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4 tháng 9 2022
a: \(=5-2\cdot\dfrac{1}{4}=5-\dfrac{1}{2}=\dfrac{9}{2}\)
b: \(=\left(\dfrac{7}{2}\right)^3+\dfrac{1}{2}=\dfrac{343}{8}+\dfrac{1}{2}=\dfrac{347}{8}\)
c: \(=\left(5+\dfrac{5}{27}-\dfrac{5}{27}\right)+\left(\dfrac{7}{23}+\dfrac{16}{23}\right)-\dfrac{1}{2}=5+1-\dfrac{1}{2}=5+\dfrac{1}{2}=5.5\)
e: \(=\dfrac{-5}{4}\left(35+\dfrac{1}{6}-45-\dfrac{1}{6}\right)=\dfrac{-5}{4}\cdot\left(-10\right)=\dfrac{50}{4}=\dfrac{25}{2}\)
ND
2
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
18 tháng 1 2024
\(\dfrac{-27}{45}\) = \(\dfrac{6}{-x}\)= \(\dfrac{y}{5}\)
\(\dfrac{-3}{5}\) = \(\dfrac{-6}{x}\) = \(\dfrac{y}{5}\)
\(x\) = (-6) : (\(\dfrac{-3}{5}\))
\(x\) = 10
y = (-\(\dfrac{3}{5}\)).5 = -3
Vậy (\(x\);y) = (10; -3)
AT
26 tháng 4 2017
a/ \(P=\dfrac{x-\dfrac{1}{3}}{3.25-x}>0\)
=> \(\left[{}\begin{matrix}x-\dfrac{1}{3}>0;75-x>0\\x-\dfrac{1}{3}< 0;75-x< 0\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x>\dfrac{1}{3};x< 75\\x< \dfrac{1}{3};x>75\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}\dfrac{1}{3}< x< 75\\75< x< \dfrac{1}{3}\left(vôlý\right)\end{matrix}\right.\)
Vậy \(\dfrac{1}{3}< x< 75\) để P > 0
b/ \(Q=\dfrac{x+3}{2x-5}< 0\)
TH1: \(\left\{{}\begin{matrix}x+3>0\\2x-5< 0\Rightarrow2x< 5\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}x>-3\\x< \dfrac{5}{2}\end{matrix}\right.\) => \(-3< x< \dfrac{5}{2}\)
TH2: \(\left\{{}\begin{matrix}x+3< 0\\2x-5>0\Rightarrow2x>5\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x< -3\\x>\dfrac{5}{2}\end{matrix}\right.\) (vô lý)
Vậy \(-3< x< \dfrac{5}{2}\) để Q < 0
17 tháng 12 2017
\(\dfrac{45^4.5^8}{75^6}=\dfrac{\left(5.9\right)^4.5^8}{\left(15.5\right)^6}=\dfrac{5^4.9^4.5^8}{15^6.5^6}=\dfrac{5^4.3^{2^4}.5^8}{\left(3.5\right)^6.5^6}=\dfrac{5^4.3^8.5^8}{3^6.5^6.5^6}=\dfrac{3^2.5^2}{5^2}=3^2=9\)
17 tháng 12 2017
\(\dfrac{45^4.5^8}{75^6}=\dfrac{5^4.9^4.5^8}{3^6.5^6.5^6}=\dfrac{1.\left(3^2\right)^4.5^2}{3^6.5^2.1}=\dfrac{3^8.1}{3^6.1}=\dfrac{3^8}{3^6}=\dfrac{3^2}{1}=9\)
TP
1
24 tháng 5 2022
\(=\dfrac{3^6\cdot\left(3^2\right)^4\cdot5^4-5^{13}\cdot3^{13}\cdot5^{-9}}{3^{12}\cdot5^6+\left(3^2\right)^6\cdot5^6}\)
\(=\dfrac{3^{14}\cdot5^4-5^4\cdot3^{13}}{3^{12}\cdot5^6+3^{12}\cdot5^6}=\dfrac{3^{13}\cdot5^4\cdot2}{2\cdot3^{12}\cdot5^6}=\dfrac{3}{5^2}=\dfrac{3}{25}\)
J
3
5 tháng 8 2018
tử số=3^6.45^4-15^13.5^-9=3^6.(5.3^2)^4-(3.5)^13.5^-9=3^6.5^4.3^8-3^13.5^13.5^-9=3^14.5^4-3^13.5^4(3-1)=2.3^13.5^4
mẫu số=27^4.25^3+45^6=3^12.5^6+3^12.5^6=2.3^12.5^6
phân số =(2.3^13.5^4)/2.3^12.5^6=3/25
J
1
12 tháng 8 2022
\(=\dfrac{3^{14}\cdot5^4-3^{13}\cdot5^4}{3^{12}\cdot5^6+3^{12}\cdot5^6}\)
\(=\dfrac{3^{13}\cdot5^4\cdot\left(3-1\right)}{2\cdot3^{12}\cdot5^6}=\dfrac{9}{25}\)
2 tháng 11 2017
a,\(A=\dfrac{1}{3.4}+\dfrac{1}{4.5}...+\dfrac{1}{29+30}\)
\(A=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{29}-\dfrac{1}{30}\)
\(A=\dfrac{1}{3}-\dfrac{1}{30}\)
\(A=\dfrac{9}{30}=\dfrac{3}{10}.\)
b, \(B=\dfrac{4}{7.11}+\dfrac{9}{11.20}+\dfrac{5}{20.25}\)
\(B=\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{20}+\dfrac{1}{20}-\dfrac{1}{25}\)
\(B=\dfrac{1}{7}-\dfrac{1}{25}\)
\(B=\dfrac{18}{175}\).
2 tháng 6 2017
\(1:5\dfrac{25}{7}+\dfrac{27}{23}+0,5-\dfrac{5}{27}+\dfrac{16}{23}\)
\(=\dfrac{60}{7}+\left(\dfrac{27}{23}+\dfrac{16}{23}\right)+0,5-\dfrac{5}{27}\)
\(=\dfrac{60}{7}+\dfrac{43}{23}+0,5-\dfrac{5}{27}\)
\(=\dfrac{1681}{161}+\dfrac{1}{2}-\dfrac{5}{27}\)
\(=\dfrac{3523}{322}-\dfrac{5}{27}\)
\(=10,7558086\)
\(2:\left(-0,75-\dfrac{1}{4}\right):\left(-5\right)+\dfrac{1}{15}-\left(-\dfrac{1}{5}\right):\left(-3\right)\)
\(=-1:\left(-0,5\right)+\dfrac{1}{15}-\dfrac{1}{15}\)
\(=2+0=2\)
PT
28 tháng 2 2017
\(S=\dfrac{5}{1.2}+\dfrac{13}{2.3}+\dfrac{25}{3.4}+\dfrac{41}{4.5}+...+\dfrac{181}{9.10}\)
\(S=\dfrac{\left(1^2+2^2\right)}{1.2}+\dfrac{\left(2^2+3^2\right)}{2.3}+...+\dfrac{\left(9^2+10^2\right)}{9.10}\)
\(S=\dfrac{\left\{\left(1-2\right)^2+2.1.2\right\}}{1.2}+\dfrac{\left\{\left(2-3\right)^2+2.2.3\right\}}{2.3}+...+\dfrac{\left\{\left(9-10\right)^2+2.9.10\right\}}{9.10}\)
\(S=\dfrac{\left\{\left(-1\right)^2\right\}}{1.2+2}+\dfrac{\left\{\left(-1\right)^2\right\}}{2.3+2}+...+\dfrac{\left\{\left(-1\right)^2\right\}}{9.10+2}\)
\(S=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}+2.9\)
\(S=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}+18\)
\(S=1-\dfrac{1}{10}+18\)
\(S=\dfrac{189}{10}\)
Có sai thì đừng ném đá nha tội mình ~~
\(\dfrac{45^4.5^5}{27^3.25^4}=\dfrac{9^4.5^4.5^5}{3^9.5^8}=\dfrac{3^8.5^9}{3^9.5^8}=\dfrac{5}{3}\)
\(\dfrac{45^{4^{ }}.5^5}{27^3.25^4}\) = \(\dfrac{9^4.5^4.5^5}{^{ }9^{3^{ }}.3^3.5^{4^{ }}.5^4}\)= \(\dfrac{9.5}{3^3}\)=\(\dfrac{5}{3}\)