=-\dfrac{30}{11}\\2x=-\dfrac{36}{11}\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=-\dfrac{15}{11}\\x=-\dfrac{18}{11}\end{matrix}\right.\)

Vậy ...

\(\left(2x+3\right)^2=\dfrac{9}{121}\)

\(\left(2x+3\right)^2=\left(\dfrac{3}{11}\right)^2\)

\(2x+3=\dfrac{2}{11}\) hoặc \(2x+3=-\dfrac{2}{11}\)

\(2x=-\dfrac{31}{11}\) hoặc \(2x=-\dfrac{35}{11}\)

\(x=-\dfrac{31}{22}\) hoặc \(x=-\dfrac{35}{22}\)