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I
1. A ronot is a speacial kind of machine.
2. No, it isn't
3. Worker Robots can help make cars, and explore volcanoes, ...
4. No, it wasn't
II
1. No, there aren't. There are 2 kinds of sports.
2. Team sports require 2 separate teams.
3. Because they want to get the best score.
4. Yes, they are.
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi D là giao điểm BM và CN.
Trên cạnh BC lấy điểm E sao cho \(BE=BN\)
Khi đó \(CE=BC-BE=BN+CM-BE=CM\)
Xét hai tam giác BDE và BDN có:
\(\left\{{}\begin{matrix}BE=BN\\\widehat{DBE}=\widehat{DBN}\left(\text{BM là phân giác}\right)\\BD\text{ chung}\end{matrix}\right.\) \(\Rightarrow\Delta BDE=\Delta BDN\left(c.g.c\right)\)
\(\Rightarrow\widehat{BDE}=\widehat{BDN}\)
Hoàn toàn tương tự, ta cũng có \(\Delta CDE=\Delta CDM\left(c.g.c\right)\Rightarrow\widehat{CDE}=\widehat{CDM}\)
Mà \(\widehat{BDN}=\widehat{CDM}\) (đối đỉnh) \(\Rightarrow\widehat{BDN}=\widehat{BDE}=\widehat{CDM}=\widehat{CDE}\)
Mà \(\widehat{BDE}+\widehat{CDE}+\widehat{CDM}=180^0\)
\(\Rightarrow3\widehat{BDE}=180^0\Rightarrow\widehat{BDE}=60^0\)
\(\Rightarrow\widehat{CDE}=60^0\)
\(\Rightarrow\widehat{BDC}=\widehat{BDE}+\widehat{CDE}=120^0\)
Theo tính chất tổng 3 góc tổng tam giác:
\(\widehat{BDC}+\widehat{DBC}+\widehat{DCB}=180^0\)
\(\Rightarrow120^0+\dfrac{1}{2}\widehat{B}+\dfrac{1}{2}\widehat{C}=180^0\)
\(\Rightarrow\widehat{B}+\widehat{C}=120^0\)
Do tổng 3 góc trong tam giác ABC bằng 180 độ
\(\Rightarrow\widehat{A}+\widehat{B}+\widehat{C}=180^0\)
\(\Rightarrow\widehat{A}+120^0=180^0\)
\(\Rightarrow A=60^0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 5:
a)
\(x^4+x^3+x+1\\ =x^3\left(x+1\right)+\left(x+1\right)\\ =\left(x^3+1\right)\left(x+1\right)\)
b)
\(x^4-x^3-x+1\\ =x^3\left(x-1\right)-\left(x-1\right)\\ =\left(x^3-1\right)\left(x-1\right)\\ =\left(x-1\right)\left(x^2+x+1\right)\left(x-1\right)\)
c)
\(3x^2-12y^2\\ =\left(\sqrt{3}x\right)^2-\left(\sqrt{12}y\right)^2\\ =\left(\sqrt{3}x-\sqrt{12}y\right)\left(\sqrt{3}x+\sqrt{12}y\right)\\ =\sqrt{3}\left(x-\sqrt{4}y\right).\sqrt{3}\left(x+\sqrt{4}y\right)\\ =3\left(x-\sqrt{4}y\right)\left(x+\sqrt{4}y\right)\)
7:
a: (2x-1)^2-25=0
=>(2x-1)^2=25
=>2x-1=-5 hoặc 2x-1=5
=>2x=6 hoặc 2x=-4
=>x=-2 hoặc x=3
b: 8x^3-50x=0
=>4x^3-25x=0
=>x(4x^2-25)=0
=>x(2x-5)(2x+5)=0
=>x=0 hoặc 2x-5=0 hoặc 2x+5=0
=>x=0;x=5/2;x=-5/2
c: 3x(x-1)+(x-1)=0
=>(x-1)(3x+1)=0
=>x=1 hoặc x=-1/3
d: =>2(x+3)-x(x+3)=0
=>(x+3)(2-x)=0
=>x=-3 hoặc x=2
e: Thiếu vế phải rồi bạn
f: x^3+27+(x+3)(x-9)=0
=>(x+3)(x^2-3x+9)+(x+3)(x-9)=0
=>(x+3)(x^2-3x+9+x-9)=0
=>(x+3)(x^2-2x)=0
=>x(x-2)(x+3)=0
=>\(x\in\left\{0;2;-3\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Lúc đầu, người bán hàng có: \(50\div\dfrac{2}{5}+1=126\) (trái)
Đ/s:..
Cảm ưn e nka, bây h cj đg dùng đt nên ko tick dc. Lúc nào cj dùng mt thì cj tick cho nka
![](https://rs.olm.vn/images/avt/0.png?1311)
\(21+3^{x-2}=48\\ \Rightarrow3^{x-2}=27\\ \Rightarrow3^{x-2}=3^3\\ \Rightarrow x-2=3\\ \Rightarrow x=5.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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101.(-162)+38(-101)+101
= 101.(-162)-38.101+101=101.(-162-38+1)=101.(-199)=-20099
31.has not had
32.is
33.sang
34.loves
35.swim
is
sang
loves
swim