Cho hình hộp ABCD.A'B'C'D' có độ dài mỗi cạnh bằng 1, \(\widehat{A'AD}=\widehat{A'AB}=120^o;\widehat{BAD}=60^o\), O là tâm của hình bình hành A'B'C'D'. Tính độ dài AC' và AO.

Cho hàm số \(y=\dfrac{x^2+mx+2}{x-1}\) có đồ thị \(\left(C_m\right)\). Tìm các giá trị của tham số m để đồ thị \(\left(C_m\right)\) có hai điểm cực trị A, B thỏa mãn diện tích tam giác OAB bằng \(3\sqrt{6}\).

61/ Customers ___ about the service.

a are complain

b complaining

c were complaining

d did complaining

62/ I ____ the marketing director of MTW, Inc.

a will be interviewing

b will be interview

c will being interviewing

d will interviewing

63/ He ____ handouts when I entered the room.

a will be distributing

b was distributing

c is distributing

d has been distributed

64/ We ____ the store in 15 minutes.

a will be closing

b were closing

c will closing

d will be closed

65/ To attract more customers, we ____ an express delivery service from next month.

a did offering

b will be offering

c were offering

d will offering

66/ The manager and the staff ____ a discussion at the moment.

a had

b are having

c has

d were having

67/ I ____ forward to meeting with you next week.

a looking

b do looking

c was looking

d am looking

68/ The community center ____ for donations to help the disabled and the elderly.

a have asked

b ask

c to asking

d is asking

69/ Small business owners ____ for chances to increase their profits all the time.

a looks

b looked

c are looking

d looking

70/ We have had a lot of difficulties ___ the past two weeks.

a for

b yet

c since

d when

6) \(4\left(6x-7\right)=92\\ \Leftrightarrow6x-7=23\\ \Leftrightarrow6x=30\\ \Leftrightarrow x=5\)

7) \(5\left(7x-32\right)=50\\ \Leftrightarrow7x-32=10\\ \Leftrightarrow7x=42\\ \Leftrightarrow x=6\)

8) \(29+\left(6x-4\right)=67\\ \Leftrightarrow6x-4=38\\ \Leftrightarrow6x=42\\ \Leftrightarrow x=7\)

9) \(\left(7x-32\right)+18=49\\ \Leftrightarrow7x-32=31\\ \Leftrightarrow7x=63\\ \Leftrightarrow x=9\)

10) \(\left(9x-70\right)+11=76\\ \Leftrightarrow9x-70=65\\ \Leftrightarrow9x=135\\ \Leftrightarrow x=15\)

11) \(\left(15+9x\right)-24=72\\ \Leftrightarrow15+9x=96\\ \Leftrightarrow9x=81\\ \Leftrightarrow x=9\)

17) \(27\left(15-x\right)=162\\ \Leftrightarrow15-x=6\\ \Leftrightarrow x=9\)

18) \(6\left(52-3x\right)=204\\ \Leftrightarrow52-3x=34\\ \Leftrightarrow3x=18\\ \Leftrightarrow x=6\)

19) \(4\left(53-5x\right)=132\\ \Leftrightarrow53-5x=33\\ \Leftrightarrow5x=20\\ \Leftrightarrow x=4\)

20) \(20+\left(17-4x\right)=29\\ \Leftrightarrow17-4x=9\\ \Leftrightarrow4x=8\\ \Leftrightarrow x=2\)

21) \(\left(205-5x\right)+142=292\\ \Leftrightarrow205-5x=150\\ \Leftrightarrow5x=55\\ \Leftrightarrow x=11\)

22) \(59-\left(8x+32\right)=11\\ \Leftrightarrow8x+32=48\\ \Leftrightarrow8x=16\\ \Leftrightarrow x=2\)

bạn bổ sung \(ĐKXĐ:a\ge0;a\ne1\) giúp mình nhé, lúc làm mình quên mất T_T

\(P=\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{\sqrt{x}+1}+\dfrac{\sqrt{x}}{1-\sqrt{x}}\right):\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}+\dfrac{1-\sqrt{x}}{\sqrt{x}+1}\right)\left(ĐKXĐ:x>0;x\ne1\right)\\ P=\left(\dfrac{\sqrt{x}+1-\sqrt{x}}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{\sqrt{x}+1}\right):\dfrac{\left(\sqrt{x}+1\right)^2-\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ P=\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{\sqrt{x}+1}\right):\dfrac{4\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ P=\left(\dfrac{\sqrt{x}+1+\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\cdot\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{4\sqrt{x}}\\ P=\dfrac{x+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{4\sqrt{x}}\\ P=\dfrac{x+1}{4\sqrt{x}}\)

\(P=\left(1+\dfrac{\sqrt{a}}{a+1}\right):\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{2\sqrt{a}}{a\sqrt{a}+\sqrt{a}-a-1}\right)\\ P=\dfrac{a+\sqrt{a}+1}{a+1}:\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{2\sqrt{a}}{a\left(\sqrt{a}-1\right)+\left(\sqrt{a}-1\right)}\right)\\ P=\dfrac{a+\sqrt{a}+1}{a+1}:\dfrac{a+1+2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(a+1\right)}\\ P=\dfrac{a+\sqrt{a}+1}{a+1}:\dfrac{\left(\sqrt{a}+1\right)^2}{\left(\sqrt{a}-1\right)\left(a+1\right)}\\ P=\dfrac{a+\sqrt{a}+1}{a+1}\cdot\dfrac{\left(\sqrt{a}-1\right)\left(a+1\right)}{\left(\sqrt{a}+1\right)^2}\\ P=\dfrac{\sqrt{a^3}-1}{\left(\sqrt{a}+1\right)^2}\)

a) \(3119\cdot121-3119\cdot11\cdot11\\ =3119\left(121-11\cdot11\right)\\ =3119\left(121-121\right)\\ =3119\cdot0=0\)

b) \(24\cdot\left(123+87\right)+\left(87+123\right)\cdot76\\ =\left(123+87\right)\left(24+76\right)\\ =210\cdot100=21000\)

10. D

11. D

12. C

13. D

14. C

15. C

16. A

17. B

18. B

19. A

20. A

21. C

22. A

23. B

24. B

25. B

26. A

27. A

28. C

29. D

30. A

31. D

32. D