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b, Áp dụng t/c dtsbn:

\(x:y:z=2:5:7\Rightarrow\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{x-y+z}{2-5+7}=\dfrac{25}{4}\\ \Rightarrow\left\{{}\begin{matrix}x=\dfrac{25}{2}\\y=\dfrac{125}{4}\\z=\dfrac{175}{4}\end{matrix}\right.\)

c, Áp dụng t/c dstbn:

\(\dfrac{x}{2}=\dfrac{y}{3};\dfrac{y}{4}=\dfrac{z}{5}\Rightarrow\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{x+y-z}{8+12-15}=\dfrac{10}{5}=2\\ \Rightarrow\left\{{}\begin{matrix}x=16\\y=24\\z=30\end{matrix}\right.\)

d, Áp dụng t/c dstbn:

\(\dfrac{x}{2}=\dfrac{y}{3};\dfrac{y}{4}=\dfrac{z}{5}\Rightarrow\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{x-y-2z}{8-12-2\cdot15}=\dfrac{36}{-34}=-\dfrac{18}{17}\\ \Rightarrow\left\{{}\begin{matrix}x=-\dfrac{144}{17}\\y=-\dfrac{216}{17}\\z=-\dfrac{270}{17}\end{matrix}\right.\)

e, Áp dụng t/c dtsbn:

\(x:y:z=3:5:\left(-2\right)\Rightarrow\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{-2}=\dfrac{5x-y+3z}{3\cdot5-5+3\left(-2\right)}=\dfrac{12}{4}=3\\ \Rightarrow\left\{{}\begin{matrix}x=9\\y=15\\z=-6\end{matrix}\right.\)

Gọi tỉ lệ cắt giảm mỗi năm của công ty là \(x\left(\%\right)\) hay \(\dfrac{x}{100}\) với \(0\le x\le100\)

Số công nhân còn lại sau năm thứ nhất là:

\(10000\left(1-\dfrac{x}{100}\right)\)

Số công nhân còn lại sau năm thứ hai là:

\(10000.\left(1-\dfrac{x}{100}\right)\left(1-\dfrac{x}{100}\right)=10000.\left(1-\dfrac{x}{100}\right)^2\)

Do sau 2 năm công ty còn lại 9000 công nhân nên:

\(10000\left(1-\dfrac{x}{100}\right)^2=9000\)

\(\Rightarrow1-\dfrac{x}{100}=\dfrac{3}{\sqrt{10}}\Rightarrow x=100-30\sqrt{10}\) (%)\(\approx5,13\left(\%\right)\)

1. 5

2. 43/31

3. >

4. 35/24

5. 16/33

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