a) \(\widehat{A_1}=\widehat{A_3}\) (vì là cặp góc sole trong)

b)\(\widehat{A_2}=\widehat{B_2}\) (vì là cặp góc đồng vị)

c) \(\widehat{B_3}+\widehat{A_4}=180^o\) (vì là cặp góc trong cùng phía)

d) \(\widehat{A_2}=\widehat{B_4}\) (vì là cặp góc sole ngoài)

Ta có

\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{y-x}{5-3}=\dfrac{24}{2}=12\\ .\dfrac{x}{3}=12\Rightarrow x=12.3=36\\ .\dfrac{y}{5}=12\Rightarrow y=12.5=60\)

Vậy\(x=36;y=60\)

a) \(\dfrac{a^{m+1}}{a^{m+2}}\)với \(a=\dfrac{-1}{2}\)

Ta có:

\(\dfrac{a^{m+1}}{a^{m+2}}=\dfrac{a^m.a}{a^m.a^2}=\dfrac{-1}{2}:\left(\dfrac{-1}{2}\right)^2=-2\)

b) \(\dfrac{a^m}{a^{2m+1}}\)với \(a=\dfrac{-1}{4};m=3\)

Ta có:

\(\dfrac{a^m}{a^{2m+1}}=\dfrac{a^3}{a^{2.3}.a}=\dfrac{a^3}{a^6.a}=\dfrac{1}{a^3.a}=\dfrac{1}{\left(-\dfrac{1}{4}\right)^3.\left(-\dfrac{1}{4}\right)}=\dfrac{1}{\left(-\dfrac{1}{4}\right)^4}=256\)

c)\(\dfrac{\left(a+3\right)^3}{\left(a+3\right)^4}\)

Ta có:

\(\dfrac{\left(a+3\right)^3}{\left(a+3\right)^4}=\dfrac{\left(a+3\right)^3}{\left(a+3\right)^3.\left(a+3\right)}=\dfrac{1}{a+3}\)

Chúc bạn học tốt

1+2+3+4+......+2013 = (2013+1)2013:2 = 2014.2013;2= 1007.2013=2027091

Ta có:

\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{x+y}{3+5}=\dfrac{16}{8}=2\\ .\dfrac{x}{3}=2\Rightarrow x=2.3=6\\ .\dfrac{y}{5}=2\Rightarrow y=2.5=10\)

Vậy x=6; y=10

Bài 1:

1) \(3^2.\dfrac{1}{243}.81^2.\dfrac{1}{3^3}\)

\(=3^2.\left(\dfrac{1}{3}\right)^5.\left(3^4\right)^2.\dfrac{1}{3^3}\)

\(=3^2.\dfrac{1}{3^5}.3^8.\dfrac{1}{3^3}\)

\(=3^2=9\)

2) \(\left(4.2^5\right):\left(2^3.\dfrac{1}{16}\right)\)

\(=\left(2^2.2^5\right):[2^3.\left(\dfrac{1}{2}\right)^4]\)

\(=2^7:2^3:\dfrac{1}{2^4}\)

\(=2^4.2^4=256\)

3)\(\left(2^{-1}+3^{-1}\right)+\left(2^{-1}.2^0\right):2^3\)

\(=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{2}.1:2^3\)

\(=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{2^4}\)

\(=\dfrac{43}{48}\)

4)\(\left(-\dfrac{1}{3}\right)^{-1}-\left(-\dfrac{6}{7}\right)^0+\left(\dfrac{1}{2}\right)^2:2\)

\(=-3-1+\dfrac{1}{4}.\dfrac{1}{2}\)

\(=-3-1+\dfrac{1}{8}\)

\(=-4+\dfrac{1}{8}\\ \)

\(=-\dfrac{31}{8}\)

5)\([\left(0,1\right)^2]^0+[\left(\dfrac{1}{7}\right)^{-1}]^2.\dfrac{1}{49}.[\left(2^2\right)^3:2^5]\\ =1+7^2.\dfrac{1}{7^2}.2^6:2^5\\ =1+1.2\\ =3\)

Chúc bạn học tốt

Kẻ tia FO cắt m tại D

Ta có: \(\widehat{DOE}+\widehat{FOE}\) = 180^o (kề bù)

\(\widehat{DOE}=180^o-110^o=70^o\)

\(\widehat{ODE}+\widehat{DOE}+\widehat{DEO}=180^o\)(tổng 3 góc trong \(\Delta DOE\))

\(\widehat{ODE}=180^o-80^o-70^o=30^o\)

\(\Rightarrow\widehat{F}=\widehat{ODE}=30^o\)

mà \(\widehat{F}\)và \(\widehat{ODE}\) nằm ở vị trí sole trong

=> n//m

Cho mình hỏi bài 1 bạn có ghi thiếu góc C không vậy?

Ta có: \(8^7-2^{18}\)

\(=\left(2^3\right)^7-2^{18}\)

\(=2^{21}-2^{18}\)

\(=2^{17+4}-2^{17+1}\)

\(=2^{17}.2^4-2^{17}.2\)

\(=2^{17}\left(2^4-2\right)\)

\(=2^{17}.14⋮14\)

Vậy \(\left(8^7-2^{18}\right)⋮14\)

Chúc bạn học tốt

Câu 4:

Ta có: \(8^7-2^{18}\)

\(=\left(2^3\right)^7-2^{18}\)

\(=2^{21}-2^{18}\)

\(=2^{17+4}-2^{17+1}\)

\(=2^{17}.2^4-2^{17}.2\)

\(=2^{17}\left(2^4-2\right)\)

\(=2^{17}.14⋮14\)

Vậy \(\left(8^7-2^{18}\right)⋮14\)