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Câu 3:
a: \(BD=\sqrt{BC^2-DC^2}=4\left(cm\right)\)
b: \(\widehat{A}=180^0-2\cdot70^0=40^0< \widehat{B}\)
nên BC<AC=AB
c: Xét ΔEBC vuông tại E và ΔDCB vuông tại D có
BC chung
\(\widehat{EBC}=\widehat{DCB}\)
Do đó:ΔEBC=ΔDCB
d: Xét ΔOBC có \(\widehat{OBC}=\widehat{OCB}\)
nên ΔOBC cân tại O
Câu 2
a) Thay y = -2 vào biểu thức đã cho ta được:
2.(-2) + 3 = -1
Vậy giá trị của biểu thức đã cho tại y = -2 là -1
b) Thay x = -5 vào biểu thức đã cho ta được:
2.[(-5)² - 5] = 2.(25 - 5) = 2.20 = 40
Vậy giá trị của biểu thức đã cho tại x = -5 là 40
1 were - would you play
2 weren't studying - would have
3 had taken - wouldn't have got
4 would you go - could
5 will you give - is
6 recycle - won't be
7 had heard - wouldn't have gone
8 would you buy - had
9 don't hurry - will miss
10 had phoned - would have given
11 were - wouldn't eat
12 will go - rains
13 had known - would have sent
14 won't feel - swims
15 hadn't freezed - would have gone
\(a,=\dfrac{x^3+2x}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{2}{x^2+x+1}-\dfrac{1}{x-1}=\dfrac{x^3+2x+2x-2-\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^3+3x-3}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^3+3}{\left(x^2+x+1\right)}\)
a: \(=\dfrac{x^3+2x+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x^3-x^2+3x-3}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^2+3}{x^2+x+1}\)
b: \(=\dfrac{x^2-2x-3+x^2+2x-3+2x-2x^2}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2x-6}{\left(x-3\right)\left(x+3\right)}=\dfrac{2}{x+3}\)
c: \(=\dfrac{6-7+x}{3\left(x-1\right)}=\dfrac{x-1}{3\left(x-1\right)}=\dfrac{1}{3}\)
d: \(=\dfrac{x^3+2x+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^3-x^2+3x-3}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^2+3}{x^2+x+1}\)
1 is explained
2 was stolen
3 will be opened
4 is being closed
5 is going to be built
Bài 1:
\(4x^3-12x^2+4x=4x.\left(x^2-3x+1\right)\)
\(5x^4y-20x^3y-15x^2y=5x^2y.\left(x^2-4x-3\right)\)
\(7x.\left(x+4\right)-14.\left(x+4\right)=\left(x+4\right).\left(7x-14\right)=7.\left(x+4\right).\left(x-2\right)\)
\(2x.\left(x-7\right)+10.\left(7-x\right)=2x.\left(x-7\right)-10.\left(x-7\right)=\left(x-7\right).\left(2x-10\right)=2.\left(x-7\right).\left(x-5\right)\)
Bài 3:
\(x^2-5x=0\)
\(\Rightarrow x.\left(x-5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=5\end{cases}}\)
\(x.\left(x-2\right)+x-2=0\)
\(\Rightarrow x.\left(x-2\right)+\left(x-2\right)=0\)
\(\Rightarrow\left(x+1\right).\left(x-2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x+1=0\\x-2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)
\(x^2-5x+4=0\)
\(\Rightarrow x^2-x-4x+4=0\)
\(\Rightarrow x.\left(x-1\right)-4.\left(x-1\right)=0\)
\(\Rightarrow\left(x-4\right).\left(x-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-4=0\\x-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=4\\x=1\end{cases}}\)