(x+1)+(2x+3)+(3x+5)+....+(100x+199)=3020
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b) \(\dfrac{x}{2}=\dfrac{y}{5};\dfrac{y}{5}=\dfrac{z}{4}\)
\(\Rightarrow\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{4}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{4}=\dfrac{x-y+z}{2-5+4}=-21\)
\(\Rightarrow\dfrac{x}{2}=-21\Rightarrow x=2\cdot-21=-42\)
\(\Rightarrow\dfrac{y}{5}=-21\Rightarrow y=-21\cdot5=-105\)
\(\Rightarrow\dfrac{z}{4}=-21\Rightarrow z=4\cdot-21=-84\)
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1, after
2, break
3, it
4, ride
5, vehicle
6, cross
7, rules
8, accidents
1 did
2 after
3 feels
4 across
5 break
6 rules
7 it
8 vehicles
9 ride
10 accidents
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1. Cyclist and motorist have to wear a C. helmet when they ride a motorbike.
2. He forgot to give a B. signal before he turned left and got a ticket.
3. All of us have to obey B. traffic rules strictly.
4. We should wait for the traffic lights C. to turn green before we cross the street.
5. Drivers have to B. fasten your seatbelt whenever they drive.
6. We should D. walk across the street at the zebra crossing.
7. C. How far is it from your house to the nearest bus stop?” – “about 50 metres”.
8. Linh used to A. do jigsaw puzzles in his spare time.
9. Public C. transport in this city is quite good, and it’s not expensive.
10. I B. used to play marbles when I was young, but now I didn’t.
11. There B. used to have a bus station in the city centre, but it has been moved to the suburbs.
12. C. How long does it take to go from Ha Noi to Ho Chi Minh City by plane?
13. Minh used to A. do his homework late in the evening.
14. If people C. obey the rules, there are no more accidents.
15. You should B. look right and left when you go across the road.
16. Hurry up or we can’t D. catch the last bus home.
17. Lan used to go to school D. by bus
18. Public D. transport in my town is good and cheap.
19. When there is a traffic jam, it A. takes me a very long time to go home.
20. Yesterday Rick and Peter C. cycled round West Lake. It took them an hour.
1. Cyclist and motorist have to wear a ______ when they ride a motorbike.
A. cap B. mask C. helmet D. hard that
2. He forgot to give a ___________ before he turned left and got a ticket.
A. hand B. signal C. sign D. light
3. All of us have to obey ____________ strictly.
A. traffic B. traffic rules C. traffic jam D. regular
4. We should wait for the traffic lights ___________ before we cross the street.
A. turn yellow B. turn green C. to turn yellow D. to turn green
5. Drivers have to ___________ your seatbelt whenever they drive.
A. tie B. fasten C. put on D. put
6. We should __________ the street at the zebra crossing.
A. walk B. walk through C. walk on D. walk across
7. _________ is it from your house to the nearest bus stop?” – “about 50 metres”.
A. How much B. How long C. How far D. How often
8. Linh used to __________ jigsaw puzzles in his spare time.
A. do B. does C. doing D. did
9. Public __________ in this city is quite good, and it’s not expensive.
A. vehicle B. travel C. transport D. journey
10. I ____________ marbles when i was young, but now i didn’t.
A. play B. used to play C. have played D. didn’t use to play
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Lời giải:
Đặt $\frac{2x-1}{5}=\frac{3y-2}{3}=k$
$\Rightarrow x=\frac{5k+1}{2}; y=\frac{3k+2}{3}$
Khi đó:
$x+y=2$
$\Rightarrow \frac{5k+1}{2}+\frac{3k+2}{3}=2$
$\Rightarrow 2,5k+k+\frac{1}{2}+\frac{2}{3}=2$
$\Rightarrow 3,5k+\frac{7}{6}=2$
$\Rightarrow 3,5k=\frac{5}{6}$
$\Rightarrow k=\frac{5}{21}$
Khi đó:
$x=\frac{5k+1}{2}=\frac{23}{21}$
$y=\frac{3k+2}{3}=\frac{19}{21}$
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Ta có:
10²⁰²¹ = 100...000 (2021 chữ số 0)
⇒ 10²⁰²¹ + 539 = 100...0539 (2018 chữ số 0)
⇒ Tổng các chữ số của 100...0539:
1 + 0 + 0 + ... + 0 + 5 + 3 + 9 = 18
Mà 18 ⋮ 9
⇒ 100...0539 ⋮ 9
Vậy (10²⁰²¹ + 539)/9 là một số tự nhiên
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1 a
2c
3d
4b
5d
6c
7a
8b
9a
10c
11d
12a
13b
14c
15d
16a
17c
18b
19a
20d
Để tra các âm bên trên, bạn có thể dùng 'Từ điển Oxford' trên google để tra cho đúng nha bạn.
⇒ https://www.oxfordlearnersdictionaries.com/
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Lời giải:
Với $a,b,c$ nguyên dương thì:
$1=\frac{1}{a}+\frac{1}{a+b}+\frac{1}{a+b+c}< \frac{3}{a}$
$\Rightarrow a< 3$
$a$ là số nguyên dương nên $a=1,2$
Nếu $a=1$ thì $\frac{1}{b+a}+\frac{1}{a+b+c}=1-\frac{1}{a}=0$ (vô lý - loại)
$\Rightarrow a=2$
Khi đó:
$\frac{1}{b+2}+\frac{1}{b+c+2}=\frac{1}{2}$
Mà $\frac{1}{b+2}+\frac{1}{b+c+2}< \frac{2}{b+2}$
$\Rightarrow \frac{1}{2}< \frac{2}{b+2}$
$\Rightarrow b+2<4\Rightarrow b<2\Rightarrow b=1$
Khi đó: $\frac{1}{3}+\frac{1}{c+3}=\frac{1}{2}$
$\frac{1}{c+3}=\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$
$\Rightarrow c+3=6\Rightarrow c=3$
(x + 1) + (2x + 3) + (3x + 5) + ... + (100x + 199) = 3020
Ta phá ngoặc và chia thành 2 vế:
(x + 2x + 3x + ... + 100x) + (1 + 3 + 5 + ... + 199) = 3 020
Đầu tiên ta tính số lượng x. Ở đây là tổng dãy số:
1 + 2 + 3 + ... + 100
Có 100 số hạng tất cả. Tổng của chúng là:
(1 + 100) x 100 : 2 = 5 050
⇒ Có 5 050x
Tiếp theo, ta tính tổng dãy số:
1 + 3 + 5 + ... + 199
Số số hạng của dãy là: 100. Do nếu thêm vào các số hạng chẵn ở sau, ta sẽ được 1 dãy gồm 200 số hạng, vậy nên chỉ cần lấy 1 nửa của 200 là 100 thôi.
Vậy tổng của dãy số là: (1 + 199) x 100 : 2 = 10 000
Ta viết lại biểu thức ban đầu:
5 050x + 10 000 = 3 020
5 050x = 3 020 - 10 000
5 050x = -6980
x = \(\dfrac{-6980}{5050}\)
Vậy x = \(\dfrac{-6980}{5050}\)