VẼ HÌNH LUÔN NHÁ!

A B D C E F 60* 1 1 2

a, Ta có: AB=AC => tg ABC cân tại A

=>\(\widehat{B_1}=\widehat{C_1}=\frac{180^o-100^o}{2}=40^o\)

BF//AC => \(\widehat{B_2}=\widehat{C_1}=40^o\left(slt\right);\widehat{BFA}=\widehat{CAF}\left(slt\right)\)

Mà \(\widehat{CAF}=\widehat{BAC}-\widehat{BAE}=100^o-60^o=40^o\)

=>\(\widehat{B_2}=\widehat{BFA};\widehat{C_1}=\widehat{CAF}\)

=> tg EFB cân tại E ; tg EAC cân tại E

=> EF=EB ; EA=EC

=>EF + EA = EB + EC 

Mà E nằm giữa F,A và B,C

=> AF = BC mà BC=AD (gt)

=>AF = AD 

=> tg ADF cân tại A

Mà góc DAF = 60 độ (gt)

=>tg ADF đều

1, \(=\frac{3\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{11}+\frac{1}{13}\right)}{7\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{11}+\frac{1}{13}\right)}=\frac{3}{7}\)

2, a, \(\Leftrightarrow\left(3x-2\right)^{10}-\left(3x-2\right)^6=0\)

\(\Leftrightarrow\left(3x-2\right)^6\left[\left(3x-2\right)^4-1\right]=0\)

TH1: (3x-2)^6=0 <=> 3x-2=0 <=> x=2/3

TH2: (3x-2)^4-1=0 <=> (3x-2)^4=1

<=> 3x-2 = 1 hoặc 3x-2=-1

<=>x=1 hoặc x=-1/3

Vậy x=2/3 hoặc x=1 hoặc x=-1/3

b, \(\Leftrightarrow\orbr{\begin{cases}2x^2-13=-5\\2x^2-13=5\end{cases}\Leftrightarrow\orbr{\begin{cases}2x^2=8\\2x^2=18\end{cases}\Leftrightarrow}\orbr{\begin{cases}x^2=4\\x^2=9\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\pm2\\x=\pm3\end{cases}}}\)

3,a, \(A=\frac{3n+9}{n-4}=\frac{3n-12+21}{n-4}=\frac{3\left(n-4\right)+21}{n-4}=3+\frac{21}{n-4}\)

Để \(A\in Z\Leftrightarrow\frac{21}{n-4}\in Z\Leftrightarrow21⋮n-4\Leftrightarrow n-4\inƯ\left(21\right)\)

Ta có bảng

Vậy..

b, tương tự a

Ta có: \(f\left(x\right)=x^2-1\)

\(\Rightarrow f\left(1-x_0\right)=\left(1-x_0\right)^2-1\)

\(=x_0^2-2x_0+1-1=x_0^2-2x_0\)

\(=x_0\left(x_0-2\right)\)

\(f\left(1-x_0\right)< 0\Leftrightarrow\)\(x_0\left(x_0-2\right)< 0\)

Mà \(x_0>x_0-2\)nên \(\hept{\begin{cases}x_0>0\\x_0-2< 0\end{cases}}\Leftrightarrow0< x_0< 2\)

Vậy \(0< x_0< 2\)thì \(f\left(1-x_0\right)\)đạt giá trị âm

Đầu bài là gì bạn ơi?

tìm gí trị lớn nhất của biểu thức sau

a, I thuộc đường trung trực của AD (Gt)

=> IA = ID (Đl)

I thuộc đường trung trực của BC (gt)

=> IB = IC (đl)

b, xét ta giác IAB và tam giác IDC có : CD = AB (gt)

IB = IC (câu a)

IA = ID (câu a)

=> tam giác IAB = tam giác IDC (c-c-c)

A C B I D

a) I \(\in\) đường trung trực của BC

\(\Rightarrow IB=IC\)

I \(\in\) đường trung trực của AD

\(\Rightarrow IA=ID\Rightarrow\Delta IAD\) cân \(\Rightarrow\widehat{IAC}=\widehat{IDC}\) ( 1 )

Xét \(\Delta IAB\) và \(\Delta IDC\) có :

\(AB=CD\)

\(IB=IC\)

\(IA=ID\)

\(\Rightarrow\Delta IAB=\Delta IDC\)

\(\Rightarrow\widehat{BAI}=\widehat{CDI}\) ( 2 )

Từ (1) và (2) \(\Rightarrow\widehat{BAI}=\widehat{IAC}\Rightarrow AI\) là phân giác của \(\widehat{BAC}\)

Gọi 2²³+1/2²⁵+1 là A;2²⁵+1/2²⁷+1 là B 

Ta có 2²A=2²⁵+4/2²⁵+1

2²A=2²⁵+1/2²⁵+1 + 3/2²⁵+1    

2²A=1+3/2²⁵+1

Có 2²B=2²⁷+4/2²⁷+1

2²B=2²⁷+1/2²⁷+1 + 3/2²⁷+1

2²B=1+3/2²⁷+1

Vì 1+3/2²⁵+1>1+3/2²⁷+1

nên 2²A>2²B

nên A>B

Vậy A>B

Cảm ơn Pé's Pơ's nhiều nha

I think bicycles are the best transport in Vietnam. It is convenient and good for health. Riding a bicycle, I can develope a strong heart and muscular limbs. Using a bike for transportation also can help you lose weight and improve your overall health. In city or countryside, when you ride bicycle, you don't need to worry about parking problems and can save money on fuel. Morever, bicycles are only means of transport with don't pollute the environment. Those are some reasons why bicycles are the best means of transport in Vietnam.

I think bicycles are the best transport in Vietnam. It is convenient and good for health. Riding a bicycle, I can develope a strong heart and muscular limbs. Using a bike for transportation also can help you lose weight and improve your overall health. In city or countryside, when you ride bicycle, you don't need to worry about parking problems and can save money on fuel. Morever, bicycles are only means of transport with don't pollute the environment. Those are some reasons why bicycles are the best means of transport in Vietnam.
❤☺

OR

I'd a bicycle and I think bicycle is the best means of transport in Vietnam, because if you want to perfectly feel the atmosphere of Vietnam daily life, hire one bicycle and ride around the city in the early morning. in Hanoi, you can see the early morning market, parks in the morning with exercises of local people, Hanoi streets with not many vehicles.

31. I’d better have a shower. I haven't had one since Thursday.
32. I don’t live with my family now and we haven't seen each other for five years.
33. Look! It is raining

My mother is cookingat the  moment.
35. How long did you know each other?
36. Did you take many photographs on your last holiday ?
37.Has she eaten at the Royal Hotel yet ?
38.Does he live here ? 

39. ShevisitedHanoi last year.

40. Mai sometimes goes out with her friends.