Xét tam giác ABM có:

  MD là tia phân giác của góc AMB

=>\(\dfrac{DA}{DB}=\dfrac{AM}{BM}\)(Tính chất đường phân giác)(1)

CMTT:\(\dfrac{EA}{EC}=\dfrac{AM}{MC}\)(2)

Ta có: BM=MC(AM là trung tuyến nên M là trung điểm BC)

 =>\(\dfrac{AM}{BM}=\dfrac{AM}{MC}\)(3)

Từ (1),(2) và (3)

=>\(\dfrac{DA}{DB}=\dfrac{EA}{EC}\)

=>DE//BC(định lí ta let áp dụng trong tam giác ABC)

Gọi nguyên tố cần tìm là :  A

pt :   4A    +     5O2 ------>       2A2O5 

       4MA g        160 g

       2 g               2,54  g

Tỉ lệ:
2    /    4MA    =       2,54    /   160

---> MA = 31, 49...  = 31 g/mol   

Vậy nguyên tố cần tìm là Photpho ( P )

Ko copy mạng cơ mà =D

5.A

6.B

7.C

8.D

9.C

10.A

11.D

12.B

13.C

Ta có:\(\dfrac{1}{4}=\dfrac{1\times5}{4\times5}=\dfrac{5}{20};\dfrac{2}{5}=\dfrac{2\times4}{5\times4}=\dfrac{8}{20};\dfrac{7}{20}\)

Vì \(\dfrac{5}{20}< \dfrac{7}{20}< \dfrac{8}{20}=>\dfrac{1}{4}< \dfrac{7}{20}< \dfrac{2}{5}=>Hải< Nam< Dương\)

a)\(\dfrac{67}{10}\)

b)\(3\dfrac{5}{8}\)

c)9,71

d)30,04

Theo đề bài ta gọi số cần tìm là n

=>\(\dfrac{18-n}{27-n}=\dfrac{1}{2}\)

=>\(2\left(18-n\right)=27-n\)

=>\(36-2n=27-n\)

=>\(2n-n=36-27\)

=>n=9

Vậy số cần tìm là 9

d)\(\dfrac{3}{14}=\dfrac{3\times4}{14\times4}=\dfrac{12}{56};\dfrac{4}{15}=\dfrac{4\times3}{15\times3}=\dfrac{12}{45};\dfrac{6}{17}=\dfrac{6\times2}{17\times2}=\dfrac{12}{34}\)

Vì \(56>45>34=>\dfrac{12}{56}< \dfrac{12}{45}< \dfrac{12}{34}=>\dfrac{3}{14}< \dfrac{4}{15}< \dfrac{6}{17}\)

e)\(\dfrac{13}{-36}=\dfrac{-13}{36};-\dfrac{7}{18}=\dfrac{-7\times2}{18\times2}=\dfrac{-14}{36};\dfrac{-5}{12}=\dfrac{-5\times3}{12\times3}=\dfrac{-15}{36}\)

Vì \(\dfrac{-13}{36}>\dfrac{-14}{36}>\dfrac{-15}{36}=>\dfrac{13}{-36}>-\dfrac{7}{18}>\dfrac{-5}{12}\)

g)\(\dfrac{-12}{17}=\dfrac{-12\times4}{17\times4}=\dfrac{-48}{68};\dfrac{-8}{15}=\dfrac{-8\times6}{15\times6}=\dfrac{-48}{90};\dfrac{16}{-2}=\dfrac{16\times3}{-2\times3}=\dfrac{-48}{6}\)

Vì \(90>68>6=>\dfrac{48}{90}>\dfrac{48}{68}>\dfrac{48}{6}=>\dfrac{-48}{90}< \dfrac{-48}{68}< \dfrac{-48}{6}=>\dfrac{-8}{15}< \dfrac{-12}{17}< \dfrac{16}{-2}\)

a)\(\dfrac{13}{21}=\dfrac{13\times2}{21\times2}=\dfrac{26}{42};\dfrac{9}{14}=\dfrac{9\times3}{14\times3}=\dfrac{27}{42}\)

Ta có:\(\dfrac{26}{42}< \dfrac{27}{42}=>\dfrac{13}{21}< \dfrac{9}{14}\)

b)\(\dfrac{6}{17}=\dfrac{6\times9}{17\times9}=\dfrac{54}{153};\dfrac{9}{25}=\dfrac{9\times6}{25\times6}=\dfrac{54}{150}\)

Vì \(153>150=>\dfrac{54}{153}< \dfrac{54}{150}=>\dfrac{6}{17}< \dfrac{9}{25}\)

c)\(\dfrac{7}{-12}=\dfrac{-7}{12}=\dfrac{-7\times3}{12\times3}=\dfrac{-21}{36};\dfrac{11}{-18}=\dfrac{-11}{18}=\dfrac{-11\times2}{18\times2}=\dfrac{-22}{36}\)

Vì \(\dfrac{-21}{36}>\dfrac{-22}{36}=>\dfrac{7}{-12}>\dfrac{11}{-18}\)