Paul owes paula 35 cents...she has a pocket full of nickels,dimes,and quarters.

largest number of coins would be : 7 nickels (7 coins)
smallest number of coins would be : 1 quarter and 1 dime (2 coins)

the difference is : 7 - 2 = 5 coins <=

4 0

3 years ago

Find the side in of point a to point c

vladimir1956 [14]

Step 1:

Calculate the measure of angle ∠ABC

$\angle DBC+\angle ABC=180(\text{ sum of angles on a straight line)}$ $\angle ABC=65^0$ $\begin{gathered} \angle DBC+\angle ABC=180 \\ \angle DBC+65^0=180^0 \\ \angle DBC=180^0-65^0 \\ \angle DBC=115^0 \end{gathered}$

From the triangle in the question,

$a=10\operatorname{km},c=15\operatorname{km},B=115^0$

Step 2:

Calculate the value of AB using the cosine rule below

$b^2=a^2+c^2-2\times a\times c\times\cos B$

By substituting the values, we will have

$\begin{gathered} b^2=a^2+c^2-2\times a\times c\times\cos B \\ b^2=10^2+15^2-2\times10\times15\times\cos 115^0 \\ b^2=100+225-300\times(-0.4226) \\ b^2=325+126.78 \\ b^2=451.78 \\ \text{Square root both sides} \\ \sqrt[]{b^2}=\sqrt[]{451.78} \\ b=21.26\operatorname{km} \end{gathered}$

Hence,

The distance of point A to point C is = 21.26km

3 0

4 months ago