\(\frac{3}{4}\left(x-\frac{1}{2}\right)-\frac{5}{6}=\frac{1}{3}\)

\(\Leftrightarrow\frac{3}{4}x=\frac{3}{8}+\frac{5}{6}+\frac{1}{3}\)

\(\Leftrightarrow\frac{3}{4}x=\frac{37}{24}\)

\(\Leftrightarrow x=\frac{37}{18}\)

3/4.( x-1/2)     =  1/3+ 5/6

3/4.(x- 1/2)      = 7/6

 x- 1/2           = 7/6: 3/4

x- 1/2             = 14/9

x                     = 14/9+ 1/2

x                     = 37/18

\(A=\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^{120}}\)

\(3A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{119}}\)

\(3A-A=\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{119}}\right)-\left(\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^{120}}\right)\)

\(=\frac{1}{3}-\frac{1}{3^{120}}\)

\(\Rightarrow A=\frac{1}{6}-\frac{1}{2.3^{120}}\)

\(\frac{a}{b}=\frac{c}{d}\)(\(b,d\ne0\))

\(\Leftrightarrow ad=bc\)

\(\Leftrightarrow2ad=2bc\)

\(\Leftrightarrow ad-bc=bc-ad\)

\(\Leftrightarrow ad-bc+ac-bd=bc-ad+ac-bd\)

\(\Leftrightarrow\left(a+b\right)\left(c-d\right)=\left(c+d\right)\left(a-b\right)\)

\(\Leftrightarrow\frac{a+b}{a-b}=\frac{c+d}{c-d}\)(\(a-b,c-d\ne0\))

a) Ta có:

IE\(\perp\)AC  (I\(\in\)BE mà BE \(\perp\)AC)
MQ\(\perp\)AC (GT)

\(\Rightarrow\)IE // MQ

Lại có:

MI \(\perp\)BE (GT)

EQ\(\perp\) BE (E;Q\(\in\)AC ; BE\(\perp\)AC)

\(\Rightarrow\)MI // EQ

mà IE // MQ (CMT)

Vậy tứ giác MIEQ có các cạnh đối song song.

b) Vì: MI // EQ (CMT)

\(\Rightarrow\)\(\widehat{ACB}\)=\(\widehat{IMB}\) (Đồng vị)

mà \(\widehat{ABC}=\widehat{ACB}\) (TG ABC cân tại A)

\(\Rightarrow\)\(\widehat{ABC}=\widehat{IMB}\)

Xét tg BKM vg tại K và tg MIB vg tại I

BM chung

\(\widehat{ABC}=\widehat{IMB}\)(CMT)

Vậy: TG BKM=TG MIB (CH-GN)

c) Vì: TG BKM=TG MIB (CMT)

\(\Rightarrow\)MK=BI ( CTỨ)

Xét tg IEM vg tại I và tg QME vg tại Q:

EM chung

\(\widehat{IEM}=\widehat{EMQ}\)(Soletrong do IE // MQ)

Vậy TG IEM= TG QME (CH-GN)

\(\Rightarrow\)MQ=IE (CTỨ)

Ta có: BE= BI + IE (B,I,E thẳng hàng)

mà\(\hept{\begin{cases}BI=MI\left(CMT\right)\\IE=MQ\left(CMT\right)\end{cases}}\)

\(\Rightarrow\)BE=MK+MQ

/x+3,4 /làm  -1,2 +0 0 -3,4

b,x-1,4+2,6 

c,

a, x : 1/3 = ( 1/3 ) ³

x=(1/3)^4

HT

Trả lời:

a, \(x\div\frac{1}{3}=\left(\frac{1}{3}\right)^3\)

\(\Leftrightarrow x=\left(\frac{1}{3}\right)^3\times\left(\frac{1}{3}\right)\)

\(\Leftrightarrow x=\left(\frac{1}{3}\right)^4\)

\(\Leftrightarrow x=\frac{1}{81}\)

b, \(x\div\left(\frac{1}{2}\right)^2=\frac{1}{16}\)

\(\Leftrightarrow x\div\left(\frac{1}{2}\right)^2=\left(\frac{1}{2}\right)^4\)

\(\Leftrightarrow x=\left(\frac{1}{2}\right)^4\times\left(\frac{1}{2}\right)^2\)

\(\Leftrightarrow x=\left(\frac{1}{2}\right)^6\)

\(\Leftrightarrow x=\frac{1}{64}\)