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(x-\(\frac{1}{3}\)):\(\frac{-12}{45}\)+1=\(\frac{1}{3}\)
(x-\(\frac{1}{3}\)):\(\frac{-12}{45}\)=\(\frac{1}{3}\)+1
(x-\(\frac{1}{3}\)):\(\frac{-12}{45}\)=\(\frac{4}{3}\)
(x-\(\frac{1}{3}\))=\(\frac{4}{3}\)x\(\frac{-12}{45}\)
(x-\(\frac{1}{3}\))=\(\frac{-16}{45}\)
x=\(\frac{-16}{45}\)+\(\frac{1}{3}\)
x=\(\frac{-1}{45}\)
\(H=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(\Rightarrow H=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(\Rightarrow\frac{3H}{5}=\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\)
\(\Rightarrow\frac{3H}{5}=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\)
\(\Rightarrow\frac{3H}{5}=\frac{1}{4}-\frac{1}{28}\)
\(\Rightarrow\frac{3H}{5}=\frac{3}{14}\)
\(\Rightarrow H=\frac{3}{14}.\frac{5}{3}\)
\(\Rightarrow H=\frac{5}{14}\)
Vậy \(H=\frac{5}{14}\)
Số cam trong vườn là :
450 . \(\frac{2}{5}\) = 180 ( cây )
Số hồng xiêm trong vườn là :
450 . 50% = 225 ( cây )
Số bưởi trong vườn là :
450 - 180 - 225 = 45 ( cây )
Đ/s : 45 cây bưởi
a) \(2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|-\dfrac{3}{2}=\dfrac{1}{5}\)
\(2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{1}{5}+\dfrac{3}{2}\)
\(2\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{17}{10}\)
\(\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{17}{10}:2\)
\(\left|\dfrac{1}{2}x-\dfrac{1}{3}\right|=\dfrac{17}{20}\)
\(\circledast\)TH1: \(\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{17}{20}\)
\(\dfrac{1}{2}x=\dfrac{17}{20}+\dfrac{1}{3}\)
\(\dfrac{1}{2}x=\dfrac{71}{60}\)
\(x=\dfrac{71}{60}:\dfrac{1}{2}\)
\(x=\dfrac{71}{30}\)
\(\circledast\)TH2: \(\dfrac{1}{2}x-\dfrac{1}{3}=-\dfrac{17}{20}\)
\(\dfrac{1}{2}x=-\dfrac{17}{20}+\dfrac{1}{3}\)
\(\dfrac{1}{2}x=-\dfrac{31}{60}\)
\(x=-\dfrac{31}{60}:\dfrac{1}{2}\)
\(x=-\dfrac{31}{30}\)
Vậy \(x\in\left\{\dfrac{71}{30};-\dfrac{31}{30}\right\}\).
b) \(\dfrac{3}{4}-2\left|2x-\dfrac{2}{3}\right|=2\)
\(2\left|2x-\dfrac{2}{3}\right|=\dfrac{3}{4}-2\)
\(2\left|2x-\dfrac{2}{3}\right|=-\dfrac{5}{4}\)
\(\left|2x-\dfrac{2}{3}\right|=-\dfrac{5}{4}:2\)
\(\left|2x-\dfrac{2}{3}\right|=-\dfrac{5}{8}\) (vô lí)
Vậy \(x\in\varnothing \).
c) \(\left(3x-1\right)\left(-\dfrac{1}{2}x+5\right)=0\)
\(\circledast\)TH1: \(3x-1=0\)
\(3x=0+1\)
\(3x=1\)
\(x=\dfrac{1}{3}\)
\(\circledast\)TH2: \(-\dfrac{1}{2}x+5=0\)
\(-\dfrac{1}{2}x=0-5\)
\(-\dfrac{1}{2}x=-5\)
\(x=-5:\left(-\dfrac{1}{2}\right)\)
\(x=10\)
Vậy \(x\in\left\{\dfrac{1}{3};10\right\}\).
A = 10,11 + 11,12 + 12,13 + . . .+ 98,99 + 99,10
Ta có :
10,11 = 10 + 0,11
11,12 = 11 + 0,12
12,13 = 12 + 0,13
. . . . . . . . . . . . . .
97,98 = 97 + 0,98
98,99 = 98 + 0,99
99,10 = 99 + 0,10
Đặt B = 10 + 11 + 12 + 13 + . .. +98 + 99
và C = 0,11 + 0,12 + 0,13 + . . . .+ 0,98 + 0,99 + 0,10
- - > 100C = 11 + 12 + 13 + . . .+ 98 + 99 + 10
Ta chỉ việc tính B là suy ra C !
B = 10 + 11 + 12 + 13 + . .. +98 + 99
B = (10+99)+(11+98)+(12+97)+. . . +(44+65) + (45 + 64)
Vì từ 10 đến 99 có tất cả 90 số . Ta sẽ có 90/2 = 45 cặp
Mỗi cặp có tổng là 10 + 99 = 11 + 98 = . .= 45 +64 = 109
Vậy ta có B = 45.109 = 4905
Với A = 4905 . Ta thấy 100C = 10 + 11 + 12 +. . + 98 + 99 =B
- - > 100C = 4905 . Hay C = 4905/100 = 49,05
Vậy A = B + C = 4905 + 49,05 = 4954,05
Ta có:
\(\dfrac{2008}{2009}>\dfrac{2008}{2009+2010+2011}\)
\(\dfrac{2009}{2010}>\dfrac{2009}{2009+2010+2011}\)
\(\dfrac{2010}{2011}>\dfrac{2010}{2009+2010+2011}\)
Do đó: \(\dfrac{2008}{2009}+\dfrac{2009}{2010}+\dfrac{2010}{2011}>\dfrac{2008+2009+2010}{2009+2010+2011}\)
\(\Rightarrow A>B\)
=> A > B