Ta có: \(\left\{{}\begin{matrix}2\widehat{B}=4\widehat{D}\\3\widehat{C}=4\widehat{D}\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\widehat{B}=2\widehat{D}\\\widehat{C}=\dfrac{4}{3}\widehat{D}\end{matrix}\right.\)

Tứ giác ABCD có:

\(\widehat{A}+\widehat{B}+\widehat{C}+\widehat{D}=360^0\)

\(\Rightarrow4\widehat{D}+2\widehat{D}+\dfrac{4}{3}\widehat{D}+\widehat{D}=360^0\)

\(\Rightarrow\widehat{D}\left(4+2+\dfrac{4}{3}+1\right)=360^0\)

\(\Rightarrow\widehat{D}.\dfrac{25}{3}=360^0\)

\(\Rightarrow\widehat{D}=360^0:\dfrac{25}{3}=43,2^0\)

\(TC:\widehat{A}+\widehat{B}+\widehat{C}+\widehat{D}=360^0\)

\(\Rightarrow\widehat{A}+\dfrac{1}{2}\widehat{A}+\dfrac{1}{3}\widehat{A}+\dfrac{1}{4}\widehat{A}=360^0\)

\(\Rightarrow\widehat{A}=172.8^0\)

\(\widehat{D}=\dfrac{1}{4}\widehat{A}=\dfrac{1}{4}\cdot172.8=43.2^0\)

a,=(2a + b - 3c).(2a + b - 3c)

=4a\(^2\)+2ab-6ac+2ab+b\(^2\)-3bc-6ac-3cb+9c\(^2\)

=4a\(^2\)+b\(^2\)+9c\(^2\)+4ab

=2\(^2\).a\(^2\)+4ab+b\(^2\)+9c\(^2\)

=(2a+b)\(^2\)+9c\(^2\)( đáng lẽ chỗ này nó phải là -9c\(^2\) nhưng t ko ra đc )

b,=(a + 2b + 3c - 4d)(a + 2b + 3c - 4d)

=a\(^2\)+2ab+3ac-4ad+2ab+4b\(^2\)+6bc-8bd+3ac+6bc+9c\(^2\)-12cd-4ad-8bd-12cd+16d\(^2\)

=a\(^2\)+4b\(^2\)+9c\(^2\)+16d\(^2\)+4ab+6ac-8ad+12bc-16bd-24cd

=(a\(^2\)+4ab+4b\(^2\))+(9c\(^2\)-24cd+16d\(^2\))+6ac-8ad+12bc-16bd

=(a+2b)\(^2\)+(3c-4d)\(^2\)+2(3ac-4ad+6bc-8bd)

=(a+2b)\(^2\)+(3c-4d)\(^2\)+2[a(3c-4d)+2b(3c-4d)]

=(a+2b)\(^2\)+(3c-4d)\(^2\)+2(a+2b)(3c-4d)

khiếp bài dài nghoằng ra ý :(

a: \(\left(2a+b-3c\right)^2\)

\(=4a^2+b^2+9c^2+4ab-12ac-6bc\)

Vì d<5

=>4d>20 hay c<20

=>3c<60 hay b<60

Vì b<60

=>2b<120 hay a<120

Vậy giá trị lớn nhất của a là 119

Căn cứ vào tính chất của nước người ta chia hồ làm mấy loại?

A.2

B.3

C.4

D.5

A

A

C

C

C

A

A

A

Ta có :

\(\frac{a}{b}=\frac{5}{6}\Rightarrow\frac{a}{b}=\frac{20}{24}\Rightarrow\frac{a}{20}=\frac{b}{24}\)\(\left(1\right)\)

\(\frac{b}{c}=\frac{8}{9}\Rightarrow\frac{b}{c}=\frac{24}{27}\Rightarrow\frac{b}{24}=\frac{c}{27}\)\(\left(2\right)\)

\(\frac{c}{d}=\frac{3}{2}\Rightarrow\frac{c}{d}=\frac{27}{18}\Rightarrow\frac{c}{27}=\frac{d}{18}\)\(\left(3\right)\)

Từ ( 1 ) ; ( 2 ) ; ( 3 ) \(\Rightarrow\frac{a}{20}=\frac{b}{24}=\frac{c}{27}=\frac{d}{18}=\frac{d-c}{18-24}=\frac{54}{-6}=-9\)

\(\frac{a}{20}=-9\Rightarrow a=-9.20=-180\)

\(\frac{b}{24}=-9\Rightarrow b=-9.24=-216\)

\(\frac{c}{27}=-9\Rightarrow c=-9.27=-243\)

\(\frac{d}{18}=-9\Rightarrow d=-9.18=-162\)

\(\Rightarrow A=a+2b+3c+4d=-180+\left(-216\right).2+\left(-243\right).3+\left(-162\right).4\)

\(=-1989\)