simplify: $\frac{9}{10}+\frac{1}{15}$\n$\frac{1}{3}$\n$\frac{29}{30}$\n$\frac{2}{5}$\n$\frac{7}{10}$\nwhat…

simplify: $\frac{9}{10}+\frac{1}{15}$\n$\frac{1}{3}$\n$\frac{29}{30}$\n$\frac{2}{5}$\n$\frac{7}{10}$\nwhat is the distance between (0,0) and (3,6)?\n$3sqrt{5}$\n9\n3\n$sqrt{3}$

simplify: $\frac{9}{10}+\frac{1}{15}$\n$\frac{1}{3}$\n$\frac{29}{30}$\n$\frac{2}{5}$\n$\frac{7}{10}$\nwhat is the distance between (0,0) and (3,6)?\n$3sqrt{5}$\n9\n3\n$sqrt{3}$

Answer

Explanation:

Step1: Find common denominator

The least - common multiple of 10 and 15 is 30. Rewrite the fractions: $\frac{9}{10}=\frac{9\times3}{10\times3}=\frac{27}{30}$ and $\frac{1}{15}=\frac{1\times2}{15\times2}=\frac{2}{30}$.

Step2: Add the fractions

$\frac{27}{30}+\frac{2}{30}=\frac{27 + 2}{30}=\frac{29}{30}$.

Step3: Calculate distance between two points

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 0,y_1 = 0,x_2 = 3,y_2 = 6$. So $d=\sqrt{(3 - 0)^2+(6 - 0)^2}=\sqrt{3^2+6^2}=\sqrt{9 + 36}=\sqrt{45}=3\sqrt{5}$.

Answer:

  1. B. $\frac{29}{30}$
  2. A. $3\sqrt{5}$