b: Ta có: \(x=-\dfrac{31}{33}=1-\dfrac{2}{33}\)

\(y=-\dfrac{49}{51}=1-\dfrac{2}{51}\)

mà \(-\dfrac{2}{33}>-\dfrac{2}{51}\)

nên x>y

 15^19 thành 16^19

Ta có:

16^19=(2^4)^19=2^76

8^25=(2^3)^25=2^75

2^76>2^75⇒16^19>8^25

đề toán bạn êy

\(\frac{-1}{6}.\frac{-15}{19}.\frac{38}{45}\)

\(\frac{\left(-1\right).\left(-15\right).2.19}{2.3.19.3.15}\)

\(=\frac{1}{3.3}=\frac{1}{9}\)

\(\left(-\frac{1}{6}\right).\left(-\frac{15}{19}\right).\frac{38}{45}\)

\(=\frac{\left(-1\right).\left(-15\right).38}{6.19.45}=\frac{1.15.38}{6.19.45}\)

\(=\frac{1.1.1}{3.1.3}=\frac{1}{9}\)

\(\frac{x}{19}=\frac{19^{17}+1}{19^{17}+19}=1-\frac{18}{19^{17}+19}\)

\(\frac{y}{19}=\frac{19^{16}+1}{19^{16}+19}=1-\frac{18}{19^{16}+19}\)

Nhận thấy 19¹⁷ + 19 > 19¹⁶ + 19

=> \(\frac{18}{19^{17}+19}< \frac{18}{19^{16}+19}\)

=> \(-\frac{18}{19^{17}+19}>-\frac{18}{19^{16}+19}\)

=> \(1-\frac{18}{19^{17}+19}>1-\frac{18}{19^{16}+19}\)

=> \(\frac{x}{19}>\frac{y}{19}\)

=> x > y

Vậy x > y

Ta có : \(\frac{x}{19}=\frac{19^{17}+1}{19^{17}+19}=1-\frac{18}{19^{17}+19}\)

\(\frac{y}{19}=\frac{19^{16}+1}{19^{16}+19}=1-\frac{18}{19^{16}+19}\)

Vì\(\frac{18}{19^{17}+19}< \frac{18}{19^{16}+19}\)\(\Rightarrow\frac{x}{19}>\frac{y}{19}\)

mà \(x,y>0\)

\(\Rightarrow x>y\)

\(5^{20}=\left(5^2\right)^{10}=25^{10}\)

\(3^{30}=\left(3^3\right)^{10}=27^{10}\)

Vì \(25^{10}< 27^{10}\) \(\Leftrightarrow5^{20}< 3^{30}\)

Mà \(3^{30}< 3^{34}\Leftrightarrow5^{20}< 3^{34}\)

a: DE>DF

=>góc F>góc E

b: Xét ΔDEF có DE>DF

mà ME,MF lần lượt là hình chiếu của DE,DF trên EF

nên ME>MF

c; DF=căn 7^2+12^2=căn 193(cm)