1. If you read many books, you will have much knowledge. ⇒ The more books you read, the more knowledge you have.
2. He speaks too much and people feel bored. ⇒ The more speaking he does, the more bored people feel.
3. The growth in the economy makes people’s living condition better. ⇒ The more growth the economy makes, the better the condition is.
4. He learned a lot of things as he traveled far. ⇒ The farther he traveled, the more things he learned.

\(\left\{{}\begin{matrix}3x-6y+2z=-4\\3x-y-3z=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}3x-6y+2z=-4\\3x-y-3z=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}3x-6y=-4-2z\\3x-y=1+3z\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}5y=1+3z+4+2z\\3x-y=1+3z\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}5y=5+5z\\3x=y+1+3z\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}y=1+z\\3x=1+z+1+3z\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}y=1+z\\x=\dfrac{4z+6}{3}\end{matrix}\right.\)

\(S=9x^2-8\left(y^2+z^2\right)\)

\(S=9\left(\dfrac{4z+2}{3}\right)^2-8\left[\left(1+z\right)^2+z^2\right]\)

\(S=9.\dfrac{16z^2+16z+4}{9}-8\left[1+2z+z^2+z^2\right]\)

\(S=16z^2+16z+4-8-16z-16z^2\)

\(S=-4\)

Đính chính \(x=\dfrac{4z+2}{3}\) không phải \(x=\dfrac{4z+6}{3}\)

1, The bigger the apartment is, the higher the rent is

2, The sooner we set off, the sooner we will arrive

3, The better the joke is, the louder the laugher is

4, The fatter she gets, the more tired she feels

5, The older she gets, the less travel he wants

1. The bigger the apartment is, the higher the rent is.
2. The sooner we set off, the sooner we will arrive.
3. The better the joke is, the louder the laughter is.
4. The fatter she gets, the more tired she feels.
5. The older he gets, the less he wants to travel.
6. The more difficult the games are, the more excited the children are.
7. The faster people dive, the more accidents happen.
8. The more I meet him, the more I hate him.
9. The less time my boss is pressed for, the better he works.
10. The more money he has, the more he wants to spend.

1. The more books you read, the more knowledge you will have

2. The more he speaks, the more bored people feel

3. The more the economy grows, the better people's living condition is

4. The farther he traveled, the more he learned

1. C

2. B

3. D

4. A

5. D

6. D

7. C

8. B

9. C

1. C. better
2. B. as
3. D. tallness
4. A. as/as
5. D. A and B are correct
6. A. as/as
7. C. faster than
8. C. better
9. A. most
10. C. higher than

1. I've never tasted a more delicious cake.
2. George is the most dependable person I've ever met.
3. Your mother is the kindest-hearted person I know.
4. Mr John is the best teacher in this school.
5. Is this one bigger than that one?

1. Her daughter is more beautiful than her.
2. Summer is the hottest season of the year.
3. That dog isn't as dangerous as it looks.
4. In the past, people were more polite than today.
5. It is colder today than it was yesterday.
6. Our hotel was cheaper than all the others in the town.
7. What's the longest river in the world?
8. It was an awful day. It was the worst day of my life.
9. Everest is the highest mountain in the world. It is higher than any other mountain.
10. I prefer this chair to the other one. It's more comfortable.

Để xác định khối lượng riêng của từng khối kim loại, ta sử dụng công thức:

Khối lượng riêng = Khối lượng / Thể tích

Với diện tích tiếp xúc của khối A với mặt bàn là 3cm x 4cm = 12cm^2 = 0.0012m^2
Áp suất do khối A gây ra trên mặt bàn là 1350 Pa

Áp suất = Lực / Diện tích
Lực = Áp suất x Diện tích
Lực = 1350 Pa x 0.0012m^2 = 1.62 N

Khối lượng của khối A = Lực / Trọng trường
Khối lượng của khối A = 1.62 N / 9.8 m/s^2 = 0.1656 kg

Khối lượng riêng của khối A = 0.1656 kg / (0.03m x 0.04m x 0.05m) = 8600 kg/m^3

Tương tự, ta tính được khối lượng riêng của khối B là 7800 kg/m^3 và khối C là 2700 kg/m^3.

Vậy khối nào có khối lượng riêng là 8600 kg/m^3 là đồng, khối nào có khối lượng riêng là 7800 kg/m^3 là sắt, và khối nào có khối lượng riêng là 2700 kg/m^3 là nhôm.

\(\Delta\)ABC cân tại A ⇒ \(\widehat{ABC}\) = \(\widehat{ACB}\)   

\(\widehat{ABD}=\widehat{DBC}\) = \(\dfrac{1}{2}\widehat{ABC}\) (vì BD là phân giác của \(\widehat{ABC}\))

\(\widehat{ACE}\) = \(\widehat{ECB}\) = \(\dfrac{1}{2}\)\(\widehat{ACB}\) (vì CE là phân giác của \(\widehat{ACB}\))

⇒ \(\widehat{ABD}=\widehat{DBC}=\widehat{ACE}=\widehat{ECB}\) (1)

Xét \(\Delta\)BCE và  \(\Delta\)CBD có:

\(\widehat{EBC}\) = \(\widehat{BCD}\) (vì tam giác ABC cân tại A)

\(\widehat{ECB}\) = \(\widehat{DBC}\)  theo (1) 

Và BC chung 

\(\Rightarrow\) \(\Delta\)BCE = \(\Delta\) CBD (g-c-g) ⇒ BE = CD ⁽²⁾

BE + EA = AD + DC (vì \(\Delta\)ABC cân tại A)

⇒ AE = AD \(\Rightarrow\) \(\dfrac{AE}{AB}\) = \(\dfrac{AD}{AC}\) \(\Rightarrow\) ED // BC ⁽³⁾ (định lý talet đảo)

\(\widehat{DBC}\) = \(\widehat{BDE}\) (so le trong)

⇒\(\widehat{EBD}\) = \(\widehat{BDE}\) (vì cùng bằng góc DBC)

⇒ \(\Delta\)BDE cân tại E \(\Rightarrow\) BE = ED ⁽⁴⁾

Kết hợp (2); (3); (4) ta có

Tứ giác BECD là hình thang cân có đáy nhỏ bằng cạnh bên. (đpcm)

Bạn xem lại đề xem chứ mình thay \(n=3,4,5,6\) đều không thỏa.