Cho \(\Delta ABC\) co AB=AC, M la trung diem cua BC

a/ Chung minh rang: AD=MC va AD// BC va AM\(\perp BC\)

b/ Goi N la trung diem cua AC, tren tia doi cua tia NM lay diem D sao cho NM=ND. Chung minh rang: AD=MC va AD//BC

c/ Chung minh rang: MN=1/2.AC

Tim so huu ti x, biet:

a/ \(5< 5^x< 625\)

b/ \(2^{x-1}=16\)

c/ \(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+6}\)\(\left(x\in Z\right)\)

Thuc hien phep tinh:

a/ \(\dfrac{2^4.6^7}{9^3.4^6}\)

b/ \(\dfrac{3^{18}.24^4}{9^4.81^5}\)

Biet rang 20 nguoi lam xong mot cong viec trong 5 ngay. Hoi neu so nguoi tang hem 5 nguoi thi thoi gian hoan thanh cong viec do giam duoc may ngay?