Oa là phân giác của góc mOt

=>\(\widehat{mOa}=\dfrac{\widehat{mOt}}{2}=\dfrac{40^0}{2}=20^0\)

Ta có: \(\widehat{mOa}+\widehat{nOa}=180^0\)(hai góc kề bù)

=>\(\widehat{nOa}=180^0-20^0=160^0\)

Sửa đề: \(7,2:\left[41-\left(2x-5\right)\right]=2^3.5\)
\(\Rightarrow7,2:\left[41-\left(2x-5\right)\right]=8.5\)
\(\Rightarrow7,2:\left[41-\left(2x-5\right)\right]=40\)
\(\Rightarrow41-\left(2x-5\right)=7,2:40\)
\(\Rightarrow41-\left(2x-5\right)=0,18\)
\(\Rightarrow2x-5=41-0,18\)
\(\Rightarrow2x-5=40,82\)
\(\Rightarrow2x=40,82+5\)
\(\Rightarrow2x=45,82\)
\(\Rightarrow x=45,82:2\)
\(\Rightarrow x=22,91\)
Vậy ...

4. In spite of my sickness, my mother told me to go to school.
5. Because of a big storm, I stayed at home.
6. Despite Tom's bad grades, he was admitted to the university.
7. Despite having a physical handicap, she has become a successful woman.
8. Although his salary was good,Tom gave up his job.
9. In spite of not being finished the paper,he went to sleep.
10. Even though the prices are high , my daughter insists on going to the movies.

4 In spite of my sickness, my mother told me to go to school 

5 Because of a big storm, I stayed at home

6 Despite his bad grades, Tom was admitted to the university 

7 Despite having a physical handicap, she has become a successful woman

8 Although his salary was good, he gave up his job

9 In spite of not having finished the paper, he went to sleep

10 Eventhough the prices are high, my sister insists on going to the movies

1. What do people say about the film?
2. My favourite film is Annabelle, a horror film directed by John R. Leonetti.
3. Let's go to the cinema tonight.
4. What kind of film is it?
5. He doesn't like that kind of film.
6. Many people cried when they saw the scenes in the film.
7. The film last night was so boring that we fell asleep.
8. There were many fights in the film. It was too violent.
9.  What film did you see recently?
10. Put your earphones near here.

1 What do people say about the film?

2 My favorite film is Annabelle, a horror film directed ny John R. Leonetti

3 Let's go to the cinema tonight

4 What kind of film is it?

5 He doesn't like that kind of film

6 Many people cried when they saw the scenes in the film

7 The film was so boring that we fell asleep last night

8 There were too many fights in the film. It was violent

9 What film did you see recently?

10 Put your earphones near here

1 are-->is

2 them-->it

3 Who--->What

4 liked-->like

   it is-->they are

5 leaves---left

   carly-->early

6 have supernatural --->has supernatural elements

7 an--> a

8 in-->at

9 review-->reviews

10 interested-->interesting

1 are => is

2 them => it

3 who => what

4 liked => like, it is => they are

5 leaves => left

6 have => is

7 an => a

8 in => At

9 review => reviews

10 interested => interesting

a: Xét ΔABD và ΔAED có

AB=AE

\(\widehat{BAD}=\widehat{EAD}\)

AD chung

Do đó: ΔABD=ΔAED

b: ΔABD=ΔAED

=>\(\widehat{ABD}=\widehat{AED}\)

Để DE\(\perp\)AC thì \(\widehat{AED}=90^0\)

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

hay \(\widehat{ABC}=90^0\)

c: Xét ΔAEK và ΔABC có

\(\widehat{AEK}=\widehat{ABC}\)

AE=AB

\(\widehat{EAK}\) chung

Do đó: ΔAEK=ΔABC

=>\(\widehat{AKE}=\widehat{ACB}\)

d: Ta có: ΔAEK=ΔABC

=>AK=AC

Ta có: AB+BK=AK

AE+EC=AC

mà AB=AE và AK=AC

nên BK=EC

ΔAEK=ΔABC

=>EK=BC

Xét ΔEBK và ΔBEC có

BE chung

BK=EC

EK=BC

Do đó: ΔEBK=ΔBEC

a: Xét ΔABE và ΔAME có

AB=AM

\(\widehat{BAE}=\widehat{MAE}\)

AE chung

Do đó: ΔABE=ΔAME

b: ΔABM có AB=AM

nên ΔABM cân tại A

Ta có: ΔABM cân tại A

mà AI là đường phân giác

nên I là trung điểm của BM

=>IB=IM

c: ΔABE=ΔAME

=>EB=EM

Xét ΔEBN và ΔEMC có

EB=EM

\(\widehat{BEN}=\widehat{MEC}\)(hai góc đối đỉnh)

EN=EC

Do đó: ΔEBN=ΔEMC

d: ΔEBN=ΔEMC

=>\(\widehat{EBN}=\widehat{EMC}\)

ΔABE=ΔAME

=>\(\widehat{ABE}=\widehat{AME}\)

\(\widehat{ABE}+\widehat{EBN}=\widehat{AME}+\widehat{CME}=180^0\)

=>A,B,N thẳng hàng

\(a,\dfrac{4}{5}.\left(\dfrac{7}{2}+\dfrac{1}{4}\right)^2\)
\(=\dfrac{4}{5}\left(\dfrac{14}{4}+\dfrac{1}{4}\right)^2\)
\(=\dfrac{4}{5}.\left(\dfrac{15}{4}\right)^2\)
\(=\dfrac{4}{5}.\dfrac{225}{16}\)
\(=\dfrac{45}{4}\)
\(b,\left|\dfrac{-3}{8}\right|.27\dfrac{1}{5}-51\dfrac{1}{5}.\dfrac{3}{8}+19\)
\(=\dfrac{3}{8}.\dfrac{136}{5}-\dfrac{256}{5}.\dfrac{3}{8}+19\)
\(=\dfrac{3}{8}.\left(\dfrac{136}{5}-\dfrac{256}{5}\right)+19\)
\(=\dfrac{3}{8}.\dfrac{-120}{5}+19\)
\(=\dfrac{3}{8}.\left(-24\right)+19\)
\(=-9+19\)
\(=10\)
\(c,\left(\dfrac{2}{3}-\dfrac{7}{15}\right):\left(\dfrac{2}{3}-\dfrac{2}{5}\right)^2\)
\(=\left(\dfrac{10}{15}-\dfrac{7}{15}\right):\left(\dfrac{10}{15}-\dfrac{6}{15}\right)^2\)
\(=\dfrac{3}{15}:\left(\dfrac{4}{15}\right)^2\)
\(=\dfrac{1}{5}:\dfrac{16}{225}\)
\(=\dfrac{45}{16}\)
\(d,\dfrac{-19}{3}.\dfrac{14}{4}-\dfrac{25}{4}.\left|\dfrac{-19}{3}\right|+4\dfrac{4}{3}\)
\(=\dfrac{19}{3}.\dfrac{-14}{4}-\dfrac{25}{4}.\dfrac{19}{3}+\dfrac{16}{3}\)
\(=\dfrac{19}{3}.\left(\dfrac{-14}{4}-\dfrac{25}{4}\right)+\dfrac{16}{3}\)
\(=\dfrac{19}{3}.\dfrac{-39}{4}+\dfrac{16}{3}\)
\(=\dfrac{-247}{4}+\dfrac{16}{3}\)
\(=\dfrac{-741}{12}+\dfrac{64}{12}\)
\(=\dfrac{-677}{12}\)

\(a,\dfrac{3}{8}.19\dfrac{1}{3}-\dfrac{3}{8}.33\dfrac{1}{3}\)
\(=\dfrac{3}{8}.\left(19\dfrac{1}{3}-33\dfrac{1}{3}\right)\)
\(=\dfrac{3}{8}.\left(\dfrac{58}{3}-\dfrac{100}{3}\right)\)
\(=\dfrac{3}{8}.\dfrac{-42}{3}\)
\(=\dfrac{-42}{8}=\dfrac{-21}{4}\)
\(b,\dfrac{21}{47}+\dfrac{9}{45}+\dfrac{26}{47}+\dfrac{4}{5}\)
\(=\left(\dfrac{21}{47}+\dfrac{26}{47}\right)+\left(\dfrac{9}{45}+\dfrac{4}{5}\right)\)
\(=\dfrac{47}{47}+\left(\dfrac{9}{45}+\dfrac{36}{45}\right)\)
\(=1+\dfrac{45}{45}\)
\(=1+1\)
\(=2\)
\(c,\dfrac{13}{25}+\dfrac{6}{41}-\dfrac{38}{25}+\dfrac{35}{41}-\dfrac{1}{2}\)
\(=\left(\dfrac{13}{25}-\dfrac{38}{25}\right)+\left(\dfrac{6}{41}+\dfrac{35}{41}\right)-\dfrac{1}{2}\)
\(=\dfrac{-25}{25}+\dfrac{41}{41}-\dfrac{1}{2}\)
\(=-1+1-\dfrac{1}{2}\)
\(=0-\dfrac{1}{2}\)
\(=\dfrac{-1}{2}\)
\(d,12,5.\left(\dfrac{-5}{7}\right)+1,5.\left(\dfrac{-5}{7}\right)\)
\(=\dfrac{-5}{7}.\left(12,5+1,5\right)\)
\(=\dfrac{-5}{7}.14\)
\(=-10\)

\(60=2^2.3.5\)

Để \(\dfrac{x+2}{60}\) viết được dưới dạng số thập phân hữu hạn

\(\Rightarrow x+2\) không được chứa ước nguyên tố nào khác \(2\) và \(5\)

\(\Rightarrow x+2\in U\left(2^2.5=20\right)=\left\{1;2;4;5;10;20\right\}\)

\(\Rightarrow x\in\left\{-1;0;2;3;8;18\right\}\)

mà \(x\in N;x< 15\)

\(\Rightarrow x\in\left\{0;2;3;8\right\}\)

\(\Rightarrow\) Có \(4\) số tự nhiên \(x< 15\) thỏa mãn đề bài

\(\Rightarrow\) Trả lời có \(4\) số