Đặt A=\(\dfrac{x}{a+2b+c}=\dfrac{y}{2a+b-c}=\dfrac{z}{4a-4b+c}\)

Ta có:

A=\(\dfrac{x}{a+2b+c}=\dfrac{y}{4a+2b-2c}=\dfrac{z}{4a-4b+c}\)=\(\dfrac{x+y+z}{a+2b+c+4a+2b-2c+4a-4b+c}\)=\(\dfrac{x+2y+z}{9a}\)(1)

A=\(\dfrac{2x}{2a+4b+2c}=\dfrac{y}{2a+b-c}=\dfrac{z}{4a-4b+c}\)=\(\dfrac{2x+y-z}{2a+4b+2c+2a+b-c-4a+4b-c}=\dfrac{2x+y-z}{9b}\)(2)

A=\(\dfrac{4x}{4a+8b+4c}=\dfrac{4y}{8a+4b-4c}=\dfrac{z}{4a-4b+c}\)=\(\dfrac{4x-4y+z}{4a+8b+4c-8a-4b+4c+4a-4b+c}\)=\(\dfrac{4x-4y+z}{9c}\)(3)

Từ (1), (2) và (3):

\(\Rightarrow\dfrac{x+2y+z}{9a}=\dfrac{2x+y-z}{9b}=\dfrac{4x-4y+z}{9c}\)

\(\dfrac{x+2y+z}{a}=\dfrac{2x+y-z}{b}=\dfrac{4x-4y+z}{c}\)

\(\Rightarrow\dfrac{a}{x+2y+z}=\dfrac{b}{2x+y-z}=\dfrac{c}{4x-4y+z}\left(đpcm\right)\)

Theo đề bài ta có:
\(\dfrac{4}{3x-2y}=\dfrac{3}{2z-4x}=\dfrac{2}{4y-3z}\)

\(\Rightarrow\)4(2z-4x) = 3(3x-2y)
3(4y-3z) = 2(2z-4x)
Ta có:

4(2z-4x) = 3(3x-2y)\(\Rightarrow\)8z-16x = 9x-6y\(\Rightarrow y=\dfrac{25x-8z}{6}\) (1)

\(\dfrac{3}{2z-4x}=\dfrac{2}{4y-3z}\Rightarrow3\left(4y-3z\right)=2\left(2z-4x\right)\)

\(\Rightarrow12y-9z=4z-8x\Rightarrow12y+8x=13z\) (2)

Thay (1) vào (2) ta có:

2(25x-8z)+8x = 13z\(\Rightarrow\)58x = 29z\(\Rightarrow\)z = 2x\(\Rightarrow\)y = \(\dfrac{3}{2}x\)

Thay vào đề bài x + y- z= - 10 ta tìm được:

x = -10; y = -20; z = -30

Theo bài ra ta có:

a-b = a\(\div b\) = 2.(a + b)

\(\Rightarrow\) a-b = 2.(a + b)

\(\Rightarrow\)a-b = 2a+2b

\(\Rightarrow\)a-2a=b+2b

\(\Rightarrow\)-a = 3b hay: a = -3b (1)

Lại có:
a-b = a\(\div\)b

\(\Rightarrow\)b(a-b) = a (2)

Từ (1) và (2) \(\Rightarrow\)-3b = (a-b)b \(\Rightarrow\)a-b = -3

Thay a-b = -3, a = -3b vào a-b ta có:

-3b-b = -3

-4b = -3

\(\Rightarrow\)b = \(\dfrac{3}{4}\); a = \(\dfrac{3}{4}.\left(-3\right)\)=\(\dfrac{-9}{4}\)

Vậy a = \(\dfrac{-9}{4};b=\dfrac{3}{4}\)

Ta có:
C=\(\dfrac{1}{3}.\dfrac{4}{6}.\dfrac{7}{9}..........\dfrac{208}{210}\)<\(\dfrac{1}{3}.\dfrac{3}{4}.\dfrac{6}{7}.......\dfrac{207}{208}\)

\(\Rightarrow\)C²<\(\dfrac{1}{3}.\dfrac{4}{6}.\dfrac{7}{9}..........\dfrac{208}{210}\).\(\dfrac{1}{3}.\dfrac{3}{4}.\dfrac{6}{7}.......\dfrac{207}{208}\)

\(\Rightarrow\)C²<\(\dfrac{1.4.7........208}{3.6.9........210}\).\(\dfrac{1.3.6.9........207}{3.4.7........208}\)

\(\Rightarrow\)C²<\(\dfrac{1}{210}.\dfrac{1}{3}\)=\(\dfrac{1}{630}< \dfrac{1}{625}\)

\(\Rightarrow\)C<\(\dfrac{1}{25}\)(đpcm)

a, Ta có:

A= \(\dfrac{3}{8^3}+\dfrac{7}{8^4}=\dfrac{3}{8^3}+\dfrac{3}{8^4}+\dfrac{4}{8^4}\)

B= \(\dfrac{7}{8^3}+\dfrac{3}{8^4}=\dfrac{3}{8^3}+\dfrac{4}{8^3}+\dfrac{3}{8^4}\)

Vì \(\dfrac{4}{8^4}< \dfrac{4}{8^3}\) nên A < B.

b, Ta có:

\(\dfrac{20}{39}>\dfrac{14}{39}\)

\(\dfrac{22}{27}>\dfrac{22}{29}\)

\(\dfrac{18}{43}< \dfrac{18}{41}\)

\(\Rightarrow\)\(\dfrac{20}{39}+\dfrac{22}{27}+\dfrac{18}{43}>\dfrac{14}{39}+\dfrac{22}{29}+\dfrac{18}{41}\)

Hay A > B

32. Hoa's new skirt was white with red and yellow flower on it.

33.Lien made a cushion in her own room.

34. Nam lives a long way from his grandparents's house.

35. Liz helped me a lot of my stamp collection.

36. Did you speak to Mr.Robinson about your vacation in Dalat?

37. Lam tired on the blue shirt because it didn't fit.

38. There is a souvenir shop near the exist of the zoo.

Tung (39) watched his neighbor, Mr. Thuan (40)planted trees in his garden. He (41)thought planting trees was a good hobby. He decided to (42)learn how to plant trees.
He (43)bought some small trees and (44)plant them in front of his house. They had lots of green leaves and some little flowers. Now, he (45)has a small garden and it (46)looks very pretty.

Hình trụ được tạo thành khi ta quay hình chữ nhật một vòng quanh một cạnh cố định.

Nếu đặt mặt đáy của hình trụ song song với mặt phẳng chiếu cạnh thì:

+ Hình chiếu đứng có dạng hình chữ nhật.

+ Hình chiếu cạnh có dạng hình tròn.

Ta có:

\(\dfrac{\left(\dfrac{2}{5}\right)^7.5^7+\left(\dfrac{9}{4}\right)^3\div\left(\dfrac{3}{16}\right)^3}{2^7.5^7+512}\)

=\(\dfrac{\left(\dfrac{2}{5}.5\right)^7+\left(\dfrac{9.16}{4.3}\right)^3}{2^7.5^7+2^9}\)=\(\dfrac{2^7+12^3}{2^7.5^7+2^9}\)=\(\dfrac{2^7+2^6.3^3}{2^7.5^7+2^9}\)

=\(\dfrac{2^6.\left(2+3^3\right)}{2^6.\left(2.5^7+2^3\right)}\)=\(\dfrac{29}{156258}\).

Hì hì sai ko bít nha

Ta có:

(2x-1)²\(\ge\)0

\(\Rightarrow\)3(2x-1)²\(\ge\)0 \(\Rightarrow\)5-3(2x-1)²\(\le\)5

Dấu "=" xảy ra \(\leftrightarrow\) 3(2x-1)=0

Hay: 2x-1=0 \(\Rightarrow\)x = \(\dfrac{1}{2}\).

Vậy GTLN của biểu thức A là 5 \(\leftrightarrow\) x = \(\dfrac{1}{2}\)

1. I took someone else's coat from the cloakroom by mistake.

2. Dave and I have arranged to meet at the bus station at 9o'clock.

3. You're wasting your time trying to persuade him; he'll never help you.

4. It's time we did away with our old- fashioned prisons.

5. We are expecting him to arrive at any moment.

6. He found learning to easy and passed his driving test the very first time.

7. In spite of, the west weather, the football match went ahead.

8. While studying he was financially dependent on.

9. Everyone felt sorry for Mr Atkins when he lost his job at the factory.

10. You can't miss my house; it's opposite the fire station.

11. To refuse to obey orders is a serious offence in the army.

12. Could you lend me some money? I'm very short of cash at the moment.