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m: \(\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+\dfrac{1}{65}+\dfrac{1}{104}+\dfrac{1}{152}\)
\(=\dfrac{2}{4}+\dfrac{2}{28}+\dfrac{2}{70}+\dfrac{2}{130}+\dfrac{2}{208}+\dfrac{2}{304}\)
\(=\dfrac{2}{1\cdot4}+\dfrac{2}{4\cdot7}+\dfrac{2}{7\cdot10}+\dfrac{2}{10\cdot13}+\dfrac{2}{13\cdot16}+\dfrac{2}{16\cdot19}\)
\(=\dfrac{2}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+\dfrac{3}{10\cdot13}+\dfrac{3}{13\cdot16}+\dfrac{3}{16\cdot19}\right)\)
\(=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{16}-\dfrac{1}{19}\right)\)
\(=\dfrac{2}{3}\cdot\dfrac{18}{19}=\dfrac{12}{19}\)
e: \(\dfrac{4}{5}+\dfrac{1}{5}\left(x+1\right)=-\dfrac{2}{5}\)
=>\(\dfrac{1}{5}\left(x+1\right)=-\dfrac{2}{5}-\dfrac{4}{5}=-\dfrac{6}{5}\)
=>x+1=-6
=>x=-6-1=-7
g: \(\dfrac{5}{4}-\dfrac{1}{4}:\left(-\dfrac{1}{2}+x\right)=-1\)
=>\(\dfrac{1}{4}:\left(x-\dfrac{1}{2}\right)=\dfrac{5}{4}+1=\dfrac{9}{4}\)
=>\(x-\dfrac{1}{2}=\dfrac{1}{4}:\dfrac{9}{4}=\dfrac{1}{9}\)
=>\(x=\dfrac{1}{9}+\dfrac{1}{2}=\dfrac{11}{18}\)
\(a,=-17+91-91+17+2011=\left(-17+17\right)+\left(91-91\right)+2011\)
\(=0+0+2011=2011\)
xy=-11, x<y
x,y nguyên => \(\hept{\begin{cases}x=-11\\y=1\end{cases}}\)
Vậy (x;y)=(-11;1)
a: \(=\dfrac{48}{36}+\dfrac{7}{5}\cdot\dfrac{20}{21}=\dfrac{4}{3}+\dfrac{4}{3}=\dfrac{8}{3}\)
b: \(=\dfrac{7}{3}-\dfrac{1}{3}\cdot\left[-\dfrac{3}{2}+\dfrac{2}{3}+\dfrac{4}{10}\cdot5\right]\)
\(=\dfrac{7}{3}-\dfrac{1}{3}\cdot\dfrac{7}{6}=\dfrac{7}{3}-\dfrac{7}{18}=\dfrac{42-7}{18}=\dfrac{35}{18}\)
c: \(=\left(29+\dfrac{1}{4}\right):\dfrac{9}{4}=\dfrac{117}{4}\cdot\dfrac{4}{9}=\dfrac{117}{9}=13\)
d: \(=\left(4-\dfrac{4}{5}\right)\cdot\dfrac{11}{8}-\dfrac{8}{5}\cdot4\)
\(=\dfrac{16}{5}\cdot\dfrac{11}{8}-\dfrac{32}{5}\)
\(=\dfrac{22}{5}-\dfrac{32}{5}=-\dfrac{10}{5}=-2\)
\(=\left(-67\right).\left(-33\right)-67.77+\left(-67\right).33-77.33\)
\(=\left[\left(-67\right).\left(-33\right)+\left(-67\right).33\right]-66.77-77.33\)
\(=-77\left(66+33\right)=-77.99=-7623\)
\(\frac{x-3}{x-1}=\frac{x-1-2}{x-1}=\frac{-2}{x-1}\)
hay : \(x-1\in\left(-2\right)=\left\{\pm1;\pm2\right\}\)
x - 1 | 1 | -1 | 2 | -2 |
x | 2 | 0 | 3 | -1 |
Đổi 3 giờ 15 phút = 3,25 giờ
Hỗn số biểu diễn vận tốc của xe khách là:
420 : 3,25 = \(\dfrac{1680}{13}\) \(=129\dfrac{3}{13}\)
=> Chọn A
A