Giúp e vs ạ , e chx hiểu lắm .
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![](https://rs.olm.vn/images/avt/0.png?1311)
1 If we continue polluting the air, the environment will be affected seriously
2 If we don't stop damaging birds' homes, there will be fewer birds left
3 If we continue polluting the water, there will be more disease in people and animals
4 If we keep polluting the land, the soil will not be safe enough for us to grow food in
5 If we use public transportation when we need, there will be less air pollution
12 Daniel signs up for a clean-up campaign so that he can join in it
13 People in my neighborhood clean the park up so that their children will have a nice place to play
14 Almost all the students in my school plant trees so that they can have much fresher air
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2: Chọn C
Bài 4:
a: \(\widehat{C}=180^0-80^0-50^0=50^0\)
Xét ΔABC có \(\widehat{A}=\widehat{C}< \widehat{B}\)
nên BC=AB<AC
b: Xét ΔABC có AB<BC<AC
nên \(\widehat{C}< \widehat{A}< \widehat{B}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Cái chỗ này mình xin lỗi bạn nhiều nha, mình bị sai chỗ này rồi
Ta có: \(\left(a-b\right)^2>=0\forall a,b\)
=>\(a^2+b^2-2ab>=0\forall a,b\)
=>\(a^2+b^2>=2ab\forall a,b\)
Dấu "=" xảy ra khi a=b
\(2\cdot\left(\dfrac{a}{2}\cdot\dfrac{b}{2}\right)< =\left(\dfrac{a}{2}\right)^2+\left(\dfrac{b}{2}\right)^2=\dfrac{a^2+b^2}{4}\)
=>\(2\cdot\left(2\cdot\dfrac{a}{2}\cdot\dfrac{b}{2}\right)< =\dfrac{2\left(a^2+b^2\right)}{4}=\dfrac{a^2+b^2}{2}\)
Bạn bỏ giúp mình dấu căn nha
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2^{10}:64\cdot16\)
\(=2^{10}:2^6\cdot2^4\)
\(=2^{10-6+4}\)
\(=2^8\)
\(2^{10}.64.16\\ =2^{10}.2^6.2^4\\ =2^{10+6+4}=2^{20}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(P=\dfrac{x^3+8y^3}{4^3+4^3}=\dfrac{\left(x+2y\right)^3-3\cdot x\cdot2y\cdot\left(x+2y\right)}{128}\)
\(=\dfrac{\left(-8\right)^3-6\cdot\left(-6\right)\cdot\left(-8\right)}{128}=\dfrac{128-6\cdot48}{128}=-\dfrac{5}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 4:
Theo định lý sin ta có:
\(\dfrac{AC}{sinB}=\dfrac{BC}{sinA}\)
\(\Rightarrow BC=a=\dfrac{b\cdot sinA}{sinB}=\dfrac{2\cdot sin60^o}{sin45^o}=\sqrt{6}\)
\(\Rightarrow\widehat{C}=180^o-60^o-45^o=75^o\)
\(\dfrac{AC}{sinB}=\dfrac{AB}{sinC}\)
\(\Rightarrow AB=c=\dfrac{b\cdot sinC}{sinB}=\dfrac{2\cdot sin75^o}{sin45^o}=1+\sqrt{3}\)
Diện tích tam giác ABC là:
\(S_{ABC}=\dfrac{1}{2}\cdot AC\cdot AB\cdot sinA=\dfrac{1}{2}\cdot2\cdot\left(1+\sqrt{3}\right)\cdot sin75^o=\dfrac{\sqrt{6}+2\sqrt{2}}{2}\) (đvdt)
Bán kình hình tròn tam giác ABC khi đó là:
\(S_{ABC}=\dfrac{abc}{4R}\)
\(\Rightarrow R=\dfrac{abc}{4S_{ABC}}=\dfrac{2\cdot\left(1+\sqrt{3}\right)\cdot\sqrt{6}}{4\cdot\left(\dfrac{\sqrt{6}+2\sqrt{2}}{2}\right)}=3-\sqrt{3}\)
Bài 3:
a) Xét tam giác ABC theo định lý côsin ta có:
\(cosC=\dfrac{a^2+b^2-c^2}{2ab}=\dfrac{8^2+10^2-13^2}{2\cdot8\cdot10}=-0,03125\)
\(\Rightarrow\widehat{C}=cos^{-1}-0,03125\approx91^o>90^o\)
Nên tam giác ABC có góc C là góc tù
c) Theo hệ thức Heron ta có diện tích tam giác ABC là:
\(S_{ABC}=\sqrt{p\cdot\left(p-a\right)\cdot\left(p-b\right)\cdot\left(p-c\right)}\)
\(\Rightarrow S_{ABC}=\sqrt{\dfrac{8+10+13}{2}\cdot\left(\dfrac{8+10+13}{2}-8\right)\cdot\left(\dfrac{8+10+13}{2}-10\right)\cdot\left(\dfrac{8+10+13}{2}-13\right)}\)
\(\Rightarrow S_{ABC}\approx40\) (đvdt)
b) Bán kính đường tròn ngoại tiếp tam giác ABC là:
\(S_{ABC}=\dfrac{abc}{4R}\)
\(\Rightarrow R=\dfrac{abc}{4S_{ABC}}=\dfrac{8\cdot10\cdot13}{4\cdot40}=6,5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
`2)`
`@` Xét `3x+6 >= 0<=>x >= -2`
`=>A=[-2;+oo)`
`@` Xét `|x-2| < 3`
`<=>-3 < x-2 < 3`
`<=>-1 < x < 5=>B=(-1;5)`
Có: `A nn B=(-1;5)`
`A uu B=[-2;+oo)`
`R \\ B=(-oo;-1]uu[5;+oo)`
_______
`3)`
`@` Xét `x+3 >= 2x+7<=>x <= -4=>A=(-oo;-4]`
`@` Xét `4x+5 > 0<=>x > -5/4=>B=(-5/4;+oo)`
`@` Xét `|x+4| < 2<=>-2 < x+4 < 2<=>-6 < x < -2 =>C=(-6;-2)`
Có: `A nn B nn C=\emptyset`
`A \\ B nn C=(-6;-4]`
`C \\ A nn B=\emptyset`.
Bài 7:
a: a>b
nên -2a<-2b
=>-2a-6<-2b-6<-2b
b: a>b
nên 3a>3b
=>3a-9>3b-9
=>3(a-3)>3(b-3)