`S = 2 + 2^2 + 2^3 + 2^4 + ... + 2^2021 + 2^2022`

`=  (2 + 2^2) + (2^3 + 2^4) + ... + (2^2021 + 2^2022)`

`= (2 + 2^2) . 1 + (2 + 2^2) . 2^2 + ... + (2 + 2^2) . 2^2020`

`= (2 + 2^2) . (1+2^2 + ... + 2^2020)`

`= 6 . (1+2^2 + ... + 2^2020)`

Do `6 ⋮ 6` nên `6 . (1+2^2 + ... + 2^2020) ⋮ 6 `

`=> S ⋮ 6  (đpcm)`

kệ

Bài 2: Bổ sung điều kiện: `x ∈ Z`

Do `x ∈ Z => 2x + 9  ∈ Z` và `x + 1 ∈ Z `

Điều kiện: `x ≠ -1`

`2x + 9 ⋮ x+1`

`<=> 2x + 2 + 7 ⋮ x+1`

`<=> 2(x + 1) + 7 ⋮ x+1`

Do `x + 1 ⋮ x+1`

`=> 2(x+1) ⋮ x+1`

Nên `7 ⋮ x+1`

`<=> x + 1 ∈ Ư(7) = {-7;-1;1;7}`

`<=> x ∈ {-8;-2;0;6}` (Thỏa mãn)

Vậy ...

Bài 1:

TH1: p=5

P+2=7; P+8=13; P+14=19; P+36=5+36=41

=>Nhận

TH2: P=5k+1

P+14=5k+1+14=5k+15=5(k+3) chia hết cho 5

=>LOại

TH3: P=5k+2

P+8=5k+2+8=5k+10=5(k+2) chia hết cho 5

=>Loại

TH4: P=5k+3

P+2=5k+3+2=5k+5=5(k+1) chia hết cho 5

=>Loại

TH5: P=5k+4

P+36=5k+4+36=5k+40=5(k+8) chia hết cho 5

=>Loại

Vậy: P=5

a: Xét ΔABC có \(\widehat{ABC}+\widehat{ACB}+\widehat{BAC}=180^0\)

=>\(\widehat{BAC}+60^0+30^0=180^0\)

=>\(\widehat{BAC}=90^0\)

AD là phân giác của góc BAC

=>\(\widehat{BAD}=\widehat{CAD}=\dfrac{\widehat{BAC}}{2}=45^0\)

Ta có: \(\widehat{BAH}+\widehat{B}=90^0\)(ΔBHA vuông tại H)

=>\(\widehat{BAH}=90^0-60^0=30^0\)

Vì \(\widehat{BAH}< \widehat{BAD}\)

nên tia AH nằm giữa hai tia AB và AD

=>\(\widehat{BAH}+\widehat{HAD}=\widehat{BAD}\)

=>\(\widehat{HAD}=45^0-30^0=15^0\)

ΔAHD vuông tại H
=>\(\widehat{HAD}+\widehat{HDA}=90^0\)

=>\(\widehat{HDA}=90^0-15^0=75^0\)

15. You couldn't do me a favour, could you?

16. My wife cooks well, doesn't she?

17. You don’t like playing games, do you?

18. They should have been able to do it, shouldn't they?

19. She doesn’t come here, does she?

20. Tom can help her, can't he?

21. You won’t be late, will you?

22. The students should keep silent, shouldn't they?

23. Mary seldom wears her dress, does she?

24. Tom and Jerry can’t live in peace, can they?

25. The case weighs thirty kilos, doesn't it?

26. They want to come, don't they?

27. Elizabeth is a dentist, isn't she?

28. They won’t be here, will they?

29. That is your umbrella, isn't it?

30. There aren’t many people here yet, are there?

31. He has a bicycle, doesn't he?

32. Peter would like to come with us to the party, wouldn't he?

33. Those aren’t Fred’s books, are they?

34. You have never been to Paris, have you?

35. Something is wrong with Jane today, isn't it?

36. Everyone can learn how to swim, can't they?

37. Nobody cheated in the exam, did they?

38. Nothing went wrong while I was gone, did it?

39. I am invited, aern't I?

40. This bridge is not very safe, is it?

41. These sausages are delicious, aren't they?

42. You haven’t lived here long, have you?

43. The weather forecast wasn’t very good, was it?

44. He’d better come to see me, hadn't he?

45. You need to stay longer, don't you?

46. These sausages are delicious, aren't they?

47. You haven’t lived here long, have you?

48. It’s quite a big garden, isn't it?

49. There aren’t many people here yet, are there?

50. You’re Rafana’s friend, aren't you?

51. You came in a sports car, didn't you?

52. We can sit on the grass in the park, can't we?

53. The weather forecast wasn’t very good, was it?

54. Nothing can happen, can it?

55. I’d better go now, hadn't I?

56. Your brothers always learn hard, don't they?

57. The number of rare animals is decreasing rapidly, isn't it?

58. Dinosaurs became extinct millions of years ago, didn't they?

59. Visitors do not help to preserve and protect national parks, do they?

60. No one has been there, has he/she?

61. Bill came on a bike, didn't he?

62. The Smiths have two cars, don't they?

15. You coundn't do me a favour, …could you…………….?

16. My wife cooks well, …………doesn't she……………?

17. You don’t like playing games, ………do you………………..?

18. They should have been able to do it , ……shoudn't you…………………………?

19. She doesn’t come here, ………does she………………………… ?

20. Tom can help her, ……………can't he……………….. ?

21. You won’t be late, ……will you……………………?

22. The students should keep silent, …shouldn't they………………………… ?

23. Mary seldom wears her dress, ............does she............................ ?

24. Tom and Jerry can’t  live in peace, ....................can they........................ ?

25. The case weights thirty kilos,................doesn't it............................. ?

26/ They want to come,………don't they………….?               

27/ Elizabeth is a dentist, ……isn't she………….. ?

28/ They won’t be here, ………will they…………?              

29/ That is your umbrella, …………isn't it……….?                       

30/ There aren’t many people here yet, ………are there…….. ?

ai giúp tui i k

Bài giải

Tầng 3 gấp tầng 9 số lần là :

9 : 3 = 3 ( lần )

Số bậc thang người đó cần phải đi để tới tầng 9 của ngôi nhà là :

42 x 3 = 128 ( bậc thang )

Vậy người đó cần đi 128 bậc thang để tới tầng 9 của ngôi nhà.

Để lên tầng 3 tòa nhà thì phải đi qua 2 cầu thang

Mỗi cầu thang có số bậc thang là: 

`42 : 2 = 21` (bậc)

Để lên tầng 9 tòa nhà thì phải đi qua 8 cầu thang

Số bậc thang người đó cần đi là: 

`21` x  `8 = 168` (bậc)

Đáp số: ...

"Tre Việt Nam" là bài thơ kiệt tác của Nguyễn Duy được nhiều người yêu thích. Đây là một phần tiêu biểu của bài thơ ấy. Bài thơ được viết theo thể thơ lục bát; trong đó câu lục đầu bài thơ được cắt thành hai dòng (2+4) và câu lục cuối bài được cắt thành ba dòng (2+2+2). Lời thơ mượt mà, có nhiều hình ảnh đẹp, giọng thơ du dương truyền cảm.
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