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6 tháng 5 2022

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)\(=\dfrac{5}{8}+\dfrac{3}{4}-\dfrac{9}{8}=\left(\dfrac{5}{8}-\dfrac{9}{8}\right)+\dfrac{3}{4}=--\dfrac{2}{4}+\dfrac{3}{4}=\dfrac{1}{4}\)

6 tháng 5 2022

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

27 tháng 5 2022

`-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`

27 tháng 5 2022

`=>(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`

7 tháng 10 2021

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 \(n\in N\)

\(\Rightarrow n\in\left\{0;1;2;4;11\right\}\)

7 tháng 10 2021

Bài 4

Ta có: \(4^{10}+4^7=4^7.4^3+4^7=4^7\left(4^3+1\right)=4^7.65\)

Vì \(65⋮65\) nên \(4^{10}+4^7⋮65\)

b) Ta có:\(10^{10}-10^9-10^8=10^8.10^2-10^8.10-10^8=10^8\left(10^2-10-1\right)=10^8.89\)

Vì \(89⋮89\) nên \(10^{10}-10^9-10^8⋮65\)

28 tháng 5 2022

`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

12 tháng 3 2018

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

5 tháng 3 2022

Vì: AB+BC>AC

 AC+BC>AB

AB+AC>BC

=> A,B,C không thẳng hàng