In Dania Beachthe library is 3 miles due west of the post office and the Dollar Generalis 5 miles due south of the libraryWhat is the distance the office to the Dollar General

The distance is 6 miles

Step-by-step explanation: Please refer to the attached diagram for details.

The library which is point L is 3 miles due west of the post office which is point P. Also the dollar general which is point D is 5 miles south of the library.

With this bit of information we now have a right angled triangle PLD and the distance from the post office point O, to the dollar general point D which is line PD is unknown.

Having derived a right angled triangle with two sides already given, we shall apply the Pythagoras theorem which states that

AC² = AB² + BC²

Where AC is the longest side or hypotenuse and AB and BC are the other two sides. With the known values the formula can now be written as;

PD² = 5² + 3²

PD² = 25 + 9

PD² = 36

Add the square root sign to both sides of the equation

√PD² = √36

PD = 6

Therefore the distance from the post office to the dollar general is 6 miles

the distance from the post office to Dollar General is 5.83 miles

Step-by-step explanation:

Here we have

Distance from the library to the post office = 3 miles

Location of the library from the  post office = 3 miles west

Location of the Dollar General from the library = 5 miles south

We note that from the description, the location the post office, the library and Dollar General form a right triangle

Therefore, the distance from the post office to Dollar General is given by the hypotenuse side of the triangle which is found as follows;

Hypotenuse² =  Adjacent² + Opposite²

Substituting we get

Hypotenuse² = 3² + 5² = 34

Therefore the distance from the post office to Dollar General = √Hypotenuse

= √34 = 5.83 miles.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."