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e) \(20\%\cdot1\dfrac{1}{4}\cdot12\cdot\dfrac{25}{45}\cdot0,6\)
\(=\dfrac{1}{5}\cdot\dfrac{5}{4}\cdot\dfrac{12}{1}\cdot\dfrac{5}{9}\cdot\dfrac{6}{10}\)
\(=1\)
\(3\left(x+3\right)=-24\)
\(x+3=-\dfrac{24}{3}\)
\(x+3=-8\)
\(x=-8-3\)
\(x=-11\)
Số số hạng:
\(\left(68-30\right):2+1=20\)(số)
Tổng của dãy số:
\(\dfrac{\left(30+68\right)\times20}{2}=980\)
\(\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot\dfrac{16}{15}\cdot...\cdot\dfrac{400}{399}\)
\(=\dfrac{2\cdot2}{1\cdot3}\cdot\dfrac{3\cdot3}{2\cdot4}\cdot\dfrac{4\cdot4}{3\cdot5}\cdot...\cdot\dfrac{20\cdot20}{19\cdot21}\)
\(=\dfrac{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot...\cdot20\cdot20}{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot...\cdot19\cdot21}\)
\(=\dfrac{2\cdot3\cdot4\cdot...\cdot20}{1\cdot2\cdot3\cdot...\cdot19}\cdot\dfrac{2\cdot3\cdot4\cdot...\cdot20}{3\cdot4\cdot5\cdot...\cdot21}\)
\(=20\cdot\dfrac{2}{21}\)
\(=\dfrac{40}{21}\)
a) \(-\dfrac{1}{6}+\dfrac{5}{13}-\dfrac{5}{13}-\dfrac{11}{12}=-\dfrac{1}{6}-\dfrac{11}{12}=-\dfrac{13}{12}\)
b) \(\dfrac{3^4\cdot4-3^6}{3^5\cdot5+10\cdot3^6}=\dfrac{3^4\left(4-3^2\right)}{3^4\left(15+10\cdot3^2\right)}=\dfrac{4-9}{15+90}=-\dfrac{1}{21}\)
c) \(\left(1-\dfrac{3}{4}\right)^2+\left|-\dfrac{4}{5}\right|-\dfrac{29}{80}\cdot2019^2\) (Câu này thì bạn bấm máy cho nhanh :))