a: \(3\dfrac{3}{7}:1\dfrac{5}{7}\)

\(=\dfrac{24}{7}:\dfrac{12}{7}\)

\(=\dfrac{24}{7}\cdot\dfrac{7}{12}=\dfrac{24}{12}=2\)

b: \(\dfrac{2}{3}+\dfrac{-3}{5}=\dfrac{2}{3}-\dfrac{3}{5}\)

\(=\dfrac{10-9}{15}\)

\(=\dfrac{1}{15}\)

c: \(\dfrac{2}{9}-\left(\dfrac{1}{20}+\dfrac{2}{9}\right)\)

\(=\dfrac{2}{9}-\dfrac{1}{20}-\dfrac{2}{9}\)

\(=-\dfrac{1}{20}\)

d: \(\dfrac{11}{23}\cdot\dfrac{12}{17}+\dfrac{11}{23}\cdot\dfrac{5}{17}+\dfrac{12}{23}\)

\(=\dfrac{11}{23}\left(\dfrac{12}{17}+\dfrac{5}{17}\right)+\dfrac{12}{23}\)

\(=\dfrac{11}{23}+\dfrac{12}{23}=\dfrac{23}{23}=1\)

Câu 4: 

a: Xét ΔABH vuông tại H và ΔACH vuông tại H có

AB=AC

AH chung

Do đó: ΔABH=ΔACH

b: Xét ΔADH vuông tại D và ΔAEH vuông tại E có

AH chung

\(\widehat{DAH}=\widehat{EAH}\)

Do đó: ΔADH=ΔAEH

Suy ra:HD=HE

`7/12 + 3/4 xx 2/9`

`= 7/12 + 1/6`

`= 9/12`

_________________

`8/9 - 4/15 : 2/5`

`= 8/9 - 2/3`

`= 2/9`

giúp me 

a) _{^{\(\dfrac{7}{12}+\dfrac{3}{4}\times\dfrac{2}{9}=\dfrac{7}{12}+\dfrac{1}{6}=\dfrac{7}{12}+\dfrac{2}{12}=\dfrac{3}{4}\)}}

b) _{^{\(\dfrac{8}{9}-\dfrac{4}{15}:\dfrac{2}{5}=\dfrac{8}{9}-\dfrac{4}{15}\times\dfrac{5}{2}=\dfrac{8}{9}-\dfrac{2}{3}=\dfrac{8}{9}-\dfrac{6}{9}=\dfrac{2}{9}\)}}

\(A=\dfrac{31\cdot\left(31^{12}-1\right)}{31\left(31^{13}+1\right)}=\dfrac{31^{13}+1-32}{31\left(31^{13}+1\right)}=\dfrac{1}{31}-\dfrac{32}{31^{14}+31}\)

\(B=\dfrac{31\left(31^{13}-1\right)}{31\left(31^{14}+1\right)}=\dfrac{1}{31}-\dfrac{32}{31^{15}+31}\)

Dễ thấy \(31^{14}+31< 31^{15}+31\Rightarrow\dfrac{32}{31^{14}+31}>\dfrac{32}{31^{15}+31}\\ \Rightarrow\dfrac{1}{31}-\dfrac{32}{31^{14}+31}< \dfrac{1}{31}-\dfrac{32}{31^{15}+31}\)

Vậy A < B

Câu 67:

Đổi 5,1 tấn = 5100 kg

Ta có: \(n_{NH_3}=\dfrac{5100}{17}=300\left(kmol\right)\)

Bảo toàn Nitơ: \(n_{NH_3}=n_{HNO_3\left(lý.thuyết\right)}=300\left(kmol\right)\)

\(\Rightarrow m_{ddHNO_3\left(thực\right)}=\dfrac{300\cdot40\%\cdot63}{63\%}=12000\left(kg\right)=12\left(tấn\right)\)

Câu 68:

Ta có: \(n_{HNO_3\left(thực\right)}=\dfrac{400\cdot12,6\%}{63}=0,8\left(mol\right)\) \(\Rightarrow n_{HNO_3\left(lý.thuyết\right)}=\dfrac{0,8}{40\%}=2\left(mol\right)\)

Bảo toàn Nitơ: \(n_{NH_3}=n_{HNO_3\left(lý.thuyết\right)}=2\left(mol\right)\) \(\Rightarrow V_{NH_3}=2\cdot22,4=44,8\left(l\right)\)

\(1,3x\left(2x^2+1\right)=6x^3+3x\left(B\right)\\ 2,\left(x^4-2x^3+4x^2\right):2x^2=\dfrac{1}{2}x^2-x+2\left(B\right)\\ 3,\left(3x+2y\right)\left(2x+3y\right)=6x^2+9xy+4xy+6y^2=6x^2+13xy+6y^2\left(D\right)\\ 4,\left(x-2\right)^3=x^3-6x^2+12x-8\left(C\right)\\ 5,P=x^2-2x+2=\left(x-1\right)^2+1=\left(1-1\right)^2+1=0+1=1\left(D\right)\\ 6,\widehat{D}=360^0-\widehat{A}-\widehat{B}-\widehat{C}=360^0-120^0-80^0-100^0=60^0\left(D\right)\\ 7,B\)

\(8,\)

Chứng minh được EF,EI,KF lần lượt là đường trung bình hình thang ABCD; tam giác ABD; tam giác ABC

\(\Rightarrow EF=\dfrac{AB+DC}{2}=5;EI+KF=\dfrac{AB}{2}+\dfrac{AB}{2}=AB=3\\ \Rightarrow IK=EF-EI-KF=5-3=2\left(C\right)\)

11a

12b