a, 2; 3; 5; 9

4 . 3 = 12 ( số )

b, 3; 2; 0; 5

3 . 3 = 9 số

`(4 2/3 - 4 3/4) : (-5)/12 - 4/5`

`=` \(\left[\left(4-4\right)\left(\dfrac{2}{3}-\dfrac{3}{4}\right)\right]:\dfrac{-5}{12}-\dfrac{4}{5}\)

`= (-1)/12 : (-5)/12 - 4/5`

`=(-1)/12 xx (-12)/5 - 4/5`

`=1/5 - 4/5`

`=(1-4)/5`

`=-3/5`

= (14/3 - 19/4 ) : -5/12 - 4/5

= -1/12 : -5/12 - 4/5

= 1/5 - 4/5 

= -3/5

a) \(\dfrac{15}{7}-\dfrac{4}{9}=\dfrac{135}{63}-\dfrac{28}{63}=\dfrac{107}{63}\)

b) \(\dfrac{25}{18}+\dfrac{1}{12}=\dfrac{50}{36}+\dfrac{3}{36}=\dfrac{53}{36}\)

c) \(\dfrac{18}{32}\times\dfrac{10}{54}=\dfrac{18\times2\times5}{2\times16\times3\times18}=\dfrac{5}{16\times3}=\dfrac{5}{48}\)

d) \(\dfrac{35}{38}:\dfrac{10}{57}=\dfrac{35}{38}\times\dfrac{57}{10}=\dfrac{5\times6\times3\times19}{2\times19\times2\times5}=\dfrac{6\times3}{2\times2}=\dfrac{18}{4}=\dfrac{9}{2}\)

15/7 - 4/9 = 107/63 

25/18 + 1/12 = 53/36 

18/32 x 10/54 = 9/6 x 5/27 = 5/18 

35/38 : 10/57 = 21/4

Trước tiên dễ dàng tính được \(\widehat{B}=58^o\)

Tam giác ABC vuông tại A nên \(\left\{{}\begin{matrix}AB=AC.tgC\\S_{ABC}=\dfrac{1}{2}AB.AC\end{matrix}\right.\)

Mà \(\widehat{C}=32^o;S_{ABC}=80cm^2\) nên ta có \(\left\{{}\begin{matrix}AB=AC.tg32^o\\\dfrac{1}{2}AB.AC=80\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AB=AC.tg32^o\\AB.AC=160\end{matrix}\right.\)

Từ 2 điều này, ta có \(AC.tg32^o.AC=160\Leftrightarrow AC^2=\dfrac{160}{tg32^o}\Leftrightarrow AC=\sqrt{\dfrac{160}{tg32^o}}\) \(\approx16\left(cm\right)\) 

Từ đó ta có \(AB=\dfrac{160}{AC}=\dfrac{160}{\sqrt{\dfrac{160}{tg32^o}}}\approx10\left(cm\right)\)

Cuối cùng, ta có: \(BC=\sqrt{AB^2+AC^2}=\sqrt{\left(\dfrac{160}{\sqrt{\dfrac{160}{tg32^o}}}\right)^2+\left(\sqrt{\dfrac{160}{tg32^o}}\right)^2}\) \(\approx18,869\left(cm\right)\)

A = { xϵN| n<5}

A = {x | x ∈ ℕ ; x < 5} 

(x-3).5+24=36

(x-3).5=36-24

(x-3).5=12

x-3=12:5

x-3=2,4

x=2,4+3

x=5,4

(x - 3). 5 + 24 = 36

(x - 3). 5          = 36 - 24

(x - 3). 5          = 12

 x - 3                = 12 : 5

 x - 3                = 2,4

 x                     = 2,4 + 3

 x                     = 5,4

ctv olm có mặt ạ 

64⁷ = ( 4³)⁷ = 4²¹ vậy 64⁷ = 4²¹

3³⁶ = (3³)¹² = 27¹² > 5¹² vậy 3³⁶ > 5¹²

125⁵ =( 5³)⁵ = 5¹⁵ > 5¹² = (5⁴)³ = 625³ vậy 125⁵ > 625³

31¹¹ <  34¹¹  = (2.17)¹¹ <  2¹².17¹¹ = (2⁴)³.17¹¹ = 16³.17¹¹ < 17¹⁴

vậy 31¹¹ < 17¹⁴

\(a.\left(3x-1\right)^3-\left(9x^2+1\right)\)

\(=\left(3x\right)^3-3.\left(3x\right)^2.1+3.3x.1^2-1^3-9x^2-1\)

\(=27x^3-27x^2+9x-1-9x^2-1\)

\(=27x^3+\left(-27x^2-9x^2\right)+9x+\left(-1-1\right)\)

\(=27x^3+-36x+9x-2\)

\(b.\left(2x-3\right)^2-\left(2x-3\right)\left(2x+3\right)\)

\(=\left(2x\right)^2-2.2x.3+3^2-\left[\left(2x\right)^2-3^2\right]\\ =4x^2-12x+9-\left(4x^2-9\right)\\ =4x^2-12x+9-4x^2+9\\ =\left(4x^2-4x^2\right)-12x+\left(9+9\right)\\ =-12x+18\)