Để sửa xong đoạn đường trong 1 ngày thì cần số công nhân:

\(8.10=80\) (người)

Muốn sửa đoạn đường đó trong 5 ngày thì cần số công nhân là:

\(80:5=16\) (người)

a: Xét ΔABD và ΔAMD có

AB=AM

\(\widehat{BAD}=\widehat{MAD}\)

AD chung

Do đó: ΔABD=ΔAMD

b: Ta có: ΔABD=ΔAMD

=>DB=DM

=>ΔDBM cân tại D

c: Ta có: AB=AM

=>A nằm trên đường trung trực của BM(1)

Ta có: DB=DM

=>D nằm trên đường trung trực của BM(2)

Từ (1) và (2) suy ra AD là đường trung trực của BM

1: \(75^3:\left(-25\right)^3=\left(\dfrac{75}{-25}\right)^3=\left(-3\right)^3=-27\)

2: \(\left(-60\right)^2:\left(-5\right)^2=\dfrac{60^2}{5^2}=12^2=144\)

3: \(169^2:\left(-13\right)^2=\dfrac{169^2}{13^2}=\left(\dfrac{169}{13}\right)^2=13^2=169\)

4: \(\left(\dfrac{1}{2}\right)^2:\left(\dfrac{3}{2}\right)^2=\left(\dfrac{1}{2}:\dfrac{3}{2}\right)^2=\left(\dfrac{1}{3}\right)^2=\dfrac{1}{9}\)

5: \(\left(\dfrac{2}{3}\right)^3:\left(\dfrac{8}{27}\right)^3=\left(\dfrac{2}{3}:\dfrac{8}{27}\right)^3=\left(\dfrac{2}{3}\cdot\dfrac{27}{8}\right)^3=\left(\dfrac{9}{4}\right)^3=\dfrac{729}{64}\)

6: \(\left(\dfrac{5}{4}\right)^4:\left(\dfrac{15}{2}\right)^4=\left(\dfrac{5}{4}:\dfrac{15}{2}\right)^4=\left(\dfrac{5}{4}\cdot\dfrac{2}{15}\right)^4=\left(\dfrac{1}{6}\right)^4=\dfrac{1}{1296}\)

7: \(\left(\dfrac{7}{8}\right)^5:\left(\dfrac{21}{16}\right)^5\)

\(=\left(\dfrac{7}{8}:\dfrac{21}{16}\right)^5\)

\(=\left(\dfrac{7}{8}\cdot\dfrac{16}{21}\right)^5=\left(\dfrac{2}{3}\right)^5=\dfrac{32}{243}\)

8: \(\left(\dfrac{5}{6}\right)^4:\left(\dfrac{25}{18}\right)^4=\left(\dfrac{5}{6}:\dfrac{25}{18}\right)^4=\left(\dfrac{5}{6}\cdot\dfrac{18}{25}\right)^4=\left(\dfrac{3}{5}\right)^4=\dfrac{81}{625}\)

9: 

\(\left(-\dfrac{3}{4}\right)^3:\left(\dfrac{9}{8}\right)^3=\left(-\dfrac{3}{4}:\dfrac{9}{8}\right)^3=\left(-\dfrac{3}{4}\cdot\dfrac{8}{9}\right)^3\)

\(=\left(-\dfrac{2}{3}\right)^3=-\dfrac{8}{27}\)

10:

\(\left(\dfrac{9}{10}\right)^6:\left(\dfrac{27}{-20}\right)^6=\left(\dfrac{9}{10}:\dfrac{-27}{20}\right)^6\)

\(=\left(\dfrac{9}{10}\cdot\dfrac{20}{-27}\right)^6=\left(-\dfrac{2}{3}\right)^6=\dfrac{64}{729}\)

a) \(\dfrac{x}{-15}=\dfrac{-60}{3}\)

\(\Rightarrow x:\left(-15\right)=-20\)

\(\Rightarrow x=-20\cdot\left(-15\right)\)

\(\Rightarrow x=300\)

b) \(\dfrac{3,5}{15}=\dfrac{-2}{x}\)

\(\Rightarrow3,5\cdot x=-2\cdot15\)

\(\Rightarrow3,5x=-30\)

\(\Rightarrow x=-30:3,5\)

\(\Rightarrow x=-\dfrac{60}{7}\)

a: \(\dfrac{x}{-15}=-\dfrac{60}{3}\)

=>\(\dfrac{x}{15}=\dfrac{60}{3}\)

=>\(\dfrac{x}{15}=20\)

=>\(x=20\cdot15=300\)

b: \(\dfrac{3.5}{15}=\dfrac{-2}{x}\)

=>\(x=\dfrac{15\cdot\left(-2\right)}{3,5}=-\dfrac{30}{3,5}=-\dfrac{60}{7}\)

a: \(\dfrac{8}{12}:\dfrac{4}{15}=\dfrac{8}{12}\cdot\dfrac{15}{4}=\dfrac{120}{48}=\dfrac{5}{2}\)

b: \(\dfrac{0.75}{2.5}=\dfrac{75}{250}=\dfrac{3}{10}\)

\(\left(-10\right)\cdot20=\left(-25\right)\cdot8\)

=>\(\dfrac{-10}{-25}=\dfrac{8}{20};\dfrac{-10}{8}=\dfrac{-25}{20};\dfrac{-25}{-10}=\dfrac{20}{8};\dfrac{8}{-10}=\dfrac{20}{-25}\)

Khi có 36g nho khô thì khối lượng bột bánh cần tới là:

\(15:100\cdot36=0,15\cdot36=5,4\left(g\right)\)

Tổng số phần bằng nhau: 3+5=8(phần)

Bạn Hùng quyên góp: 400 000 : 8 x 5 = 250 000 (đồng)

Bạn Minh quyên góp: 400 000 : 8 x 3 = 150 000 (đồng)

Bạn Dũng quyên góp: 400 000 : 8 x 4 = 200 000 (đồng)

a) \(\dfrac{3}{5}\times\dfrac{7}{9}+\dfrac{3}{5}\times\dfrac{2}{9}+\dfrac{-3}{5}\)

\(=\dfrac{3}{5}\times\dfrac{7}{9}+\dfrac{3}{5}\times\dfrac{2}{9}+\dfrac{3}{5}\times\left(-1\right)\)

\(=\dfrac{3}{5}\times\left(\dfrac{7}{9}+\dfrac{2}{9}-1\right)\)

\(=\dfrac{3}{5}\times\left(1-1\right)\)

\(=\dfrac{3}{5}\times0=0\)

b) \(\dfrac{2}{3}\cdot\dfrac{17}{13}-\dfrac{2}{3}\cdot\dfrac{4}{13}\)

\(=\dfrac{2}{3}\cdot\left(\dfrac{17}{13}-\dfrac{4}{13}\right)\)

\(=\dfrac{2}{3}\cdot1=\dfrac{2}{3}\)