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17 tháng 12 2022

\(3^2\left(x+4\right)-5^2=5\cdot2^2\\ 9\left(x+4\right)-25=20\\ 9\left(x+4\right)=20+25\\ 9\left(x+4\right)=45\\ x+4=45:9\\ x+4=5\\ x=5-4\\ x=1\)

17 tháng 12 2022

sai

30 tháng 4 2017

Bài 1:

a) \(\dfrac{2}{5}\cdot x-\dfrac{1}{4}=\dfrac{1}{10}\)

\(\dfrac{2}{5}\cdot x=\dfrac{1}{10}+\dfrac{1}{4}\)

\(\dfrac{2}{5}\cdot x=\dfrac{7}{20}\)

\(x=\dfrac{7}{20}:\dfrac{2}{5}\)

\(x=\dfrac{7}{8}\)

Vậy \(x=\dfrac{7}{8}\).

b) \(\dfrac{3}{5}=\dfrac{24}{x}\)

\(x=\dfrac{5\cdot24}{3}\)

\(x=40\)

Vậy \(x=40\).

c) \(\left(2x-3\right)^2=16\)

\(\left(2x-3\right)^2=4^2\)

\(\circledast\)TH1: \(2x-3=4\\ 2x=4+3\\ 2x=7\\ x=\dfrac{7}{2}\)

\(\circledast\)TH2: \(2x-3=-4\\ 2x=-4+3\\ 2x=-1\\ x=\dfrac{-1}{2}\)

Vậy \(x\in\left\{\dfrac{7}{2};\dfrac{-1}{2}\right\}\).

Bài 2:

a) \(25\%-4\dfrac{2}{5}+0.3:\dfrac{6}{5}\)

\(=\dfrac{1}{4}-\dfrac{22}{5}+\dfrac{3}{10}:\dfrac{6}{5}\)

\(=\dfrac{1}{4}-\dfrac{22}{5}+\dfrac{3}{10}\cdot\dfrac{5}{6}\)

\(=\dfrac{1}{4}-\dfrac{22}{5}+\dfrac{1}{4}\)

\(=\dfrac{5}{20}-\dfrac{88}{20}+\dfrac{5}{20}\)

\(=\dfrac{5-88+5}{20}\)

\(=\dfrac{78}{20}=\dfrac{39}{10}\)

b) \(\left(\dfrac{1}{6}-\dfrac{1}{5^2}\cdot5+\dfrac{1}{30}\right)\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=\left(\dfrac{1}{6}-\dfrac{1}{25}\cdot5+\dfrac{1}{30}\right)\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=\left(\dfrac{1}{6}-\dfrac{1}{5}+\dfrac{1}{30}\right)\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=\left(\dfrac{5}{30}-\dfrac{6}{30}+\dfrac{1}{30}\right)\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=\left(\dfrac{5-6+1}{30}\right)\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=0\cdot\left(\dfrac{2011}{2010}+\dfrac{2010}{1009}+\dfrac{2009}{2008}\right)\)

\(=0\)

Bài 3:

a) \(\dfrac{4}{19}\cdot\dfrac{-3}{7}+\dfrac{-3}{7}\cdot\dfrac{15}{19}\)

\(=\dfrac{-3}{7}\left(\dfrac{4}{19}+\dfrac{15}{19}\right)\)

\(=\dfrac{-3}{7}\cdot1\)

\(=\dfrac{-3}{7}\)

b) \(7\dfrac{5}{9}-\left(2\dfrac{3}{4}+3\dfrac{5}{9}\right)\)

\(=\dfrac{68}{9}-\dfrac{11}{4}-\dfrac{32}{9}\)

\(=\dfrac{68}{9}-\dfrac{32}{9}-\dfrac{11}{4}\)

\(=4-\dfrac{11}{4}\)

\(=\dfrac{16}{4}-\dfrac{11}{4}\)

\(\dfrac{5}{4}\)

Bài 4:

\(\dfrac{4}{12\cdot14}+\dfrac{4}{14\cdot16}+\dfrac{4}{16\cdot18}+...+\dfrac{4}{58\cdot60}\)

\(=2\left(\dfrac{1}{12\cdot14}+\dfrac{1}{14\cdot16}+\dfrac{1}{16\cdot18}+...+\dfrac{1}{58\cdot60}\right)\)

\(=2\left(\dfrac{1}{12}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{18}+...+\dfrac{1}{58}-\dfrac{1}{60}\right)\)

\(=2\left(\dfrac{1}{12}-\dfrac{1}{60}\right)\)

\(=2\left(\dfrac{5}{60}-\dfrac{1}{60}\right)\)

\(=2\cdot\dfrac{1}{15}\)

\(=\dfrac{2}{15}\)

27 tháng 6 2017

bài 1) a) \(1+2+3+4+........+2005+2006\)

\(\Leftrightarrow\) \(\left(1+2006\right)+\left(2+2005\right)+........+\left(1003+1004\right)\)

\(\Leftrightarrow\) \(2007.\dfrac{2006}{2}=2007.1003=2013021\)

b) \(5+10+15+.......+2000+2005\)

\(\Leftrightarrow\) \(\left(2005+5\right)\left(2000+10\right)+.......+\left(1000+1010\right)\)

\(\Leftrightarrow\) \(2010.\dfrac{2005}{5}=2010.401=405010\)

c) \(140+136+132+.......+64+60\)

\(\Leftrightarrow\) \(\left(140+60\right)+\left(136+64\right)+.......+\left(100+100\right)\)

\(\Leftrightarrow\) \(200.10\) = \(2000\)

27 tháng 6 2017

1)

a) \(1+2+3+4+.....+2005+2006\)

Số các số hạng của dãy trên là:

\((2006-1):1+1=2006\)

Tổng dãy là:

\(\dfrac{2006\left(2006+1\right)}{2}=2013021\)

b) \(5+10+15+.....+2000+2005\)

Số các số hạng của dãy là:

\((2005-5):5+1=401\)

Tổng dãy là:

\(\dfrac{401\left(2005+5\right)}{2}=403005\)

c)\(140+136+132+.....+64+60\)

\(=60+64+.....+132+136+140\)

Số số hạng của dãy là:

\((140-60):4+1=11\)

Tổng dãy là:

\(\dfrac{11\left(60+140\right)}{2}=1100\)

1 tháng 7 2019

a) \(2x-\frac{2}{3}-7x=\frac{3}{2}-1\\ 2x-7x-\frac{2}{3}=\frac{1}{2}\\ -5x=\frac{1}{2}+\frac{2}{3}\\ -5x=\frac{7}{6}\\ x=\frac{7}{6}:\left(-5\right)\\ x=\frac{-7}{30}\)Vậy \(x=\frac{-7}{30}\)

b) \(\frac{3}{2}x-\frac{2}{5}=\frac{1}{3}x-\frac{1}{4}\\ \frac{3}{2}x-\frac{1}{3}x=\frac{2}{5}-\frac{1}{4}\\ \frac{7}{6}x=\frac{3}{20}\\ x=\frac{3}{20}:\frac{7}{6}\\ x=\frac{9}{70}\)Vậy \(x=\frac{9}{70}\)

c) \(\frac{2}{3}-\frac{5}{3}x=\frac{7}{10}x+\frac{5}{6}\\ \frac{2}{3}-\frac{5}{6}=\frac{7}{10}x+\frac{5}{3}x\\ \frac{-1}{6}=\frac{71}{30}x\\ x=\frac{-1}{6}:\frac{71}{30}\\ x=\frac{-5}{71}\)Vậy \(x=\frac{-5}{71}\)

d) \(2x-\frac{1}{4}=\frac{5}{6}-\frac{1}{2}x\\ 2x+\frac{1}{2}x=\frac{5}{6}+\frac{1}{4}\\ \frac{5}{2}x=\frac{13}{12}\\ x=\frac{13}{12}:\frac{5}{2}\\ x=\frac{13}{30}\)Vậy \(x=\frac{13}{30}\)

e) \(3x-\frac{5}{3}=x-\frac{1}{4}\\ 3x-x=\frac{5}{3}-\frac{1}{4}\\ 2x=\frac{17}{12}\\ x=\frac{17}{12}:2\\ x=\frac{17}{24}\)Vậy \(x=\frac{17}{24}\)

1 tháng 7 2019

Èo, chăm thế? Chăm hơn cả mik cơ, gần 11 h rồi onl thì thấy bài được bạn HISI làm hết rồi :((

26 tháng 12 2017

1. tìm x

a,70-5.(x-3)=5.32

70-5.(x-3)=45

5.(x-3)=70-45

5.(x-3)=25

(x-3)=25:5

x-3 =5

x =5+3

x =8

vậy x =8

b,2x-3=16

2x-3=24

x-3 =4

x =4+3

x =7

2.thực hiện phép tính

a,248+(-12)+2064+(-236)

= +(248-12)+2064+(-236)

= 236+2064+(-236)

=2300+(-236)

=2064

b,|-23|+(-15)+(-34)

=23+(-15)+(-34)

= +(23-15)+(-34)

=8+(-34)

= -26

c,465+[56+(-465)+(-38)]

=465+[(409+(-38)]

=465+(-447)

=18

26 tháng 12 2017

Cảm ơn bạn nhìu yeu

\(.2.\)

\(a.\)

\(2x+\dfrac{1}{2}=-\dfrac{5}{3}\)

\(\Rightarrow2x=-\dfrac{5}{3}-\dfrac{1}{2}=-\dfrac{13}{6}\)

\(\Rightarrow x=-\dfrac{13}{6}:2=-\dfrac{13}{12}\)

Vậy : \(x=-\dfrac{13}{12}\)

\(b.\)

\(\dfrac{1}{7}-\dfrac{3}{5}x=\dfrac{3}{5}\)

\(\Rightarrow\dfrac{3}{5}x=\dfrac{1}{7}-\dfrac{3}{5}=-\dfrac{16}{35}\)

\(\Rightarrow x=-\dfrac{16}{35}:\dfrac{3}{5}=-\dfrac{16}{21}\)

Vậy : \(x=-\dfrac{16}{21}\)

\(c.\)

\(\dfrac{3}{4}x+\dfrac{1}{2}=-\dfrac{3}{5}\)

\(\Rightarrow\dfrac{3}{4}x=-\dfrac{3}{5}-\dfrac{1}{2}=-\dfrac{11}{10}\)

\(\Rightarrow x=-\dfrac{11}{10}:\dfrac{3}{4}=-\dfrac{22}{15}\)

Vậy : \(x=-\dfrac{22}{15}\)

\(d.\)

\(-\dfrac{2}{15}-x=-\dfrac{3}{10}\)

\(\Rightarrow x=-\dfrac{2}{15}-\left(-\dfrac{3}{10}\right)=\dfrac{1}{6}\)

Vậy : \(x=\dfrac{1}{6}\)

9 tháng 3 2017

còn bài 1

29 tháng 9 2016

a) \(3^{x+1}-2.3^x=81\)

\(\Rightarrow3^x.3-2.3^x\)

\(\Rightarrow3^x\left(3-2\right)=81\)

\(\Rightarrow3^x=3^4\)

\(\Rightarrow x=4\)

Vậy \(x=4\)

b) \(2^{x+2}+2^x=40\)

\(\Rightarrow2^x.2^2+2^x=40\)

\(\Rightarrow2^x.\left(2^2+1\right)=40\)

\(\Rightarrow2^x.5=40\)

\(\Rightarrow2^x=8\)

\(\Rightarrow2^x=2^3\)

\(\Rightarrow x=3\)

Vậy \(x=3\)

c) \(\left(x+1\right)^5-12=20\)

\(\Rightarrow\left(x+1\right)^5=32\)

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

\(\Rightarrow x+1=2\)

\(\Rightarrow x=1\)

Vậy \(x=1\)

d) \(56-\left(x-2\right)^2=20\)

\(\Rightarrow\left(x-2\right)^2=36\)

\(\Rightarrow x-2=\pm6\)

+) \(x-2=6\Rightarrow x=8\)

+) \(x-2=-6\Rightarrow x=-4\)

Vậy \(x=8\) hoặc \(x=-4\)

29 tháng 9 2016

Buồn ngủ quá

23 tháng 7 2019

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{5.6}=\frac{2-1}{1.2}+\frac{3-2}{2.3}+...+\frac{6-5}{5.6}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{5}-\frac{1}{6}=1-\frac{1}{6}=\frac{5}{6}\)

23 tháng 7 2019

Tham khảo Câu hỏi của hoang - Toán lớp 6 - Học toán với OnlineMath

13 tháng 7 2020

bài 1 tắt quá

13 tháng 7 2020

Câu 1:

Đặt: \(A=\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+....+\frac{1}{100^2}\)

\(=\frac{1}{3.3}+\frac{1}{4.4}+\frac{1}{5.5}+\frac{1}{6.6}+....+\frac{1}{100.100}\)

\(A< \frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{99.100}\)

\(\Rightarrow A< \frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow A< \frac{1}{2}-\frac{1}{100}\)

\(\Rightarrow A< \frac{49}{100}< \frac{50}{100}=\frac{1}{2}\)

\(\Rightarrow A< \frac{1}{2}\)

Vậy:.............

Câu 2:

\(\left(\frac{1}{2}+1\right)\left(\frac{1}{3}+1\right)\left(\frac{1}{4}+1\right)...\left(\frac{1}{98}+1\right)\left(\frac{1}{99}+1\right)\)

\(=\left(\frac{1}{2}+\frac{2}{2}\right)\left(\frac{1}{3}+\frac{3}{3}\right)\left(\frac{1}{4}+\frac{4}{4}\right)...\left(\frac{1}{98}+\frac{98}{98}\right)\left(\frac{1}{99}+\frac{99}{99}\right)\)

\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{99}{98}.\frac{100}{99}\)

\(=\frac{3.4.5....99.100}{2.3.4...98.99}\)

\(=\frac{100}{2}=50\)

15 tháng 10 2016

Nguyễn Huy Tú cậu on ko giúp tớ với

 

15 tháng 10 2016

mik ko biết bài này Leona