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.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt