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ex 4.
1 seeing
2 to pay
3 sneezing
4 to clean up
5 to work
6 cutting
7 to iron - ironing
8 driving
9 to have
10 to invite
11 being
12 to find
13 holding - drinking
14 to repair
15 explaining
ex 5.
2. Pamela continued dancing for an hour.
3. I'd rather sit in the front row.
4. Richard expects to do well.
5. What do you intend to do for the summer?
6. I hate clearing up my room.
7. Helen agreed to go to the party with me.
8. My boss refused to let me leave early.
9. I really look forward to hearing from you soon.
10. What do you want to do this evening?
11. The manager promised to speak to you about this.
12. Fiona succeeded in persuading her father to change his mind.
13. Where do you feel like going this evening?
14. The detective happened to discover the secret.
15. It was very late, but she went on tidying up the kitchen.
ex6.
1. The room will be cleaned today.
2. The car might be stolen.
3. That tree had to be cut down.
4. The old houses are going to be demolished.
5. The picture can't be restored.
6. An appointment must be made in advance.
7. I don't want to be made a fool.
8. The garden has to be looked after.
9. He wants to be served.
10. He is going to be interviewed next week.
Bài 2:
a: \(201^3=8120601\)
b: \(199^3=7880599\)
c: \(52^3-8=140600\)
d: \(23^3-27=12140\)
e: \(99^3=970299\)
f: \(62\cdot58=3596\)
Bài 1:
a: \(\left(2x+y\right)^2-\left(y-2x\right)^2\)
\(=4x^2+4xy+y^2-y^2+4xy-4x^2\)
=8xy
b: \(\left(5x+5\right)^2+10\cdot\left(x-3\right)\left(x+1\right)+x^2-6x+9\)
\(=\left(5x+5\right)^2+2\cdot\left(5x+5\right)\cdot\left(x-3\right)+\left(x-3\right)^2\)
\(=\left(6x+2\right)^2\)
\(=36x^2+24x+4\)
c: \(\left(x-y\right)^3+3xy\left(x-y\right)\)
\(=x^3-3x^2y+3xy^2-y^3+3x^2y-3xy^2\)
\(=x^3-y^3\)
d: \(\left(1-2x\right)\left(1+2x+4x^2\right)+8\left(x-1\right)\left(x^2+x+1\right)\)
\(=1-8x^3+8\left(x^3-1\right)\)
\(=1-8x^3+8x^3-8\)
=-7
a) \(x-3=0\)
\(\Leftrightarrow\) \(x=0+3\)
\(\Leftrightarrow\) \(x=3\)
b) \(2x+6=0\)
\(\Leftrightarrow\) \(2x=0-6\)
\(\Leftrightarrow2x=-6\)
\(\Leftrightarrow x=-3\)
c) \(2x+3=x+9\)
\(\Leftrightarrow2x+3-x=9\)
\(\Leftrightarrow x+3=9\)
\(\Leftrightarrow x=9-3\)
\(\Leftrightarrow x=6\)
d) \(\left(x-4\right)\left(2x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\2x+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\2x+4+\left(-4\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-2\end{matrix}\right.\)
3.
Gọi vận tốc xe thứ nhất là x (km/h) với x>0
Vận tốc xe thứ hai là: \(1,2x\) (km/h)
Thời gian xe thứ nhất đi hết quãng đường AB: \(\dfrac{120}{x}\) giờ
Thời gian xe thứ hai đi hết quãng đường AB: \(\dfrac{120}{1,2x}=\dfrac{100}{x}\) giờ
Do xe thứ hai đến sớm hơn xe thứ nhất là 30 phút =1/2 giờ nên ta có pt:
\(\dfrac{120}{x}-\dfrac{100}{x}=\dfrac{1}{2}\)
\(\Rightarrow\dfrac{20}{x}=\dfrac{1}{2}\Rightarrow x=40\) (km/h)
Vậy vận tốc xe thứ nhất là 40 km/h, xe thứ hai là \(40\times1,2=48\) (km/h)
4.
Áp dụng định lý phân giác ta có:
\(\dfrac{IE}{IF}=\dfrac{DE}{DF}=\dfrac{6}{10}=\dfrac{4}{5}\)
Bài 2:
BC=6,5(cm)
AH=3(cm)
\(AB=\sqrt{BH\cdot BC}=\sqrt{13}\left(cm\right)\)
\(AC=\sqrt{CH\cdot BC}=\dfrac{3}{2}\sqrt{13}\left(cm\right)\)