c1:\(\hept{\begin{cases}5x+8y=65\\x-y=0\end{cases}}\)

\(< =>\hept{\begin{cases}5x-5y+13y=65\\5x-5y=0\end{cases}}\)

\(< =>13y=65< =>y=\frac{65}{13}=5\)

Từ \(x-y=0< =>x=y< =>x=y=5\)

c2: \(\hept{\begin{cases}5x+8y=65\\x-y=0\end{cases}}\)

\(< =>\hept{\begin{cases}5x+8y=65\\x=y\end{cases}< =>5x+8x=65< =>x=\frac{65}{13}=5}\)

\(< =>x=y=5\)

I. Choose the word / phrase (A, B, C or D) that best fits the space in each sentence.
1. Tornadoes can suck up anything ________ is in their path.
A. what B. who C. that D. where
2. When the shaking first started, Yuki thought that it ______ just another standard aftershock.
A. is B. will be C. has D. was
3. I couldn’t sleep _______________________ very tired.
A. despite I was B. in spite of I was C. because of D. although I was
4. The weather _______________ for tomorrow is very worrying.
A. news B. foresee C. forecast D. foreman
5. He is always polite and _________________ towards his employees.
A. priority B. composes C. nominates D. considerate
6. Those buckets must be filled _______________ water for future use.
A. into B. on C. with D. by
7. Mary:” I’d to congratulate you on your drawing, Tom! “  Tom: ________________
A. Yes, I think so C. It’s very good. B. Thanks, it’s O.K D. It’s very nice of you to say so
8. Tet is a festival which occurs ________ late January or early February.
A. at B. from C. on D. in
9. Scientists can usually ________ when a volcano will erupt.
A. mean B. estimate C. report D. predict
10. He is famous for his _________ . He is very helpful to those less fortunate than himself.
A. kind B. unkind C. kindly D. kindness
11. After a while Yuki realized that something __________ wrong once the shaking did not stop.
A. is B. has been C. was D. will be
12. Tet is a festival which _______________________in late January or early February.
A. holds B. celebrates C. decorates D. occurs
13. In Australia, a 120-km tropical storm is known as a ______________________.
A. hurricane B. tornado C. cyclone D. typhoon
14. Passover is celebrated by ____________________people.
A. English B. Vietnamese C. Japanese D. Jewish
15. Auld Lang Syne is a song ____________________is sung on New Year’s Eve.
A. when B. which C. where D. it
16. ______________Mr Pike is old and weak, he goes jogging every day.
A. Therefore B. Because C. Although D. However
17. Most earthquakes occur ____________________the Pacific Rim.
A. along B. around C. through D. over
18. His sense of humor distinguishes him _____________________others.
A. among B. between C. from D. with
19. “I suggest going to the seaside on the weekend.” – “_____________________.”
A. That’s a reason B. That’s a trip C. That’s a fine day D. That’s a good idea
20. Many people were injured when the building ______________ .
A. collapsed B. destroyed C. struck D. erupt
21. We will arrive ________ the morning of the sixth.
A. in B. for C. on D. at
22. Tuan was an effective ____ in that volunteer program. He spent his free time heping people.
A. active B. activist C. actor D. activity
23. The ___________ of the volcano was a terrible disaster .
A. prediction B. eruption C. cyclone D. shift
24. Thank you for your donation. It was very generous________________ you.
A. in B. at C. since D. of
25. Are they preparing for a military _________ to celebrate National Day?
A. parade B. celebration C. exhibition D. nomination
26. When tropical storm reaches 120 kilometers per hour, it is called a ___________ in America.
A. cyclone B. hurricane C. tornado D. typhoon
27. They went on walking _____________ it started to rain heavily.
A. so B. though C. because D. despite
28. The women and animals _____________ you saw on TV were from China.
A. that B. which C. whom D. who
29. “Thank you very much for that!” - “_______________.”
A. of course B. thank you C. I don’t mind D. Not at all
30. Let me congratulate you ______________ your nomination.
A. about B. for C. with D. on

31. ___________ Easter Day , many children and adults enjoy painting eggs.
A. On B. At C. During D. In
32. My friend Nigel, _____________ works in the City Bank, earns much more than I do.
A. that B. which C. who D. whose
33. “I suggest going to London for the weekend.”
A. That‘s fine day B. That‘s a good idea. C. That’s a trip. D. That‘s reason.
34. ________________ the man felt very tired, he did not stop working.
A. Though B. Because C. If D. Despite
35. ___________ a sudden shaking of the earth's surface that often causes a lot of damage.
A. Earthquake B. Tidal wave C. Typhoon D. Tornado
36. I think that nothing is more precious than __________________.
A. acquaintance B. parade C. damage D. freedom
37. Easter is a joyful festival which ____________ in late March or early April.
A. celebrates B. holds C. organizes D. occurs
38. Hurricane Andrew, _____swept through southern Florida in 1992, killed 41 people.
A. which B. that C. who D. both A and B
39. “That’s a delicious cake, my daughter.” “Thanks, Mom._____________.”
A. I’m a clever girl. B. Well done. C. It is very kind of you to say so. D. Yes, of course

a) Hàm số y=ax² đi qua điểm (-1;3) nên

=> 3==a(-1)²

=> a=3

=> Hàm số là y=3x²

b) Các điểm cách đều 2 trục tọa độ có: |x|=|y|

\(\Rightarrow\orbr{\begin{cases}x=y\\x=-y\end{cases}\Leftrightarrow\orbr{\begin{cases}y=3\cdot y^2\\x=3\cdot\left(-y\right)^2\end{cases}\Rightarrow}x=3y^2}\)

<=> y(3y-1)=0

=> \(\orbr{\begin{cases}y=0\\3y-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}y=0\\y=\frac{1}{3}\end{cases}\Rightarrow}\orbr{\begin{cases}x=0\\x=\frac{-1}{3}\end{cases}}}\)

=> 2 điểm thỏa mãn là: (0;0) và \(\left(\frac{-1}{3};\frac{1}{3}\right)\)

\(\hept{\begin{cases}2x+9y=49\\x+y=7\end{cases}\Rightarrow}\hept{\begin{cases}2x+9y=49\\2x+2y=14\end{cases}}\Rightarrow\left(2x+9y\right)-\left(2x+2y\right)=35\)

\(\Rightarrow7y=35\Rightarrow y=5\Rightarrow x=2\)

Vậy x=2;y=5

C1:\(\hept{\begin{cases}2x+9y=49\\x+y=7\end{cases}}\)

\(< =>\hept{\begin{cases}2x+9y=49\\x=7-y\end{cases}< =>\hept{\begin{cases}2\left(7-y\right)+9y=49\\x+y=7\end{cases}}}\)

\(< =>\hept{\begin{cases}14-2y+9y=49\\x+y=7\end{cases}< =>\hept{\begin{cases}7y=49-14=35\\x+y=7\end{cases}}}\)

\(< =>\hept{\begin{cases}y=\frac{35}{7}=5\\5+x=7\end{cases}< =>\hept{\begin{cases}y=5\\x=2\end{cases}}}\)

C2:\(\hept{\begin{cases}2x+9y=49\\x+y=7\end{cases}}\)

\(< =>\hept{\begin{cases}2x+2y+7y=49\\x+y=7\end{cases}< =>\hept{\begin{cases}14+7y=49\\x+y=7\end{cases}}}\)

\(< =>\hept{\begin{cases}y=\frac{49-14}{7}=\frac{35}{7}=5\\x+5=7\end{cases}< =>\hept{\begin{cases}y=5\\x=2\end{cases}}}\)

Vậy ...

Labor is study 

123456789

em nghĩ bài này tìm giá trị lớn nhất ạ

\(P^2=\left(\sqrt{a+b}+\sqrt{b+c}+\sqrt{c+a}\right)^2=\left(1\cdot\sqrt{a+b}+1\cdot\sqrt{b+c}+1\cdot\sqrt{c+a}\right)^2\)

áp dụng bđt Cauchy-Schwartz, ta có:

\(P^2\le\left[\left(a+b\right)+\left(b+c\right)+\left(c+a\right)\right]\left[1^2+1^2+1^2\right]\)

\(P^2\le2\cdot3=6\)

Vậy \(P\le\sqrt{6}\)

dấu "="xảy ra <=> \(a=b=c=\frac{1}{3}\)