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a) Ta có: \(\widehat{B}+\widehat{C}=140^0+40^0=180^0\)
Mà 2 góc này là 2 góc trong cùng phía
=> AB//CD
=> ABCD là hthang
b) Ta có:
\(\left\{{}\begin{matrix}\widehat{A}+\widehat{D}=180^0\\\widehat{A}-\widehat{D}=110^0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}\widehat{A}=\left(180^0+110^0\right):2=145^0\\\widehat{D}=\left(180^0-110^0\right):2=35^0\end{matrix}\right.\)
3.(⅓x - ¼)² = ⅓
=> (\(\dfrac{1}{3x}\)- \(\dfrac{1}{4}\) )2 = \(\dfrac{1}{9}\)
=>\(\left[{}\begin{matrix}\dfrac{1}{3x}-\dfrac{1}{4}=\dfrac{-1}{3}\\\dfrac{1}{3x}-\dfrac{1}{4}=\dfrac{1}{3}\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}\dfrac{1}{3x}=\dfrac{-1}{12}\\\dfrac{1}{3x}=\dfrac{7}{12}\end{matrix}\right.\) => \(\left[{}\begin{matrix}x=-4\\x=\dfrac{12}{21}=\dfrac{4}{7}\end{matrix}\right.\)
Vậy, tập nghiệm x thỏa mãn là S=\(\left\{-4;\dfrac{4}{7}\right\}\)
=>(50x+50x+250+65x+11050)*1,1=216500
=>165x+11300=196818,1818
=>165x=185518,1818
=>\(x\simeq124.353\)
gọi 2021-x = a
2023-x=b
2x-4044=c
ta có a + b + c=2021-x+2023-x+2x-4044=0
suy ra a + b = -c
suy ra (a+b)^3 =-c^3
ta có a^3 + b^3 + c^3=(a+b)^3 -3ab(a+b) + c^3 = -c^3 +3abc +c^3 = 3abc
ta có (2021-x)^3 + (2023-x)^3 + (2x-4044)^3 = 0
=> 3(2021-x)(2023-x)(2x-4044)=0
=> th 1 x = 2021, th 2 x = 2023; th3 x = 2022
ĐKXĐ:\(x\ne-2\)
\(\dfrac{1}{x+2}-1=\dfrac{5x+7}{x+2}\\ \Leftrightarrow\dfrac{1}{x+2}-\dfrac{5x+7}{x+2}=1\\ \Leftrightarrow\dfrac{1-5x-7}{x+2}=1\\ \Leftrightarrow-5x-6=x+2\\ \Leftrightarrow x+2+5x+6=0\\ \Leftrightarrow6x+8=0\\ \Leftrightarrow x=-\dfrac{4}{3}\left(tm\right)\)
a.3x2-3xy-2x+2y =(3x2-3xy)-(2x-2y)
=3x.(x-y)-2.(x-y)
=(x-y).(3x-2)
b.6x2+3xy-2ax-ay =(6x2-2ax)+(3xy-ay)
=2x.(3x-a)+y.(3x-a)
=(3x-a).(2x+y)
c.x3-6x2+9x=x.(x2-6x+9)
=x.(x-3)2
d.2xy-x2-y2+25= -(-2xy+x2+y2-25)
= -[(x2-2xy+y2)-52)]
= -[(x-y)2-52 ]
= -(x-y+5).(x-y-5)
e.x2-y2-4yz-4z2= -(-x2+y2+4yz+4z2)
= -[(y2+4yz+4z2)-x2 ]
= -[ (y+2z)2-x2 ]
= -(y+2z+x).(y+2z-x)
f.2a2-4ab+2b2-8c2=2a2-2ab-2ab+2b2-4c2-4c2
=2.(a2-ab-ab+b2-2c2-2c2
=2.(a2-2ab+b2-4c2)
=2.[(a-b)2-(2c)2 ]
=2.(a-b+2c).(a-b-2c)
Mong là đúng