`0,5 + 1/3 + 0,4 + 5/7 + 1/6 - 4/35`

`=1/2 + 1/3 + 2/5 + 5/7 + 1/6 - 4/35`

`=(1/2 + 1/3 + 1/6) + ( 2/5 - 4/35 + 5/7)`

`= (3/6 + 2/6 + 1/6) + ( 14/35 - 4/35 + 25/35)`

`=((3+2+1)/6) + (( 14-4+25)/35)`

`= 6/6+ 35/35`

`=1+1`

`=2`

\(0,5+\dfrac{1}{3}+0,4+\dfrac{5}{7}+\dfrac{1}{6}-\dfrac{4}{35}\)

\(=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{2}{5}+\dfrac{5}{7}+\dfrac{1}{6}-\dfrac{4}{35}\)

\(=\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\right)+\left(\dfrac{5}{7}+\dfrac{2}{5}-\dfrac{4}{35}\right)\)

\(=1+\dfrac{39}{35}-\dfrac{4}{35}\)

\(=1+1=2\)

`3.x^2 - 18= 0 `

`3.x^2 = 0+18`

`3.x^2=18`

`x^2=18:3`

`x^2=9`

`x^2=3^2`

`=> x=2`

3x^2-18=0

=>x^2=6

=>x=\(+-\sqrt{6}\)

\(\left|2x-\dfrac{1}{2}\right|=\dfrac{17}{4}\)

\(\left[{}\begin{matrix}2x=\dfrac{17}{4}+\dfrac{1}{2}=\dfrac{19}{4}\\2x=-\dfrac{17}{4}+\dfrac{1}{2}=-\dfrac{15}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{19}{4}:2=\dfrac{19}{8}\\x=-\dfrac{15}{8}\end{matrix}\right.\)

\(3,5-|2x-\dfrac{1}{2}|=-0,75\)

\(|2x-\dfrac{1}{2}|=3,5-(-0,75)=4,25\)

\(\bullet TH1: 2x-\dfrac{1}{2}=4,25\)

     \(=>2x=4,25+\dfrac{1}{2}=4,75\)

    \(=>x=4,75:2=2,375\)

\(\bullet TH2:2x-\dfrac{1}{2}=-4,75\)

    \(=>2x=-4,75+\dfrac{1}{2}=-4,25\)

   \(=>x=-4,25:2=-2,125\)

`2/3x - 1/2 = (-2/3)^2`

`2/3x - 1/2= 4/9`

`2/3x = 4/9+1/2`

`2/3x=17/18`

`x=17/18:2/3`

`x=17/18 xx 3/2`

`x=17/12`

\(\dfrac{2}{3}x-\dfrac{1}{2}=\left(-\dfrac{2}{3}\right)^2\)

\(\dfrac{2}{3}x-\dfrac{1}{2}=\dfrac{4}{9}\)

\(\dfrac{2}{3}x=\dfrac{4}{9}+\dfrac{1}{2}\)

\(\dfrac{2}{3}x=\dfrac{17}{18}\)

x\(=\dfrac{17}{18}:\dfrac{2}{3}\)

x= \(\dfrac{17}{12}\)

`(5/2 - 4/3).6/7 + (-3/2)^5 : (-3/2)^3`

`=(5/2 - 4/3).6/7 + \(\left(-\dfrac{3}{2}\right)^{5-3}\)

`=(5/2 - 4/3).6/7 +(-3/2)^2`

`=(15/6 - 8/6) . 6/7 + 9/4`

`=7/6 . 6/7 +9/4`

`=(7xx6)/(6xx7) + 9/4`

`=1+9/4`

`=4/4+9/4`

`=13/4`

\(\dfrac{5}{2}\) - \(\dfrac{4}{3}\) . \(\dfrac{6}{7}\)= \(\dfrac{5}{2}\) - \(\dfrac{8}{7}\) = \(\dfrac{35}{14}\) - \(\dfrac{16}{14}\) = \(\dfrac{19}{14}\)

(\(\dfrac{-3}{2}\))⁵ : (\(\dfrac{-3}{2}\))³ = (\(\dfrac{-3}{2}\))²  = \(\dfrac{9}{4}\)

Help me hurry

A = \(\dfrac{8a+19}{8a+1}\)\(=\dfrac{8a+2+17}{8a+1}=2+\dfrac{17}{8a+1}\)

Để A có giá trị nguyên thì :     17 phải chia hết cho 8a+1 ⇒ 8a+1 ∈ Ư17={ ±1 ; ±17 }

⇒ Có 4TH là : a+1 ∈ { ±1 ; ± 17 }

TH1 : 8a+1 = 1     ⇒a = 0 / Chọn /

TH2 : 8a+1 = -1   ⇒a = -0,25 / Loại /

TH3 : 8a+1 = 17  ⇒a = 2 / Chọn /

TH4 : 8a+1 = -17 ⇒a = -2,25 / Loại /

Vậy a = { 0 ; 2 }

B,\(\dfrac{5a-17}{4a-23}\) có giá trị lớn nhât

\(B=\dfrac{5a-17}{4a-23}=\dfrac{\dfrac{5}{4}.\left(4a-23\right)+\dfrac{115}{4}-17}{4a-23}=\dfrac{5}{4}+\dfrac{47}{4.\left(4a-23\right)}\)

Để B lớn nhất thì: \(\dfrac{1}{4a-23}\) là số dương lớn nhất => 4a - 23 là nhỏ nhất mà a là số tự nhiên => 4a - 23 = 1 => a = 6

Vậy a = 6 thì A lớn nhất bằng \(\dfrac{5}{4}+\dfrac{47}{4}=\dfrac{52}{4}=13\)

\(\left(-\dfrac{1}{7}\right)^0\) \(-2\dfrac{4}{9}\) + \(\left(-\dfrac{2}{3}\right)^2\)

\(=1-\dfrac{22}{9}\) + \(\dfrac{4}{9}\)

\(=\dfrac{9}{9}-\dfrac{22}{9}+\dfrac{4}{9}\)

\(=-\dfrac{9}{9}=-1\)

\(\left(-\dfrac{1}{7}\right)^0-2\dfrac{4}{9}+\left(-\dfrac{2}{3}\right)^2\)

\(=1-\dfrac{22}{9}+\dfrac{4}{9}=\dfrac{9}{9}-\dfrac{22}{9}+\dfrac{4}{9}\)

\(=\dfrac{9-22+4}{9}=\dfrac{-9}{9}=-1\)

a, Ta có ^B + ^C = ^A = 90⁰ 

=> ^C = ^A - ^B = 90⁰ - 30⁰ = 60⁰

b, Xét tam giác ACD và tam giác MCD có 

CD _ chung ; ^ACD = ^MCD ; AC = MC 

Vậy tam giác ACD = tam giác MCD (c.g.c) 

c, Xét tam giác CAD và tam giác ACK có 

AC _ chung ; ^ACD = ^CAK ( soletrong )  ; ^CAD = ^ACK 

Vậy tam giác CAD = tam giác ACK (g.c.g)

bổ sung : AK = CD ( 2 cạnh tương ứng )