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10 tháng 10 2023

h) x/y = 9/10 ⇒  y/10 = x/9

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

y/10 = x/9 = (y - x)/(10 - 9) = 120/1 = 120

*) x/9 = 120 ⇒ x = 120.9 = 1080

*) y/10 = 120 ⇒ y = 120.10 = 1200

Vậy x = 1080; y = 1200

k) x/y = 3/4

⇒ x/3 = y/4

⇒ 5y/20 = 3x/9

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

5y/20 = 3x/9 = (5y - 3x)/(20 - 9) = 33/11 = 3

*) 3x/9 = 3 ⇒ x = 3.9:3 = 9

*) 5y/20 = 3 ⇒ y = 3.20:5 = 12

Vậy x = 9; y = 12

30 tháng 9 2023

\(2\left(x-3\right)+3x+0,5=\dfrac{3}{4}\\ \Leftrightarrow2x-6+3x+\dfrac{1}{2}=\dfrac{3}{4}\\ \Leftrightarrow x\left(2+3\right)=\dfrac{3}{4}-\dfrac{1}{2}+6\\ \Leftrightarrow5x=\dfrac{25}{4}\\ \Leftrightarrow x=\dfrac{25}{4}:5=\dfrac{5}{4}\\ ---\\ 4^{x+2}+4^x=272\\ \Leftrightarrow4^x\left(4^2+1\right)=272\\ \Leftrightarrow4^x.17=272\\ \Leftrightarrow4^x=\dfrac{272}{17}=16=4^2\\ Vậy:x=2\\ ----\\ \left(1,2-5x\right)\left(2\dfrac{1}{8}+\dfrac{1}{2}x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}1,2-5x=0\\2,125+0,5x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5x=1,2\\0,5x=-2,125\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1,2}{5}=0,24\\x=\dfrac{-2,125}{0,5}=-4,25\end{matrix}\right.\)

1 tháng 10 2023

a) \(2\left(x-3\right)+3x+0,5=\dfrac{3}{4}\)

\(\Rightarrow2x-6+3x+\dfrac{1}{2}=\dfrac{3}{4}\)

\(\Rightarrow5x-6=\dfrac{3}{4}-\dfrac{1}{2}\)

\(\Rightarrow5x-6=\dfrac{1}{4}\)

\(\Rightarrow5x=\dfrac{1}{4}+6\)

\(\Rightarrow5x=\dfrac{25}{4}\)

\(\Rightarrow x=\dfrac{25}{4}:5\)

\(\Rightarrow x=\dfrac{5}{4}\)

b) \(4^{x+2}+4^x=272\)

\(\Rightarrow4^x\cdot4^2+4^x\cdot1=272\)

\(\Rightarrow4^x\cdot\left(16+1\right)=272\)

\(\Rightarrow4^x\cdot17=272\)

\(\Rightarrow4^x=16\)

\(\Rightarrow4^x=4^2\)

\(\Rightarrow x=2\)

c) \(\left(1,2-5x\right)\left(2\dfrac{1}{8}+\dfrac{1}{2}x\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}1,2-5x=0\\\dfrac{15}{8}+\dfrac{1}{2}x=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}5x=1,2\\\dfrac{1}{2}x=-\dfrac{15}{8}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1,2}{5}\\x=-\dfrac{15}{8}:\dfrac{1}{2}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{6}{25}\\x=-\dfrac{15}{4}\end{matrix}\right.\)

19 tháng 10 2021

\(a,\Leftrightarrow\left[{}\begin{matrix}-\dfrac{4}{3}x+\dfrac{1}{2}=\dfrac{1}{2}\\-\dfrac{4}{3}x+\dfrac{1}{2}=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{3}{4}\end{matrix}\right.\\ c,\Leftrightarrow\left(\dfrac{1}{2}\right)^x\left(1+\dfrac{1}{4}\right)=\dfrac{5}{4}\\ \Leftrightarrow\left(\dfrac{1}{2}\right)^x=1\Leftrightarrow x=0\)

19 tháng 10 2021

b: Ta có: \(3^x+3^{x+2}=20\)

\(\Leftrightarrow3^x\cdot10=20\)

\(\Leftrightarrow3^x=2\left(loại\right)\)

31 tháng 10 2023

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12 tháng 11 2021

\(\Rightarrow\left[{}\begin{matrix}2^{x+1}=8=2^3\\\dfrac{x}{3}=\dfrac{3}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x+1=3\\x=\dfrac{3\cdot3}{4}=\dfrac{9}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{9}{4}\end{matrix}\right.\)

12 tháng 11 2021

\(\Leftrightarrow\left[{}\begin{matrix}2^{x+1}=8\\\dfrac{x}{3}=\dfrac{3}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{9}{4}\end{matrix}\right.\)

24 tháng 7 2017

mn ơi giúp nhé

a: \(\dfrac{31-2x}{x+23}=\dfrac{9}{4}\)

=>121-8x=9x+207

=>-17x=86

hay x=-86/17

b: \(\dfrac{\left|2x-1\right|}{\dfrac{1}{2}}=\dfrac{18}{5}\)

=>|2x-1|=9/5

=>2x-1=9/5 hoặc 2x-1=-9/5

=>2x=14/5 hoặc 2x=-4/5

=>x=7/5 hoặc x=-2/5

a: \(A=\left(5xy-2xy+4xy\right)+3x-2y-y^2\)

\(=7xy+3x-2y-y^2\)

b: \(B=\left(\dfrac{1}{2}ab^2-\dfrac{7}{8}ab^2-\dfrac{1}{2}ab^2\right)+\left(\dfrac{3}{4}a^2b-\dfrac{3}{8}a^2b\right)\)

\(=\dfrac{-7}{8}ab^2+\dfrac{3}{8}a^2b\)

c: \(C=\left(2a^2b+5a^2b\right)+\left(-8b^2-3b^2\right)+\left(5c^2+4c^2\right)\)

\(=7a^2b-11b^2+9c^2\)

23 tháng 5 2022

\(A=5xy-y^2-2xy+4xy+3x-2y\)

\(A=-y^2+7xy+3x-2y\)

\(B=\dfrac{1}{2}ab^2-\dfrac{7}{8}ab^2+\dfrac{3}{4}a^2b-\dfrac{3}{8}a^2b-\dfrac{1}{2}ab^2\)

\(B=\dfrac{3}{8}a^2b-\dfrac{7}{8}ab^2\)

\(C=2a^2b-8b^2+5a^2b+5c^2-3b^2+4c^2\)

\(C=7a^2b-11b^2+9c^2\)

10 tháng 9 2017

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

\(\Leftrightarrow\dfrac{-1}{15}+3x=\dfrac{3}{4}\)

\(\Leftrightarrow3x=\dfrac{49}{60}\)

\(\Leftrightarrow x=\dfrac{49}{180}\)

Vậy....

b/ \(\dfrac{3}{2}-1+4x=\dfrac{2}{3}-7x\)

\(\Leftrightarrow\dfrac{1}{2}+4x=\dfrac{2}{3}-7x\)

\(\Leftrightarrow4x+7x=\dfrac{2}{3}-\dfrac{1}{2}\)

\(\Leftrightarrow11x=\dfrac{1}{6}\)

\(\Leftrightarrow x=\dfrac{1}{66}\)

Vậy....

c/ \(2\left(\dfrac{3}{4}-5x\right)=\dfrac{4}{5}-3x\)

\(\Leftrightarrow\dfrac{3}{2}-10x=\dfrac{4}{5}-3x\)

\(\Leftrightarrow-10x+3x=\dfrac{4}{5}-\dfrac{3}{2}\)

\(\Leftrightarrow-7x=-\dfrac{7}{10}\)

\(\Leftrightarrow x=-\dfrac{1}{10}\)

Vậy .....

10 tháng 9 2017

d/ \(4\left(\dfrac{1}{2}-x\right)-5\left(x-\dfrac{3}{10}\right)=\dfrac{7}{4}\)

\(\Leftrightarrow2-4x-5x-\dfrac{3}{2}=\dfrac{7}{4}\)

\(\Leftrightarrow2+\left(-4x\right)+\left(-5x\right)+\left(\dfrac{-3}{2}\right)=\dfrac{7}{4}\)

\(\Leftrightarrow-9x+\dfrac{1}{2}=\dfrac{7}{4}\)

\(\Leftrightarrow-9x=\dfrac{5}{4}\)

\(\Leftrightarrow x=-\dfrac{5}{36}\)