Ta có:

X = \(\frac{3.1+4.3+5.4+6.7+7.8+8.9+9.8+10.5+11.3+12n}{1+3+4+7+8+9+8+5+3+n}=7,68\)

=> \(\frac{3+12+20+42+56+72+72+50+33+12n}{48+n}=7,68\)

=> \(\frac{360+12n}{48+n}=7,68\)

=> 360 + 12n = 7,68(48 + n)

=> 360 + 12n = 368,64 + 7,68n

=> 360 - 368,64 = 7,68n - 12n

=> -8,64 = -4,32n

=> n = -8,64 : (-4,32)

=> n = 2

Vậy n = 2

Detective Conan is a famous Japanese detective story, written by Aoyama Gosho. Since its launch, the story has become a companion of many people, not only children but also adults all over the world. In addition to comics, it is also adapted into electronic games, music CDs as well as live action movies to meet the need of readers. The content revolves around the story of Kudo Shinichi, a intelligent student detective. However, during one case investigation, he was taken by members of the Black Organization to drink poison that immediately made his body shrink and since then, he took another nickname, Edogawa Conan, continuing the investigation to unmask this organization. He was sent to live in detective Mori’s house for a short time, helping him successfully investigate many cases. Reading each page of the book, we go from surprise to surprise by the attractive story situation and the talented intellectual speculation of the detective guy.
k nha!

Good luck!

Detective Conan is a famous Japanese detective story, written by Aoyama Gosho. Since its launch, the story has become a companion of many people, not only children but also adults all over the world. In addition to comics, it is also adapted into electronic games, music CDs as well as live action movies to meet the need of readers. The content revolves around the story of Kudo Shinichi, a intelligent student detective. However, during one case investigation, he was taken by members of the Black Organization to drink poison that immediately made his body shrink and since then, he took another nickname, Edogawa Conan, continuing the investigation to unmask this organization. He was sent to live in detective Mori’s house for a short time, helping him successfully investigate many cases. Reading each page of the book, we go from surprise to surprise by the attractive story situation and the talented intellectual speculation of the detective guy.

Ta có:\(\left|\frac{1}{2}x\right|\ge0\Rightarrow3-2x\ge0\Rightarrow3\ge2x\Rightarrow x\le\frac{3}{2}\)

TH1:\(x< 0\),khi đó:

\(\left|\frac{1}{2}x\right|=3-2x\)

\(\Rightarrow\frac{-x}{2}=3-2x\)

\(\Rightarrow-x=6-4x\)

\(\Rightarrow3x=6\)

\(\Rightarrow x=2\)(loại)

TH2:\(x\ge0\) thì khi đó:

\(\left|\frac{1}{2}x\right|=3-2x\)

\(\Rightarrow\frac{x}{2}=3-2x\)

\(\Rightarrow x=6-4x\)

\(\Rightarrow5x=6\)

\(\Rightarrow x=\frac{6}{5}\)(thỏa mãn)

Vậy \(x=\frac{6}{5}\)

AB=AE
=> tam giác ABE vuông cân
=> AG đồng thời là đường phân giác
=> GB/GC=AB/AC (t/c đường phân giác)(1)
tc  ΔABC~ ΔHAC(g.g)
=> AB/AC=HA/HC (t/c...)(2)
từ 1 và 2 => GB/GC=HA/HC
GB/(GB+GC)=HA/(HA+HC)(t/c của dãy tỉ số = nhau)
GB/BC=HA/(HA+HC)
mà HA=HD
=>GB/GC=HD(HA+HC) (ĐPCM)

Xét tam giác ABC có góc A = 90độ(gt) => theo định lý Py-ta-go ta có:
BC² = AB² + AC² => AC² = BC² - AB² = 10² - 6² = 100 - 36 = 64
=> AC = 8(cm)
Xét tam giác ABC có BD là phân giác trong góc B(gt) => AD/DC = AB/BC = 6/10
=> AD/DC = 3/5
=> AD/(DC + AD) = 3/(3 + 5) (tính chất tỷ lệ thức)
=> AD/AC = 3/8 => AD/8 = 3/8
=> AD = 3(cm)
Áp dụng định lý Py-ta-go cho tam giác vuông ABD ta tính được: BD² = AB² + AD² = 6² + 3² => BD² = 45 (cm) => BD = √45 = √(9.5) = 3√5
Do BE là phân giác ngoài góc B(gt) => ta có:
EA/EC = AB/BC(tính chất phân giác góc ngoài)
=> AE/(AE + AC) = 6/10
=> 10AE = 6(AE + AC)
<=> 10AE = 6AE + 6AC
<=> 4AE = 48 (vì AC = 8cm)
<=> AE = 12(cm)
=> ED = AE + AD =12 + 3 = 15(cm)
Áp dụng định lý: 2 tia phân giác của 1 góc kề kù thì vuông góc với nhau (bạn tự chứng minh - không khó) ta được: BE ⊥ BD => góc EBD = 90độ.
Xét tam giác EBD vuông tại B, áp dụng định lý Py-ta-go ta có:
ED² = BE² + BD² => BE² = ED² - BD² = 15² - 45 = 180
=> ED = √180 = √(36.5) = 6√5 (cm)
Vậy EB = 3√5 cm và ED = 6√5 cm

f(x)=f(2x+1)=(x-12)(x+13)=f(31) =>2x+1=31 =>x=15

=>f(31)=(x-12)(x+13)=(15-12)(15+13)=84

đề sai hay sao ấy