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a)\(\dfrac{2}{3}+\dfrac{1}{-4}-\dfrac{5}{18}=\dfrac{8}{12}-\dfrac{3}{12}-\dfrac{5}{18}=\dfrac{5}{18}-\dfrac{5}{18}=\dfrac{5}{36}\)
b)\(=\dfrac{5}{8}+\dfrac{3}{4}-\dfrac{9}{8}=\left(\dfrac{5}{8}-\dfrac{9}{8}\right)+\dfrac{3}{4}=--\dfrac{2}{4}+\dfrac{3}{4}=\dfrac{1}{4}\)
c)\(=\dfrac{6}{7}+\dfrac{1}{7}:\left(-\dfrac{21}{28}+\dfrac{24}{28}\right)=\dfrac{6}{7}+\dfrac{1}{7}\times\dfrac{28}{3}=\dfrac{6}{7}+\dfrac{4}{3}=\dfrac{46}{21}\)
e)\(=\dfrac{9}{17}-\dfrac{5}{13}-\dfrac{8}{13}+\dfrac{1}{17}=\left(\dfrac{9}{17}+\dfrac{1}{17}\right)+\left(-\dfrac{5}{13}-\dfrac{8}{13}\right)\)
\(=\dfrac{8}{17}-1=-\dfrac{9}{17}\)
\(=\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{50}+\dfrac{1}{51}-\dfrac{102}{51\cdot52}\)
\(=\dfrac{1}{2}+\dfrac{1}{51}-\dfrac{102}{51\cdot52}\)
\(=\dfrac{1}{2}+\dfrac{52-102}{51\cdot52}=\dfrac{1}{2}+\dfrac{-50}{51\cdot52}=\dfrac{319}{663}\)
Bài 2:
a: \(x-\dfrac{1}{2}=\dfrac{7}{13}\cdot\dfrac{13}{28}\)
=>\(x-\dfrac{1}{2}=\dfrac{7}{28}=\dfrac{1}{4}\)
=>\(x=\dfrac{1}{4}+\dfrac{1}{2}=\dfrac{3}{4}\)
b: \(\dfrac{x}{15}=\dfrac{-3}{11}\cdot\dfrac{77}{36}\)
=>\(\dfrac{x}{15}=\dfrac{-3}{36}\cdot\dfrac{77}{11}=7\cdot\dfrac{-1}{12}=-\dfrac{7}{12}\)
=>\(x=-\dfrac{7}{12}\cdot15=-\dfrac{105}{12}=-\dfrac{35}{4}\)
c: \(x:\dfrac{15}{11}=\dfrac{-3}{12}:8\)
=>\(x:\dfrac{15}{11}=-\dfrac{1}{4}:8=-\dfrac{1}{32}\)
=>\(x=-\dfrac{1}{32}\cdot\dfrac{15}{11}=\dfrac{-15}{352}\)
Bài 1:
a: \(\dfrac{-12}{25}\cdot\dfrac{10}{9}=\dfrac{-12}{9}\cdot\dfrac{10}{25}=\dfrac{-4}{3}\cdot\dfrac{2}{5}=\dfrac{-8}{15}\)
b: \(\dfrac{10}{21}-\dfrac{3}{8}\cdot\dfrac{4}{5}\)
\(=\dfrac{10}{21}-\dfrac{12}{40}\)
\(=\dfrac{10}{21}-\dfrac{3}{10}=\dfrac{100-63}{210}=\dfrac{37}{210}\)
c: \(\dfrac{28}{11}:\dfrac{21}{22}\cdot9=\dfrac{28}{11}\cdot\dfrac{22}{21}\cdot9\)
\(=\dfrac{28}{21}\cdot\dfrac{22}{11}\cdot9=\dfrac{4}{3}\cdot2\cdot9=\dfrac{4}{3}\cdot18=24\)
d: \(-\dfrac{10}{21}\cdot\left[\dfrac{9}{15}+\left(\dfrac{3}{5}\right)^2\right]\)
\(=\dfrac{-10}{21}\cdot\left[\dfrac{3}{5}+\dfrac{9}{25}\right]\)
\(=\dfrac{-10}{21}\cdot\dfrac{15+9}{25}\)
\(=\dfrac{-10}{25}\cdot\dfrac{24}{21}=\dfrac{-2}{5}\cdot\dfrac{8}{7}=\dfrac{-16}{35}\)
e: \(\left(\dfrac{2}{3}-\dfrac{1}{2}-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}-\dfrac{1}{7}\right)\)
\(=\left(\dfrac{1}{3}-\dfrac{1}{2}\right)\cdot\dfrac{28-7-4}{28}\)
\(=\dfrac{-1}{6}\cdot\dfrac{17}{28}=\dfrac{-17}{168}\)
f: \(\left(\dfrac{15}{21}:\dfrac{5}{7}\right):\left(\dfrac{6}{5}:2\right)\)
\(=\left(\dfrac{5}{7}\cdot\dfrac{7}{5}\right):\left(\dfrac{6}{5\cdot2}\right)\)
\(=1:\dfrac{6}{10}=\dfrac{10}{6}=\dfrac{5}{3}\)
a: =>4y+15/16=1
=>4y=1/16
=>y=1/64
b: =>10y+1/2+1/4+...+1/1024=1
=>10y+1023/1024=1
=>10y=1/1024
=>y=1/10240
`-1 5/27-(3x-7/9)^3=-24/27`
`-32/27-(3x-7/9)^3=-24/27`
`(3x-7/9)^3=-8/27`
`(3x-7/9)^3=(-2/3)^3`
`3x-7/9=-2/3`
`3x=1/9`
`x=1/27`
`=>(3x-7/9)^3=-32/27+24/27`
`(3x-7/9)^3=-8/27`
`(3x-7/9)^3=(-2/3)^3`
`=>3x-7/9=-2/3`
`=>3x=-2/3+7/9`
`=>3x=-1/9`
`=>x=-1/27`
Bài 4:
a) \(4^{10}+4^7=4^7\left(4^3+1\right)=4^7.65⋮65\)
b) \(10^{10}-10^9-10^8=10^8\left(10^2-10-1\right)=10^8.89⋮89\)
Bài 5:
a) \(\Rightarrow n\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)
Do \(n\in N\)
\(\Rightarrow n\in\left\{1;2;4\right\}\)
b) \(\Rightarrow\left(n+2\right)+4⋮\left(n+2\right)\)
\(\Rightarrow\left(n+2\right)\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)
Do \(n\in N\)
\(\Rightarrow n\in\left\{0;2\right\}\)
c) \(\Rightarrow3\left(n-2\right)+7⋮\left(n-2\right)\)
\(\Rightarrow\left(n-2\right)\inƯ\left(7\right)=\left\{-7;-1;1;7\right\}\)
Do \(n\in N\)
\(\Rightarrow n\in\left\{1;3;9\right\}\)
d) \(\Rightarrow2\left(3n+9\right)⋮\left(2n-1\right)\)
\(\Rightarrow3\left(2n-1\right)+21⋮\left(2n-1\right)\)
\(\Rightarrow\left(2n-1\right)\inƯ\left(21\right)=\left\{-21;-7;-3;-1;1;3;7;21\right\}\)
Do \(n\in N\)
\(\Rightarrow n\in\left\{0;1;2;4;11\right\}\)
`G=5/(1.7)+...+5/(51.57)`
`=5/6 .(6/(1.7)+...+6/(51.57))`
`=5/6 .(1-1/7+...+1/51-1/57)`
`=5/6 .(1-1/57)`
`=5/6 .(57/57-1/57)`
`=5/6 . 56/57`
`=140/171`
= 25,67 * 99 + 25,67
= 25,67 * 99 + 25,67 * 1
= 25,67 * ( 99 + 1 )
=25,67 * 100
=2567
25,67 x 99 + 24 + 1,67 = 25,67 x 99 + 25,67
= 25,67 x 99 + 25,67 x 1
= 25,67 x ( 99 + 1 )
= 25,67 x 100
= 2567
Vì AB+BC>AC; AC+BC>AB; AB+AC>BC
nên ba điểm A,B,C không thẳng hàng