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2 tháng 7 2019

a, \(\frac{-5}{9}.\left(\frac{3}{10}-\frac{2}{5}\right)\)

\(=\frac{-5}{9}.\left(\frac{3}{10}-\frac{4}{10}\right)\)

\(=\frac{-5}{9}.\frac{-1}{10}\)

\(=\frac{5}{90}\)

\(=\frac{1}{18}\)

b,\(\frac{2}{3}+\frac{-1}{3}+\frac{7}{15}\)

\(=\frac{10}{15}-\frac{5}{15}+\frac{7}{15}\)

\(=\frac{12}{15}\)

\(=\frac{4}{5}\)

c, \(\frac{3}{8}.3\frac{1}{3}\)

\(=\frac{3}{8}.\frac{10}{3}\)

\(=\frac{10}{8}\)

\(=\frac{5}{4}\)

d, \(\frac{-3}{5}+0,8.\left(-7\frac{1}{2}\right)\)

\(=\frac{-3}{5}+\frac{4}{5}.\frac{-15}{2}\)

\(=\frac{-3}{5}+\frac{-60}{10}\)

\(=\frac{-3}{5}+\frac{-30}{5}\)

\(=\frac{-33}{5}\)

e, \(\frac{2}{5}.8\frac{1}{3}+1\frac{2}{3}.\frac{2}{5}\)

\(=\frac{2}{5}.\left(8\frac{1}{3}+1\frac{2}{3}\right)\)

\(=\frac{2}{5}.10\)

\(=4\)

f, \(\frac{3}{7}.19\frac{1}{3}-\frac{3}{7}.33\frac{1}{3}\)

\(=\frac{3}{7}.\left(19\frac{1}{3}-33\frac{1}{3}\right)\)

\(=\frac{3}{7}.-14\)

\(=-6\)

~Study well~

#KSJ

20 tháng 7 2019

Bài 2 

| x - \(\frac{1}{3}\)| + \(\frac{4}{5}\)= | ( -3,2) + \(\frac{2}{5}\)|

=> | x - \(\frac{1}{3}\)| + \(\frac{4}{5}\)= | -2,8|

=> | x - \(\frac{1}{3}\)| + \(\frac{4}{5}\)= -2,8

=> | x - \(\frac{1}{3}\)| = -2,8 - \(\frac{4}{5}\)

=> | x - \(\frac{1}{3}\)| = - 3,6

=> x - \(\frac{1}{3}\)= -3,6

=> x = -3,6 + \(\frac{1}{3}\)

=> x = \(\frac{-49}{15}\)

21 tháng 7 2019

Bài 3 :

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\frac{a_1-1}{9}=\frac{a_2-2}{8}=...=\frac{a_9-9}{1}=\frac{a_1-1+a_2-2+...+a_9-9}{9+8+...+1}\)

\(=\frac{\left[a_1+a_2+...+a_9\right]-\left[1+2+...+9\right]}{9+8+...+1}=\frac{90-45}{45}=1\)

Ta có : \(\frac{a_1-1}{9}=1\Rightarrow a_1=10\)

Tương tự : \(a_1=a_2=....=a_9=10\)

6 tháng 7 2019

a)\(\frac{1}{2}-2.\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+.....+\frac{1}{48.50}\right)\)

=\(\frac{1}{2}-\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+.....+\frac{2}{48.50}\right)\)

=\(\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+.....+\frac{1}{48}-\frac{1}{50}\right)\)

=\(\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{50}\right)\)

=\(\frac{1}{50}\)

6 tháng 7 2019

\(1)a)\frac{1}{2}-2\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{48.50}\right)\)

\(=\frac{1}{2}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{24.25}\right)\)

\(=\frac{1}{2}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{24}-\frac{1}{25}\right)\)

\(=\frac{1}{2}-\left(1-\frac{1}{25}\right)\)

\(=\frac{1}{2}-\frac{24}{25}=\frac{-23}{50}\)

\(\)

Bài 1

\(a,\left(\frac{3}{5}\right)^2-\left[\frac{1}{3}:3-\sqrt{16}.\left(\frac{1}{2}\right)^2\right]-\left(10.12-2014\right)^0\)

\(=\frac{9}{25}-\left[\frac{1}{9}-4.\frac{1}{4}\right]-1\)

\(=\frac{9}{25}-\left(-\frac{8}{9}\right)-1\)

\(=\frac{9}{25}+\frac{8}{9}-1\)

\(=\frac{56}{225}\)

\(b,|-\frac{100}{123}|:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)\)

\(=\frac{100}{123}:\left(\frac{4}{3}\right)+\frac{23}{123}:\frac{4}{3}\)

\(=\left(\frac{100}{123}+\frac{23}{123}\right):\frac{4}{3}\)

\(=1:\frac{4}{3}=\frac{3}{4}\)

Phần c đăng riêng vì mk chưa tìm đc cách giải bt mỗi đáp án :v 

\(c,\frac{\left(-5\right)^{32}.20^{43}}{\left(-8\right)^{29}.125^{25}}\)

\(=\frac{\left(-5\right)^{32}.\left(4.5\right)^{43}}{\left[4.\left(-2\right)\right]^{29}.\left(-5^3\right)^{25}}\)

\(=\frac{-5^{32}.4^{43}.5^{43}}{4^{29}.\left(-2\right)^{29}.\left(5\right)^{75}}\)

\(=\frac{\left(-5^4\right)^8.4^{43}.5^{43}}{4^{29}.\left(-2\right)^{29}.\left(5^3\right)^{25}}\)

\(=-\frac{1}{2}\)

15 tháng 6 2019

a/ \(\left(\frac{-2}{3}\right)^4:24=\frac{16}{81}:24=\frac{2}{243}\)

b/ \(\left(\frac{3}{4}\right)^3.4^4=\frac{27}{64}.256=108\)

c/ \(\frac{3.0,8^5}{2,4^4}=\frac{3.0,32768}{33,1776}=\frac{0,98304}{33,1776}=\frac{4}{135}\)

d/ \(\frac{3^3-0,9^5}{2,7^4}=\frac{27-0,59049}{53,1441}=\frac{26,40951}{53,1441}=0,4969415231\)

e/\(\left(\frac{-7}{2}\right)^2+\left(\frac{-3}{4}\right)^3.64-\left(\frac{-61}{5}\right)\)

\(=\frac{49}{4}+\frac{-27}{64}.64+\frac{61}{5}\)

\(=12,25-27+12,2\)

\(=-2,55\)

f/ \(\frac{2^4.2^6}{\left(2^5\right)^2}-\frac{2^5.15^3}{6^3.10^2}=\frac{2^{10}}{2^{10}}-\frac{2^5.5^3.3^3}{2^3.3^3.5^2.2^2}\)

                                      \(=1-\frac{2^5.5^3.3^3}{2^5.3^3.5^2}=1-\frac{5}{1}=-4\)

                                       \(\)

chúc bạn học tốt

A=\(\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right).............\left(\frac{1}{9801}-1\right).\left(\frac{1}{10000}-1\right)\)

A=\(\left(\frac{1-4}{4}\right).\left(\frac{1-9}{9}\right).\left(\frac{1-16}{16}\right).............\left(\frac{1-9801}{9801}\right).\left(\frac{1-10000}{10000}\right)\)

A=\(\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}.....................\frac{-9800}{9801}.\frac{-9999}{10000}\)

A=\(\frac{-1.3}{2^2}.\frac{-2.4}{3^2}.\frac{-3.5}{4^2}.....................\frac{-98.100}{99^2}.\frac{-99.101}{100^2}\)

A=\(\frac{\left[\left(-1\right).\left(-2\right).\left(-3\right)....................\left(-98\right).\left(-99\right)\right].\left(3.4.5............100.101\right)}{\left(2.3.4.........99.100\right).\left(2.3.4...............99.100\right)}\)

A=\(\frac{1.101}{100.2}\)=\(\frac{101}{200}\)

2

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.................+\frac{2}{x.\left(x+1\right)}=\frac{2015}{2017}\)

\(\frac{1}{3.2}+\frac{1}{6.2}+\frac{1}{10.2}+.................+\frac{2}{2.x.\left(x+1\right)}=\frac{1}{2}.\frac{2015}{2017}\)

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.................+\frac{1}{x.\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+..................+\frac{1}{x.\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+..............+\frac{1}{x}-\frac{1}{x+1}=\frac{2015}{2017}.\frac{1}{2}\)

\(\frac{1}{2}-\frac{1}{x+1}=\frac{2015}{2017}.\frac{1}{2}\)

\(\frac{x+1}{2.\left(x+1\right)}-\frac{2}{2.\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)

\(\frac{\left(x+1\right)-2}{2.\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)

\(\frac{x-1}{2.\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}\)

=>\(\frac{x-1}{x+1}=\frac{2015}{2017}.\frac{1}{2}:\frac{1}{2}\)

\(\frac{x-1}{x+1}=\frac{2015}{2017}\)

=>x+1=2017

=>x=2018-1

=>x=2016

Vậy x=2016

Còn bài 3 em ko biết làm em ms lớp 6

Chúc anh học tốt

25 tháng 10 2018

\(a.9\cdot3^2\cdot\frac{1}{81}=\frac{3^2.3^2.1}{3^4}=\frac{3^4}{3^4}=1\)

\(b.2\frac{1}{2}+\frac{4}{7}:\left(\frac{-8}{9}\right)\)

\(=\frac{5}{2}+\frac{4}{7}.\left(\frac{-9}{8}\right)\)

\(=\frac{5}{2}+\frac{-9}{14}=\frac{13}{7}\)

\(c.3,75.\left(7,2\right)+2,8.\left(3,75\right)\)

\(=3,75.\left(7,2+2,8\right)\)

\(=3,75.10=37,5\)

\(d.\left(\frac{-5}{13}\right).\frac{3}{7}+\left(\frac{-8}{13}\right).\frac{3}{7}+\left(\frac{-4}{7}\right)\)

\(=\frac{3}{7}.\left[\left(\frac{-5}{13}\right)+\left(\frac{-8}{13}\right)\right]+\left(\frac{-4}{7}\right)\)

\(=\frac{3}{7}.\left(-1\right)+\frac{-4}{7}\)

\(=\frac{-3}{7}+-\frac{4}{7}=-1\)

\(e.\sqrt{81}-\frac{1}{8}.\sqrt{64}+\sqrt{0,04}\)

\(=9-\frac{1}{8}.8+0,2\)

\(=9-1+0,2=8+0,2=8,2\)

25 tháng 10 2018

\(a-c\left(tựlm\right)\)

\(b.\left(x-1\right)^5=-32\)

\(\Rightarrow\left(x-1\right)^5=\left(-2\right)^5\)

\(\Rightarrow x-1=-2\)

\(x=-2+1=-1\)

\(d.\left(2^3:4\right).2^{x+1}=64\)

\(2.2^{x+1}=64\)

\(\Rightarrow2^{1+x+1}=64=2^6\)

\(\Rightarrow2+x=6\Rightarrow x=6-2=4\)