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1:
a: =7/5(40+1/4-25-1/4)-1/2021
=21-1/2021=42440/2021
b: =5/9*9-1*16/25=5-16/25=109/25
Lời giải:
a. $\frac{2-x}{4}=\frac{3x-1}{3}$
$\Rightarrow 3(2-x)=4(3x-1)$
$\Rightarrow 6-3x=12x-4$
$\Rightarrow 6+4=12x+3x$
$\Rightarrow 10=15x$
$\Rightarrow x=\frac{10}{15}=\frac{2}{3}$
b.
$\frac{x}{7}=\frac{x+16}{35}$
$\Rightarrow \frac{5x}{35}=\frac{x+16}{35}$
$\Rightarrow 5x=x+16$
$\Rightarrow 4x=16$
$\Rightarrow x=4$
c.
$\sqrt{x^2+1}=3$
$\Rightarrow x^2+1=9$
$\Rightarrow x^2=8\Rightarrow x=\pm \sqrt{8}=\pm 2\sqrt{2}$
a: \(=\dfrac{-8}{9}-\dfrac{6}{5}+\dfrac{8}{9}=-\dfrac{6}{5}\)
c: \(=\dfrac{2}{3}-\dfrac{1}{3}=\dfrac{1}{3}\)
a: \(=2\cdot\dfrac{5}{4}-3\cdot\dfrac{7}{6}+4\cdot\dfrac{9}{8}=\dfrac{5}{2}-\dfrac{7}{2}+\dfrac{9}{2}=\dfrac{7}{2}\)
b: \(=18-16\cdot\dfrac{1}{2}+\dfrac{1}{16}\cdot\dfrac{3}{4}\)
=10+3/64
=643/64
c: \(=\dfrac{2}{3}\cdot\dfrac{9}{4}-\dfrac{3}{4}\cdot\dfrac{8}{3}+\dfrac{7}{5}\cdot\dfrac{5}{14}=\dfrac{3}{2}-2+\dfrac{1}{2}=2-2=0\)
a) \(4.\left(-\dfrac{1}{2}\right)^3-2.\left(-\dfrac{1}{2}\right)^2+3.\left(-\dfrac{1}{2}\right)+1\)
\(=4.\left(-\dfrac{1}{8}\right)-2.\dfrac{1}{4}+3.\left(-\dfrac{1}{2}\right)+1\)
\(=-\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{3}{2}+1\)
\(=-\dfrac{3}{2}\)
b) \(8.\sqrt{9}-\sqrt{64}\)
\(=8.3-8\)
\(=24-8\)
\(=16\)
c) \(\sqrt{\dfrac{9}{16}}+\dfrac{25}{46}:\dfrac{5}{23}-\dfrac{7}{4}\)
\(=\dfrac{3}{4}+\dfrac{5}{2}-\dfrac{7}{4}\)
\(=-1+\dfrac{5}{2}\)
\(=\dfrac{3}{2}\)
a) \(\dfrac{x}{-9}=\dfrac{-40}{45}\)
\(\Leftrightarrow x.45=\left(-9\right).\left(-40\right)\)
\(\Leftrightarrow x.45=360\)
\(\Leftrightarrow x=\dfrac{360}{45}=8\)
Vậy x=8
b: \(\Leftrightarrow\left|2x+\dfrac{1}{3}\right|+\dfrac{4}{9}=-5+\dfrac{4}{9}\)
=>|2x+1/3|=-5(vô lý)
a: \(\Leftrightarrow x=\dfrac{-40\cdot\left(-9\right)}{45}=8\)
a) Vì \(\dfrac{x}{y} = \dfrac{5}{3} \Rightarrow \dfrac{x}{5} = \dfrac{y}{3}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\begin{array}{l}\dfrac{x}{5} = \dfrac{y}{3} = \dfrac{{x + y}}{{5 + 3}} = \dfrac{{16}}{8} = 2\\ \Rightarrow x = 2.5 = 10\\y = 2.3 = 6\end{array}\)
Vậy x=10, y=6
b) Vì \(\dfrac{x}{y} = \dfrac{9}{4} \Rightarrow \dfrac{x}{9} = \dfrac{y}{4}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\begin{array}{l}\dfrac{x}{9} = \dfrac{y}{4} = \dfrac{{x - y}}{{9 - 4}} = \dfrac{{ - 15}}{5} = - 3\\ \Rightarrow x = ( - 3).9 = - 27\\y = ( - 3).4 = - 12\end{array}\)
Vậy x = -27, y = -12.
\(\dfrac{3}{2}-|x-\dfrac{3}{4}|=\sqrt{\dfrac{9}{16}}\)
⇔ \(\dfrac{3}{2}-|x-\dfrac{3}{4}|=\dfrac{3}{4}\)
⇔ \(|x-\dfrac{3}{4}|=-\dfrac{3}{4}\)
⇔ \(x-\dfrac{3}{4}=-\dfrac{3}{4}\) hoặc \(x-\dfrac{3}{4}=\dfrac{3}{4}\)
⇔ \(x\) \(=0\) ⇔ \(x\) \(=\dfrac{3}{2}\)
Vậy pt có nghiệm : \(x=0\) hoặc \(x=\dfrac{3}{2}\)