There is a rumor that daddy warbucks is starting a new airline. he plans to serve six cities: san francisco, los angeles, dallas, chicago, new york, and miami. there will be direct flights between each pair of cities. how many different routes will this create?

 15

Step-by-step explanation:

The number of combinations of n things where r things taken at a time is given by :-

Given : Total number of places (San Francisco, Los Angeles, Dallas, Chicago, New York, and Miami.)= 6

Then , the number of possible pairs of any two city will be :-

Hence, the number of different routes will this create = 15

a² + b²= c²

24² + 7² = c²

c= 25

(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