Bài 1: 

a: Xét ΔABI và ΔACI có

AB=AC

AI chung

BI=CI

Do đó: ΔABI=ΔACI

D

D

Câu 5:

\(\dfrac{x}{y}=a\Rightarrow\dfrac{x}{a}=\dfrac{y}{1}=\dfrac{x-y}{a-1}=\dfrac{x+y}{a+1}\)

\(\Rightarrow\dfrac{x+y}{x-y}=\dfrac{a+1}{a-1}\)

Câu 6:

\(9x=5y\Rightarrow\dfrac{x}{5}=\dfrac{y}{9}\)

\(\Rightarrow\dfrac{x}{5}=\dfrac{y}{9}=\dfrac{3x}{15}=\dfrac{2y}{18}=\dfrac{3x-2y}{15-18}=\dfrac{12}{-3}=-4\)

\(\Rightarrow\left\{{}\begin{matrix}x=\left(-4\right).5=-20\\y=\left(-4\right).9=-36\end{matrix}\right.\)

Câu 7:

\(\dfrac{x}{-5}=\dfrac{y}{7}=\dfrac{x+y}{-5+7}=\dfrac{-10}{2}=-5\)

\(\Rightarrow\left\{{}\begin{matrix}x=\left(-5\right).\left(-5\right)=25\\y=\left(-5\right).7=-35\end{matrix}\right.\)

Bài 1:

a) \(\dfrac{4}{5}-\dfrac{7}{6}+\dfrac{-6}{15}=\dfrac{24}{30}-\dfrac{35}{30}+\dfrac{-12}{30}=\dfrac{24-35+-12}{30}=\dfrac{-23}{30}\) 

b) \(\dfrac{-5}{9}.\dfrac{7}{13}+\dfrac{6}{13}.\dfrac{-5}{9}+3\dfrac{7}{9}\) 

\(=\dfrac{-5}{9}.\left(\dfrac{7}{13}+\dfrac{6}{13}\right)+\dfrac{34}{9}\) 

\(=\dfrac{-5}{9}.1+\dfrac{34}{9}\) 

\(=\dfrac{-5}{9}+\dfrac{34}{9}\) 

\(=\dfrac{29}{9}\) 

c) \(6\dfrac{3}{8}-\left(4\dfrac{3}{8}-\dfrac{1}{2}\right)=\dfrac{51}{8}-\dfrac{35}{8}+\dfrac{1}{2}=\left(\dfrac{51}{8}-\dfrac{35}{8}\right)+\dfrac{1}{2}=2+\dfrac{1}{2}=\dfrac{5}{2}\) 

d) \(2\dfrac{1}{3}.1,5-\left(\dfrac{11}{10}+50\%\right):\dfrac{4}{15}\) 

\(=\dfrac{7}{3}.1,5-\dfrac{8}{5}:\dfrac{4}{15}\) 

\(=\dfrac{7}{2}-6\) 

\(=\dfrac{-5}{2}=-2,5\) 

Bài 2:

a) \(\dfrac{3}{2}+x=\dfrac{-5}{3}\) 

           \(x=\dfrac{-5}{3}-\dfrac{3}{2}\) 

           \(x=\dfrac{-19}{6}\) 

b) \(5\dfrac{2}{3}-\left(\dfrac{3}{2}+x\right)=4\dfrac{1}{3}\) 

                   \(\dfrac{3}{2}+x=\dfrac{17}{3}-\dfrac{13}{3}\) 

                   \(\dfrac{3}{2}+x=\dfrac{4}{3}\) 

                          \(x=\dfrac{4}{3}-\dfrac{3}{2}\) 

                          \(x=\dfrac{-1}{6}\) 

b) \(\left|x-\dfrac{1}{2}\right|+75\%=\dfrac{9}{10}\) 

               \(\left|x-\dfrac{1}{2}\right|=\dfrac{9}{10}-75\%\) 

               \(\left|x-\dfrac{1}{2}\right|=\dfrac{3}{20}\) 

\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=\dfrac{3}{20}\\x-\dfrac{1}{2}=\dfrac{-3}{20}\end{matrix}\right.\) 

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{13}{20}\\x=\dfrac{7}{20}\end{matrix}\right.\)

a: Thay \(x=9+4\sqrt{2}\) vào A, ta được:

\(A=\dfrac{2\sqrt{2}+1+7}{2\sqrt{2}+1-1}=\dfrac{8+2\sqrt{2}}{2\sqrt{2}}=2\sqrt{2}+1\)

\(p=738mmHg=98391,9312Pa\)

Áp suất tại chân cột:\(p_2\)

Áp suất tương ứng với độ cao cột thủy ngân:

\(p=d\cdot h\Rightarrow p=\left(p_2-738\right)\cdot136000Pa\)

Đổi 738 mmHg =0,738 mHg

\(P=d_{Hg}.h=136000\cdot0,738=100368\left(Pa\right)\)