Samuel has kept a diary since 1997

Cấu trúc: 

S + started/began + V-ing/ to V + ... + khoảng thời gian + ago

                                                          +  in + mốc thời gian

                                                          + when + clause

=> S + have/has + V3/ed + for + khoảng thời gian

                                         + since + mốc thời gian

He is tired of staying up late to work

(be tired of sth: mệt mỏi vì điều gì đó)

Thôi để làm lại luôn=)

\(\left(x^4\right)^{11}=x\\ \Leftrightarrow x^{4.11}=x\\ \Leftrightarrow x^{44}=x\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\\ \Rightarrow x\in\left\{0;1\right\}\)

\(2^x+2^{x+1}+2^{x+2}+2^{x+3}+...+2^{x+2015}=2^{2019-8}\)

\(\Leftrightarrow2^x\left(1+2+2^2+2^3+...+2^{2015}\right)=2^{2019-8}\) (1)

Đặt \(A=1+2+2^2+2^3+...+2^{1015}\\ \Rightarrow2A=2+2^2+2^3+...+2^{2016}\\ \Leftrightarrow2A-A=\left(2+2^2+2^3+...+2^{2016}\right)-\left(1+2+2^2+2^3+...+2^{2015}\right)\\ \Leftrightarrow A=2^{2016}-1\)

Thay \(A=2^{2016}-1\) vào (1) ta có:

\(2^x\left(2^{2016}-1\right)=2^3\left(2^{2016}-1\right)\\ \Leftrightarrow2^x=2^3\\ \Rightarrow x=3\)

33 There is a TV in my bedroom

34 The table is behind the wardrobe

35 Let's go to the city center by bus

36 My house is between a bakery and a bookshop

Many accidents are caused by careless drivers

Sửa đề: case => cause

engage sb to do sth

=> engage + to V

1 I advise you to buy a better dictionary

2 Working in an office is not as nice as working outdoors

3 Sheila prefers tea to coffee

4 He is a good computer programmer

5 What is the depth of the lake to the left of your house?

6 How about spending our holiday in Hawaii?

7 You had better use a dictionary while doing the reading

8 My sister loses her temper very easily in the morning