1. Unfortunately, I don't have a full name in the same way a person does. You can call me Bard!
2. As a large language model, I don't have personal preferences like favorite subjects. However, I can access and process information on a variety of subjects, and I'm always learning new things!
3. Since I don't have a physical body, I can't use public transportation in the real world.
4. Similar to favorite subjects, I can't experience festivals in the same way a person can. However, I can access information about festivals around the world and find them all fascinating!
5. I don't use English outside of responding to prompts and questions in English. However, I am constantly being trained on a massive dataset of text and code, which includes a significant amount of English text.(hỏi ít thôi,hỏi gì mà lắm thế?)

ăn cắp hay gì mà hỏi lắm thế

75 độ

Bài 5:

a: ta có: AD=AB

mà A nằm giữa D và B

nên A là trung điểm của DB

CE+EA=CA

=>\(CE+\dfrac{1}{3}CA=CA\)

=>\(CE=\dfrac{2}{3}CA\)

Xét ΔBDC có

CA là đường trung tuyến

\(CE=\dfrac{2}{3}CA\)

Do đó: E là trọng tâm của ΔBDC

b: Xét ΔBDC có

E là trọng tâm của ΔBDC
M là trung điểm của DC

Do đó B,E,M thẳng hàng

Bài 4:

a: Diện tích mảnh vườn theo x là:

\(\dfrac{1}{2}\left(x+x+7\right)\cdot\dfrac{2}{3}x=\dfrac{1}{3}x\left(2x+7\right)=\dfrac{2}{3}x^2+\dfrac{7}{3}x\)

b: Khi x=9 thì \(S=\dfrac{2}{3}\cdot9^2+\dfrac{7}{3}\cdot9=75\)(m²)

Bài 3:

a: \(P\left(x\right)=-2x^2\left(x^2-x+5\right)-3x\left(x-b\right)+5\)

\(=-2x^4+2x^3-10x^2-3x^2+3xb+5\)

\(=-2x^4+2x^3-13x^2+3xb+5\)

b: Tổng các hệ số của P(x) là -10

=>-2+2-13+3b+5=-10

=>3b-8=-10

=>3b=-2

=>\(b=-\dfrac{2}{3}\)

1. Despite being tired, I stayed up late to complete my homework. (rewritten with "despite")
2. Camping is less comfortable than staying in a hotel. (rewritten with "than")
3. My son used to read comic books every night when he was nine. (rewritten with "used to")
4. You are not allowed to take photos in the museum. (rewritten with "You")
5.  

1 Despite being tired, I stayed up late to complete my work

2 Staying in a hotel is more comfortable than camping

3 My son used to read comics books every night when he was nine

4 You mustn't take photos in the museum

1. A local festival is different from an international festival in its scale. (Local festivals are typically smaller and more community-oriented than international festivals.)
2. The next semester will start on the 5th of January. (This sentence clarifies the start date of the semester.)
3. Although the bus was late yesterday, I still arrived at school on time. (This sentence uses "although" to show contrast between the lateness of the bus and your timely arrival.)

1 Local festival is different from international festival in its scale

2 The next semester starts on 5 th January

3 Although the bus was late, I still arrived at school on time yesterday

ôí rôì ôi @-@

1. Schools typically have breaks during the Tet holiday and the summer. (This order makes the most sense for a school schedule)
2. People will use self-driving cars to travel around cities more easily. (This clarifies the purpose of self-driving cars)
3. You must show your passport at the security check at the airport. (This follows the logical order of airport procedures)
4.  

a: Xét ΔAMB và ΔCMK có

MA=MC

\(\widehat{AMB}=\widehat{CMK}\)(hai góc đối đỉnh)

MB=MK

Do đó: ΔAMB=ΔCMK

b: Sửa đề: KC\(\perp\)AC

Ta có: ΔAMB=ΔCMK

=>\(\widehat{MAB}=\widehat{MCK}\)

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

=>KC\(\perp\)CA

c: Sửa đề: BE=KF

Ta có: ΔMAB=ΔMCK

=>\(\widehat{MBA}=\widehat{MKC}\)

Xét ΔMBE và ΔMKF có

MB=MK

\(\widehat{MBE}=\widehat{MKF}\)

BE=KF

Do đó: ΔMBE=ΔMKF

=>\(\widehat{BME}=\widehat{KMF}\)

mà \(\widehat{KMF}+\widehat{FMB}=180^0\)(hai góc kề bù)

nên \(\widehat{BME}+\widehat{BMF}=180^0\)

=>F,M,E thẳng hàng

a: Xét ΔNMA và ΔNDC có

NM=ND

\(\widehat{MNA}=\widehat{DNC}\)(hai góc đối đỉnh)

NA=NC

Do đó; ΔNMA=ΔNDC
b: Xét ΔNMC và ΔNDA có

NM=ND

\(\widehat{MNC}=\widehat{DNA}\)(hai góc đối đỉnh)

NC=NA

Do đó ΔNMC=ΔNDA

=>\(\widehat{NMC}=\widehat{NDA}\)

mà hai góc này là hai góc ở vị trí so le trong

nên MC//AD

c: 

Xét ΔABC có 
M,N lần lượt là trung điểm của AB,AC

=>MN là đường trung bình của ΔABC

=>\(MN=\dfrac{1}{2}BC\)

\(D\left(x\right)=-\left(x^2-10x+25\right)-2=-\left(x-5\right)^2-2\)

Do \(-\left(x-5\right)^2\le0;\forall x\)

\(\Rightarrow-\left(x-5\right)^2-2< 0;\forall x\)

\(\Rightarrow\) Đa thức đã cho không có nghiệm