Gọi chiều dài ba cạnh và ba chiều cao tương ứng của tam giác đó lần lượt là a,b,c ,h₁,h_2,h₃

Ta có:a.h₁=b.h₂=c.h₃(=2.S)

Theo bài ra ta có:\(\dfrac{h_1}{3}=\dfrac{h_2}{4}=\dfrac{h_3}{5}\)

=>\(\dfrac{a.h_1}{a.3}=\dfrac{b.h_2}{b.4}=\dfrac{c.h_3}{c.5}\)

mà a.h₁=b.h₂=c.h3=> để \(\dfrac{a.h_1}{a.3}=\dfrac{b.h_2}{b.4}=\dfrac{c.h_3}{c.5}\) thì a.3=b.4=c.5

=>\(\dfrac{a}{\dfrac{1}{3}}=\dfrac{b}{\dfrac{1}{4}}=\dfrac{c}{\dfrac{1}{5}}\)

=>\(\dfrac{a}{20}=\dfrac{b}{15}=\dfrac{c}{12}\)

Vậy ba cạnh tương ứng với ba chiều cao đó tỉ lệ với 20,15,12

Bài 5:

Có \(\dfrac{3x-y}{x+y}=\dfrac{3}{4}\)

=> 4(3x-y)=3(x+y)

=>12x-4y=3x+3y

=>12x-3x=3y+4y

=>9x=7y

=>\(\dfrac{x}{y}=\dfrac{7}{9}\)

kho qua kho

\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}=\frac{5.2^{30}.3^{18}-2^2.2^{27}.3^{20}}{5.2^9.2^{19}.3^{19}-7.2^{29}-3^{18}}=\frac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{28}.3^{18}\left(5.3-7.2\right)}=\frac{2.1}{1}=2\)

\(y=\frac{7.9+14.27+21.36}{21.27+42.81+63.108}=\frac{7.9+2.7.3.9-3.7.4.9}{3.7.3.9+2.3.7.9.9+7.9.4.3.9}=\frac{7.9\left(1+6-12\right)}{3.7.9\left(3+18+36\right)}=\frac{-5}{3.57}=\frac{-5}{171}\)

Hãy xác định những câu dưới đây là Đúng hay Sai hay Không có trong bài.

Vietnamese water puppetry is a unique folk art. It's said that ‘Not watching a performance of water puppetry means not visiting Vietnam yet.' That's why water puppetry is a must-see show for tourists in Vietnam. Watching this show can help you escape from your busy life and refresh your minds with unforgettable moments.

During the shows, you can only see the puppets and a small folk orchestra of about 7 people; the puppeteers stand behind a curtained backdrop in a pool. All puppets are made of fig wood which goes along well with water. Then they are carved and painted. The themes of the shows are very familiar to Vietnamese people. They focus on the daily life of farmers and common aspects of Vietnamese spiritual life.

Vietnamese water puppetry has been introduced to many countries all over the world and received much love from audiences. Foreigners don't understand Vietnamese, but they enjoy the shows because the puppets clearly demonstrate Vietnamese life and culture through their actions. Thang Long Water Puppet Theatre on Dinh Tien Hoang Street near Hoan Kiem Lake is the most popular theatre for water puppetry.

Question. Audiences can see the puppets, the orchestra and the puppeteers during the show.

A. True

B. False

C. Not Given

Có :\(\left(x-1\right)^4+\left(y+1\right)^4=0\)

=>\(\left(x-1\right)^4=-\left(y+1\right)^4\)

mà 4=4

=> x-1= -(y+1)

=>x+1=-y-1

=>x+y=0

=>y=-x

Có \(C=x^3+xy^3-x^3y+y^3\)

\(C=x^3+x\left(-x\right)^3-x^3\left(-x\right)+\left(-x\right)^3\)

\(C=x^3-x^4+x^4-x^3\)

C=0

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}\)=k (1)

=> a=bk ,c=dk

a.Có \(\dfrac{a+c}{b+d}=\dfrac{bk+dk}{b+d}=\dfrac{k\left(b+d\right)}{b+d}=k\left(2\right)\)

Từ (1) và (2)=>\(\dfrac{a+c}{b+d}=\dfrac{a}{b}\left(=k\right)\)

b. Có \(\dfrac{ac}{bd}=\dfrac{bk.dk}{bd}=k^2\)

\(\dfrac{a^2+c^2}{b^2+d^2}=\dfrac{\left(bk\right)^2+\left(dk\right)^2}{b^2+d^2}=\dfrac{k^2\left(b^2+d^2\right)}{b^2+d^2}=k^2\)

=>\(\dfrac{ac}{bd}=\dfrac{a^2+c^2}{b^2+d^2}\left(=k^2\right)\)

Biết m 0  là giá trị của tham số m để hàm số y = x 3 − 3 x 2 + m x − 1  có hai điểm cực trị x 1 , x 2  sao cho x 1 2 + x 2 2 − x 1 x 2 = 13.  Mệnh đề nào dưới đây đúng?

A.  m 0 ∈ − 1 ; 7

B.  m 0 ∈ 7 ; 10

C.  m 0 ∈ − 15 ; − 7

D.  m 0 ∈ − 7 ; − 1

Kim loại nào sau đây là kim loại kiềm thổ?

A. Ca

B. Fe

C. Na

D. Al