15: \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{2021}{2022}\)

=>\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2021}{2022}\)

=>\(1-\dfrac{1}{x+1}=\dfrac{2021}{2022}\)

=>\(\dfrac{1}{x+1}=\dfrac{1}{2022}\)

=>x+1=2022

=>x=2021

14: \(3^{x+1}+3^{x+1}\cdot4=45\)

=>\(3^x\cdot3+3^x\cdot12=45\)

=>\(3^x=3\)

=>x=1

11: \(\dfrac{13}{15}-\left(\dfrac{13}{21}+x\right)\cdot\dfrac{7}{12}=\dfrac{7}{10}\)

=>\(\dfrac{7}{12}\left(x+\dfrac{13}{21}\right)=\dfrac{13}{15}-\dfrac{7}{10}=\dfrac{1}{6}\)

=>\(x+\dfrac{13}{21}=\dfrac{1}{6}:\dfrac{7}{12}=\dfrac{1}{6}\cdot\dfrac{12}{7}=\dfrac{2}{7}\)

=>\(x=\dfrac{2}{7}-\dfrac{13}{21}=-\dfrac{7}{21}=-\dfrac{1}{3}\)

12: \(720:\left[41-\left(2x-5\right)\right]=2^2\cdot5\)

=>\(41-\left(2x-5\right)=\dfrac{720}{20}=36\)

=>2x-5=5

=>2x=10

=>x=5

9: \(\dfrac{4}{x}=\dfrac{y}{21}=\dfrac{28}{49}\)

=>\(\dfrac{4}{x}=\dfrac{y}{21}=\dfrac{4}{7}\)

=>\(\left\{{}\begin{matrix}x=7\\y=21\cdot\dfrac{4}{7}=12\end{matrix}\right.\)

\(\left(\dfrac{31}{42}\times\dfrac{17}{25}+\dfrac{31}{42}\right)\times\left(-5\right)^2\)

\(=\dfrac{31}{42}\times\left(\dfrac{17}{25}+1\right)\times25\)

\(=\dfrac{31}{42}\times\dfrac{42}{25}\times25=31\)

d: \(\left(\dfrac{2}{5}-\dfrac{2}{3}\right)-\dfrac{7}{5}=\dfrac{2}{5}-\dfrac{7}{5}-\dfrac{2}{3}=-1-\dfrac{2}{3}=-\dfrac{5}{3}\)

b: \(\dfrac{14}{13}+\left(-\dfrac{1}{13}-\dfrac{19}{20}\right)=\dfrac{14}{13}-\dfrac{1}{13}-\dfrac{19}{20}=1-\dfrac{19}{20}=\dfrac{1}{20}\)

f: \(\dfrac{7}{8}-\dfrac{3}{8}\left(1-\dfrac{2}{3}\right)\)

\(=\dfrac{7}{8}-\dfrac{3}{8}\cdot\dfrac{1}{3}\)

\(=\dfrac{7}{8}-\dfrac{1}{8}=\dfrac{6}{8}=\dfrac{3}{4}\)

\(d,\left(\dfrac{2}{5}-\dfrac{2}{3}\right)-\dfrac{7}{5}\)

\(=\dfrac{2}{5}-\dfrac{2}{3}-\dfrac{7}{5}\)

\(=\left(\dfrac{2}{5}-\dfrac{7}{5}\right)-\dfrac{2}{3}\)

\(=-1-\dfrac{2}{3}\)

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

\(e,\dfrac{14}{13}+\left(-\dfrac{1}{13}-\dfrac{19}{20}\right)\)

\(=\dfrac{14}{13}+-\dfrac{1}{13}-\dfrac{19}{20}\)

\(=\left(\dfrac{14}{13}+-\dfrac{1}{13}\right)-\dfrac{19}{20}\)

\(=1-\dfrac{19}{20}\)

\(=\dfrac{1}{20}\)

\(f,\dfrac{7}{8}-\dfrac{3}{8}.\left(1-\dfrac{2}{3}\right)\)

\(=\dfrac{7}{8}-\dfrac{3}{8}.\dfrac{1}{3}\)

\(=\dfrac{7}{8}-\dfrac{1}{8}.1\)

\(=\dfrac{6}{8}=\dfrac{3}{4}\)

Chiều dài hình chữ nhật là \(\dfrac{8}{5}:\dfrac{5}{7}=\dfrac{8}{5}\times\dfrac{7}{5}=\dfrac{56}{25}\left(m\right)\)

\(2460+300\times\left\{96:8+15\right\}\)

\(=2460+300\times\left\{12+15\right\}\)

\(=2460+300\times27\)

\(=2460+8100\)

\(=10560\)

2460+300.(96:8+15)

=2460+300.(12+15)

=2460+300.27

=2460+8100=10560

a: Xét ΔABC vuông tại A và ΔAMC vuông tại A có

AB=AM

AC chung

Do đó: ΔABC=ΔAMC

b: ΔABC=ΔAMC

=>\(\widehat{BAC}=\widehat{MAC}\)

Xét ΔCFA vuông tại F và ΔCEA vuông tại E có

CA chung

\(\widehat{FCA}=\widehat{ECA}\)

Do đó: ΔCFA=ΔCEA

=>AE=AF

giống mee:> chúc thi tútttt ạ!

tui khi ngày 10 tháng 5 nhưng hồi hợp lắm nha 

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{90}\)

\(=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{9\times10}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\)

\(=1-\dfrac{1}{10}=\dfrac{9}{10}\)

help me