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2:
Xét ΔBAD và ΔABC có
AB chung
BD=AC
AD=BC
=>ΔBAD=ΔABD
=>góc OAB=góc OBA
=>OA=OB
OA+OC=AC
OB+OD=BD
mà OA=OB và AC=BD
nên OC=OD
1:
a: Xét ΔABC có AD/AB=AE/AC
nên DE//BC
=>BDEC là hình thang
mà góc B=góc C
nên BDEC là hình thang cân
b: góc B=góc C=(180-50)/2=65 độ
góc BDE=góc DEC=180-65=115 độ
Bài 4:
Gọi vận tốc dự định là x
Thời gian dự định là: \(\dfrac{60}{x}\)
Thời gian thực tế là: \(\dfrac{30}{x+10}+\dfrac{30}{x-6}\)
Theo đề, ta có: \(\dfrac{30}{x+10}+\dfrac{30}{x-6}=\dfrac{60}{x}\)
\(\Leftrightarrow\dfrac{1}{x+10}+\dfrac{1}{x-6}=\dfrac{2}{x}\)
Suy ra: \(x\left(x-6\right)+x\left(x+10\right)=2\left(x+10\right)\left(x-6\right)\)
\(\Leftrightarrow2\left(x^2+4x-60\right)=x^2-6x+x^2+10x\)
\(\Leftrightarrow8x-120-4x=0\)
\(\Leftrightarrow4x=120\)
hay x=30
Vậy: Thời gian dự định là 2 giờ
Bài 2:
1: ĐKXĐ: x<>1
\(\dfrac{x}{x-1}+\dfrac{1}{1-x}\)
\(=\dfrac{x}{x-1}-\dfrac{1}{x-1}\)
\(=\dfrac{x-1}{x-1}=1\)
2: ĐKXĐ: x<>3/2
\(\dfrac{11x}{2x-3}-\dfrac{x-18}{3-2x}\)
\(=\dfrac{11x}{2x-3}+\dfrac{x-18}{2x-3}\)
\(=\dfrac{11x+x-18}{2x-3}=\dfrac{12x-18}{2x-3}\)
\(=\dfrac{6\left(2x-3\right)}{2x-3}\)
=6
3: ĐKXĐ: x<>1/2
\(\dfrac{4x+5}{2x-1}+\dfrac{5-9x}{1-2x}\)
\(=\dfrac{4x+5}{2x-1}+\dfrac{9x-5}{2x-1}\)
\(=\dfrac{4x+5+9x-5}{2x-1}=\dfrac{13x}{2x-1}\)
4: ĐKXĐ: x<>2/5
\(\dfrac{2x-7}{10x-4}-\dfrac{3x+5}{4-10x}\)
\(=\dfrac{2x-7}{10x-4}+\dfrac{3x+5}{10x-4}\)
\(=\dfrac{2x-7+3x+5}{10x-4}=\dfrac{5x-2}{10x-4}=\dfrac{1}{2}\)
5: ĐKXĐ: \(x\ne\pm y\)
\(\dfrac{xy}{x^2-y^2}-\dfrac{x^2}{y^2-x^2}\)
\(=\dfrac{xy}{x^2-y^2}+\dfrac{x^2}{x^2-y^2}\)
\(=\dfrac{x\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{x}{x-y}\)
6: ĐKXĐ: \(x\notin\left\{0;7\right\}\)
\(\dfrac{4x+13}{5x\left(x-7\right)}-\dfrac{x-48}{5x\left(7-x\right)}\)
\(=\dfrac{4x+13}{5x\left(x-7\right)}+\dfrac{x-48}{5x\left(x-7\right)}\)
\(=\dfrac{4x+13+x-48}{5x\left(x-7\right)}\)
\(=\dfrac{5x-35}{x\left(5x-35\right)}=\dfrac{1}{x}\)
7: ĐKXĐ: \(x\ne1\)
\(\dfrac{x+2}{x-1}-\dfrac{x-9}{1-x}-\dfrac{x-9}{1-x}\)
\(=\dfrac{x+2}{x-1}+\dfrac{x-9}{x-1}+\dfrac{x-9}{x-1}\)
\(=\dfrac{x+2+x-9+x-9}{x-1}=\dfrac{3x-16}{x-1}\)
8: ĐKXĐ:x<>1
\(\dfrac{2x^2-x}{x-1}+\dfrac{x+1}{1-x}+\dfrac{2-x^2}{x-1}\)
\(=\dfrac{2x^2-x}{x-1}-\dfrac{x+1}{x-1}+\dfrac{2-x^2}{x-1}\)
\(=\dfrac{2x^2-x-x-1+2-x^2}{x-1}=\dfrac{x^2-2x+1}{x-1}\)
=x-1
9: ĐKXĐ: x<>3
\(\dfrac{4-x^2}{x-3}+\dfrac{2x-x^2}{3-x}+\dfrac{5-4x}{x-3}\)
\(=\dfrac{4-x^2}{x-3}+\dfrac{x^2-2x}{x-3}+\dfrac{5-4x}{x-3}\)
\(=\dfrac{4-x^2+x^2-2x+5-4x}{x-3}=\dfrac{-6x+9}{x-3}\)
10: ĐKXĐ: x<>5
\(\dfrac{x+1}{x-5}+\dfrac{x-18}{5-x}+\dfrac{x+2}{x-5}\)
\(=\dfrac{x+1}{x-5}-\dfrac{x-18}{x-5}+\dfrac{x+2}{x-5}\)
\(=\dfrac{x+1-x+18+x+2}{x-5}=\dfrac{3x-15}{x-5}=3\)
8.3
$7x=4y\Rightarrow x=\frac{4}{7}y$. Khi đó:
$y-x=24$
$y-\frac{4}{7}y=24$
$\frac{3}{7}y=24$
$y=56$
$x=\frac{4}{7}y=\frac{4}{7}.56=32$
(oh) hóa trị 1 mà zn hóa trị 2=> cthh la zn(oh)2
với lại ko có oh2 dau chi co OH hoac la H2O
1: \(\dfrac{15x}{7y^3}\cdot\dfrac{2y^2}{x^2}\)
\(=\dfrac{15x\cdot2y^2}{7y^3\cdot x^2}=\dfrac{30xy^2}{7x^2y^3}=\dfrac{30}{7xy}\)
2: \(\dfrac{6x^3}{7y^4}\cdot\dfrac{35y^2}{24x}\)
\(=\dfrac{6x^3}{24x}\cdot\dfrac{35y^2}{7y^4}\)
\(=\dfrac{x^2}{4}\cdot\dfrac{5}{y^2}=\dfrac{5x^2}{4y^2}\)
3: \(\dfrac{4y^2}{x^4}\cdot\dfrac{-3x^2}{8y}\)
\(=\dfrac{4y^2}{8y}\cdot\dfrac{-3x^2}{x^4}=\dfrac{y}{2}\cdot\dfrac{-3}{x^2}=\dfrac{-3y}{2x^2}\)
4: \(\dfrac{-18y^3}{25x^4}:\dfrac{9y^3}{-15x^2}\)
\(=\dfrac{18y^3}{25x^4}\cdot\dfrac{15x^2}{9y^3}\)
\(=\dfrac{18y^3}{9y^3}\cdot\dfrac{15x^2}{25x^4}=2\cdot\dfrac{3}{5x^2}=\dfrac{6}{5x^2}\)
5: \(\dfrac{8y^2}{9x^2}:\dfrac{4y}{3x^2}\)
\(=\dfrac{8y^2}{9x^2}\cdot\dfrac{3x^2}{4y}=\dfrac{8y^2}{4y}\cdot\dfrac{3x^2}{9x^2}=\dfrac{1}{3}\cdot2y=\dfrac{2y}{3}\)
6: \(\dfrac{-20x}{3y^2}:\dfrac{-4x^3}{5y}\)
\(=\dfrac{20x}{3y^2}:\dfrac{4x^3}{5y}\)
\(=\dfrac{20x}{3y^2}\cdot\dfrac{5y}{4x^3}=\dfrac{20x}{4x^3}\cdot\dfrac{5y}{3y^2}=\dfrac{5}{3y}\cdot\dfrac{5}{x^2}=\dfrac{25}{3x^2y}\)
7: \(\dfrac{\left(x+4\right)^2}{4x+12}:\dfrac{x+4}{3x+9}\)
\(=\dfrac{\left(x+4\right)^2}{4\left(x+3\right)}:\dfrac{x+4}{3\left(x+3\right)}\)
\(=\dfrac{\left(x+4\right)^2}{4\left(x+3\right)}\cdot\dfrac{3\left(x+3\right)}{x+4}=\dfrac{3\left(x+4\right)}{4}\)
8: \(\dfrac{5x+10}{4x-8}\cdot\dfrac{4-2x}{x+2}\)
\(=\dfrac{5\left(x+2\right)}{4\left(x-2\right)}\cdot\dfrac{-2\left(x-2\right)}{x+2}\)
\(=\dfrac{5\cdot\left(-2\right)}{4}=-\dfrac{10}{4}=-\dfrac{5}{2}\)
9: \(\dfrac{x^2-36}{2x+10}\cdot\dfrac{3}{6-x}\)
\(=\dfrac{\left(x-6\right)\left(x+6\right)}{2\left(x+5\right)}\cdot\dfrac{-3}{x-6}\)
\(=\dfrac{-3\left(x+6\right)}{2\left(x+5\right)}\)
10: \(\dfrac{x^2-4}{x^2-x}:\dfrac{x^2+2x}{x-1}\)
\(=\dfrac{\left(x-2\right)\left(x+2\right)}{x\left(x-1\right)}\cdot\dfrac{x-1}{x\left(x+2\right)}\)
\(=\dfrac{\left(x-2\right)}{x^2\left(x+2\right)}\)
giúp gì???????