-2/5 x 4/7 + (-3/5) x 2/7 + (-3/5)
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10x=15y=21z
=>\(\dfrac{10x}{210}=\dfrac{15y}{210}=\dfrac{21z}{210}\)
=>\(\dfrac{x}{21}=\dfrac{y}{14}=\dfrac{z}{10}\)
mà 3x-7y+5z=30
nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x}{21}=\dfrac{y}{14}=\dfrac{z}{10}=\dfrac{3x-7y+5z}{3\cdot21-7\cdot14+5\cdot10}=\dfrac{30}{15}=2\)
=>\(x=2\cdot21=42;y=2\cdot14=28;z=2\cdot10=20\)
\(10x=15y=21z\Rightarrow\dfrac{10x}{210}=\dfrac{15y}{210}=\dfrac{21z}{210}\Rightarrow\dfrac{x}{21}=\dfrac{y}{14}=\dfrac{z}{10}\)
Áp dụng t/c dãy tỉ số bằng nhau:
\(\dfrac{x}{21}=\dfrac{y}{14}=\dfrac{z}{10}=\dfrac{3x}{63}=\dfrac{7y}{98}=\dfrac{5z}{50}=\dfrac{3x-7y+5z}{63-98+50}=\dfrac{30}{15}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=21.2=42\\y=14.2=28\\z=10.2=20\end{matrix}\right.\)
May 1 chiếc khăn hết số mét vải là:
4 : 5 = 0,8 (m)
Đ/S : 0,8 m vải
:>
\(\dfrac{20}{1\cdot6}+\dfrac{20}{6\cdot11}+...+\dfrac{20}{101\cdot106}\)
\(=4\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{101\cdot106}\right)\)
\(=4\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\right)\)
\(=4\left(1-\dfrac{1}{106}\right)=4\cdot\dfrac{105}{106}=\dfrac{105\cdot2}{53}=\dfrac{210}{53}\)
a: \(\dfrac{4}{13}+\dfrac{-12}{39}=\dfrac{4}{13}-\dfrac{4}{13}=0\)
b: \(\dfrac{27}{23}-\dfrac{-5}{21}-\dfrac{4}{23}+\dfrac{16}{21}+\dfrac{1}{2}\)
\(=\left(\dfrac{27}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+\dfrac{1}{2}\)
\(=1+1+\dfrac{1}{2}=\dfrac{5}{2}\)
c: \(\dfrac{-8}{9}+\dfrac{1}{9}\cdot\dfrac{2}{9}+\dfrac{1}{9}\cdot\dfrac{7}{9}\)
\(=\dfrac{-8}{9}+\dfrac{1}{9}\left(\dfrac{2}{9}+\dfrac{7}{9}\right)\)
\(=\dfrac{-8}{9}+\dfrac{1}{9}=\dfrac{-7}{9}\)
d: \(\dfrac{2}{\left(-3\right)^2}+\dfrac{5}{-12}-\dfrac{-3}{4}\)
\(=\dfrac{2}{9}-\dfrac{5}{12}+\dfrac{3}{4}\)
\(=\dfrac{8}{36}-\dfrac{15}{36}+\dfrac{27}{36}=\dfrac{19}{36}\)
Tổng thời gian Hoàng đi hết quãng đường là:
6p35s+9p20s+7p48s
=22p103s
=23p43s
\(\dfrac{-2}{5}\cdot\dfrac{4}{7}+\dfrac{-3}{5}\cdot\dfrac{2}{7}+\dfrac{-3}{5}\)
\(=\dfrac{-2}{5}\cdot\dfrac{4}{7}+\dfrac{-3}{5}\left(\dfrac{2}{7}+1\right)\)
\(=\dfrac{-2}{5}\cdot\dfrac{4}{7}+\dfrac{-3}{5}\cdot\dfrac{9}{7}\)
\(=\dfrac{-8-27}{35}=\dfrac{-35}{35}=-1\)