a: BC=5cm

\(\widehat{B}=37^0\)

\(\widehat{C}=53^0\)

a: Xét ΔADC có

E là trung điểm của AD

K là trung điểm của AC

Do đó: EK là đường trung bình của ΔADC

Suy ra: EK//DC và \(EK=\dfrac{CD}{2}\)

Xét ΔCAB có

K là trung điểm của AC
F là trung điểm của BC

Do đó: KF là đường trung bình của ΔCAB

Suy ra: KF//AB và \(KF=\dfrac{AB}{2}\)

a: \(x^3+8=\left(x+2\right)\left(x^2-2x+4\right)\)

b: \(27y^3+1=\left(3y+1\right)\left(9y^2-3y+1\right)\)

c: \(x^3-27=\left(x-3\right)\left(x^2+3x+9\right)\)

d: \(x^3-1=\left(x-1\right)\left(x^2+x+1\right)\)

e: \(8x^3+1=\left(2x+1\right)\left(4x^2-2x+1\right)\)

f: \(27x^3+64y^3=\left(3x+4y\right)\left(9x^2-12xy+16y^2\right)\)

g: \(x^3-\dfrac{1}{8}=\left(x-\dfrac{1}{2}\right)\left(x^2+\dfrac{1}{2}x+\dfrac{1}{4}\right)\)

a: \(A=x^3+6x^2+12x+8=\left(x+2\right)^3\)

\(=50^3=125000\)

b: \(B=27x^3-54x^2y+36xy^2-8y^3=\left(3x-2y\right)^3\)

\(=\left(3\cdot4-2\cdot6\right)^3=0\)

c: \(C=x^3-3x^2+3x-1=\left(x-1\right)^3\)

\(=1000^3=1000000000\)

2 Without his sister's help, John couldn't have done his homework

3 Instead of driving to work, I go by bus today

4 Mai doesn't mind giving you a hand

5 They don't know much about English

6 The noise prevented him from sleeping

7 The police have investigated the case for a week

8 We never had an intention of travelling abroad

9 Mary is believed to get the scholatship

10 Instrad of slowing down, he drove faster

1B  2B  3D  4C  5B  6B  7A  8D  9A  10C  11D  12A

1B

2B

3D

4C

5B

6B

7A

8D

9B

10C

11D

12A