Ireally need .the coordinate plane below represents a city. points a through f are schools in the city.
the graph is below.
part a: using the graph above, create a system of inequalities that only contain points c and f in the overlapping shaded regions. explain how the lines will be graphed and shaded on the coordinate grid above.
part b: explain how to verify that the points c and f are solutions to the system of inequalities created in part a.
part c: natalie can only attend a school in her designated zone. natalie's zone is defined by y < −2x + 2. explain how you can identify the schools that natalie is allowed to attend.

Part A) The system of inequalities is

 and  

Part B) In the procedure

Part C) The schools that Natalie is allowed to attend are A,B and D

Step-by-step explanation:

Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions

we have

Points C(2,2), F(3,4)

The system of inequalities could be

-----> inequality A

The solution of the inequality A is the shaded area at the right of the solid line x=2

-----> inequality B

The solution of the inequality B is the shaded area above of the solid line y=2

see the attached figure N 1

Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify point C

C(2,2)    

Inequality A

-----> ----> is true

Inequality B

------> ----> is true

therefore

Point C is a solution of the system of inequalities

Verify point D

F(3,4)    

Inequality A

-----> ----> is true

Inequality B

------> ----> is true

therefore

Point D is a solution of the system of inequalities

Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.

we have

The solution of the inequality is the shaded area below the dotted line

The y-intercept of the dotted line is the point (0,2)

The x-intercept of the dotted line is the point (1,0)

To graph the inequality, plot the intercepts and shade the area below the dotted line

see the attached figure N 2

therefore

The schools that Natalie is allowed to attend are A,B and D

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2