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thích làm mỗi bài 3 vi các bai khac vua de, vua dai viet mệt
3) 3n : 3n-1 = 3n-n+1 = 3
Số nguyên n thỏa mãn đẳng thức -81/(-3)^n =-243 <=> (-3)^n x (-243) = -81 <=> (-3)^n x (-3)^5 = (-3)^4
<=> (-3)^n = (-3)^4 : (-3)^5 <=> (-3)^n = (-3)^4-5 <=> (-3)^n = (-3)^(-1) => n=-1.
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=\(\frac{\left(-2\right)^8}{5^4}\times\frac{\left(-1\right)^2}{2^2}\div\frac{\left(-1\right)^3}{5^3}\)
=\(\frac{2^8}{5^4}\times\frac{1}{2^2}\times\frac{-5^3}{1}\)
=\(\frac{-64}{5}\)
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a, \(2,5:4x=0,5:0,2\)
\(\Rightarrow4x=\dfrac{2,5.0,2}{0,5}\)
\(\Rightarrow4x=1\Rightarrow x=\dfrac{1}{4}\)
b, \(\dfrac{1}{5}x:3=\dfrac{2}{3}:0,5\)
\(\Rightarrow\dfrac{1}{5}x=\dfrac{3.\dfrac{2}{3}}{0,5}\)
\(\Rightarrow\dfrac{1}{5}x=4\Rightarrow x=20\)
c, \(1,25:0,8=\dfrac{3}{8}:0,2x\)
\(\Rightarrow0,2x=\dfrac{0,8.\dfrac{3}{8}}{1,25}\)
\(\Rightarrow0,2x=0,24\Rightarrow x=1,2\)
Chúc bạn học tốt!!
a, \(2,5:4x=0,5:0,2\)
\(2,5:4x=2,5\)
\(4x=2,5:2,5\)
\(4x=1\)
\(x=1:4\)
\(x=\dfrac{1}{4}\)
Vậy .............
b, \(\dfrac{1}{5}x:3=\dfrac{2}{3}\)
\(\dfrac{1}{5}x=\dfrac{2}{3}.3\)
\(\dfrac{1}{5}x=2\)
\(x=2:\dfrac{1}{5}\)
\(x=10\)
Vậy .....
c, \(1,25:0,8=\dfrac{3}{8}:0,2x\)
\(1,5625=\dfrac{3}{8}:0,2x\)
\(0,2x=\dfrac{3}{8}:1,5625\)
\(0,2x=0,24\)
\(x=0,24:0,2\)
\(x=1,2\)
Vậy ...
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Bài 1:
a) 0,24 = 6/25
b) 0,245 = 49/200
c) 2,5324 = 5/2
d) 0,5 = 1/2
a) \(0,\left(24\right)=\frac{24}{99}=\frac{8}{33}\)
b)\(0,2\left(45\right)=\frac{245-2}{990}=\frac{243}{990}=\frac{27}{110}\)
c)\(2,5\left(324\right)=2+0,5\left(324\right)=2+\frac{5324-5}{9990}=2+\frac{197}{370}=\frac{937}{370}\)
d) \(0,5\left(3\right)=\frac{53-5}{90}=\frac{48}{90}=\frac{8}{15}\)
Bài 2 : \(M=\frac{0,5+0,\left(3\right)-0,1\left(6\right)}{2,5+1,\left(6\right)-0,8\left(3\right)}\)
\(M=\frac{\frac{1}{2}+\frac{1}{3}-\frac{16-1}{90}}{\frac{5}{2}+\frac{5}{3}-\frac{83-8}{90}}\)
\(M=\frac{\frac{1}{2}+\frac{1}{3}-\frac{1}{6}}{\frac{5}{2}+\frac{5}{3}-\frac{5}{6}}=\frac{\frac{1}{2}+\frac{1}{3}-\frac{1}{6}}{5\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{6}\right)}=\frac{1}{5}\)
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a ) \(\frac{-3}{7}+x=\frac{1}{3}\Rightarrow x=\frac{1}{3}-\frac{-3}{7}\Rightarrow x=\frac{16}{21}\)
b) \(\frac{3}{4}+\frac{1}{4}:x=\frac{2}{5}\Rightarrow\frac{1}{4}:x=\frac{2}{5}-\frac{3}{4}\Rightarrow\frac{1}{4}:x=-\frac{7}{20}\Rightarrow x=\frac{1}{4}:\left(-\frac{7}{20}\right)=-\frac{5}{7}\)
c) \(1\frac{1}{3}:0,8=\frac{2}{3}:0,1x\Rightarrow\frac{2}{3}:0,1x=\frac{5}{3}\Rightarrow0,1x=\frac{2}{5}\Rightarrow x=4\)
d) \(\left|x-3\right|=\frac{1}{2}\Rightarrow\orbr{\begin{cases}x-3=\frac{1}{2}\\x-3=-\frac{1}{2}\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{7}{2}\\x=\frac{5}{2}\end{cases}}}\)
e) \(1\frac{1}{2}.x-4=0,5\Rightarrow\frac{3}{2}x=4,5\Rightarrow x=3\)
g) \(2^{x-1}=16\Rightarrow2^{x-1}=2^4\Rightarrow x-1=4\Rightarrow x=5\)
h) \(\left(x-1\right)^2=25\Rightarrow\orbr{\begin{cases}x-1=5\\x-1=-5\end{cases}\Rightarrow\orbr{\begin{cases}x=6\\x=-4\end{cases}}}\)
i) \(\left|2x-1\right|=5\Rightarrow\orbr{\begin{cases}2x-1=5\\2x-1=-5\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\x=-2\end{cases}}}\)
k) \(0,2-\left|4,2-2x\right|=0\Rightarrow\left|4,2-2x\right|=0,2\Rightarrow\orbr{\begin{cases}4,2-2x=0,2\\4,2-2x=-0,2\end{cases}\Rightarrow\orbr{\begin{cases}x=2\\x=2,2\end{cases}}}\)
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a)\(\frac{7}{3}.\left( { - 2,5} \right).\frac{6}{7} = \frac{7}{3}.\frac{6}{7}.\left( { - 2,5} \right) = 2.\left( { - 2,5} \right) = - 5\)
b)
\(\begin{array}{l}0,8.\frac{{ - 2}}{9} - \frac{4}{5}.\frac{7}{9} - 0,2\\ = \frac{4}{5}.\frac{{ - 2}}{9} - \frac{4}{5}.\frac{7}{9}-\frac{2}{10}\\ = \frac{4}{5}.\left( {\frac{{ - 2}}{9} - \frac{7}{9}} \right) -\frac{1}{5}\\ = \frac{4}{5}.\left( { - 1} \right)-\frac{1}{5} \\= \frac{{ - 4}}{5}-\frac{1}{5}\\=\frac{-5}{5}\\=-1.\end{array}\)
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\(\left(-2,5\right).\left(-4\right)=10\)
\(\left(-2,5\right).0,5.\left(-2\right).2=\left[\left(-2,5\right).\left(-2\right).\left(0,5.2\right)\right]=5.1=5\)
\(\left(-0,5\right).0,5.\left(-2\right).2=\left[\left(-0,5\right).\left(-2\right).\left(0,5.2\right)\right]=1.1=1\)
\(25.\left(-5\right).\left(-0,4\right).\left(-0,2\right)=\left[25.\left(-0,4\right).\left(-5\right).\left(-0,2\right)\right]=-10.1=-10\)