Question

The coordinate plane below represents a city. Points A through F are schools in the city. graph of coordinate plane. Point A is at negative 3, negative 4. Point B is at negative 4, 3. Point C is at 2, 2. Point D is at 1, negative 2. Point E is at 5, negative 4. Point F is at 3, 4. Part A: Using the graph above, create a system of inequalities that only contains points C and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points) Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A. (3 points) 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. (2 points)

Answer 1

Answer:

Part A;

There are many system of inequalities that can be created such that only contain points D and E in the overlapping shaded regions.

Any system of inequalities which is satisfied by (-4, 2) and (-1, 5) but is not satisfied by (1, 3), (3, 1), (3, -3) and (-3, -3) can serve.

An example of such system of equation is

x < 0

y > 0

The system of equation above represent all the points in the second quadrant of the coordinate system.

The area above the x-axis and to the left of the y-axis is shaded.Part B:

Part B

It can be verified that points D and E are solutions to the system of inequalities above by substituting the coordinates of points D and E into the system of equations and see whether they are true.

Substituting D(-4, 2) into the system we have:

-4 < 0

2 > 0

As can be seen the two inequalities above are true, hence point D is a solution to the set of inequalities.

Also, substituting E(-1, 5) into the system we have:

-1 < 0

5 > 0

As can be seen the two inequalities above are true, hence point E is a solution to the set of inequalities.

Part C

:This part is different from yours because my equation is y> 4x + 3 and it's been a long time since I did that task and I don't remember anything. I hope you can do yours from my example.

Given that chicken can only be raised in the area defined by y > 3x - 4.

To identify the farms in which chicken can be raised, we substitute the coordinates of the points A to F into the inequality defining chicken's area.

For point A(1, 3): 3 > 3(1) - 4 ⇒ 3 > 3 - 4 ⇒ 3 > -1 which is true

For point B(3, 1): 1 > 3(3) - 4 ⇒ 1 > 9 - 4 ⇒ 1 > 5 which is false

For point C(3, -3): -3 > 3(3) - 4 ⇒ -3 > 9 - 4 ⇒ -3 > 5 which is false

For point D(-4, 2): 2 > 3(-4) - 4; 2 > -12 - 4 ⇒ 2 > -16 which is true

For point E(-1, 5): 5 > 3(-1) - 4 ⇒ 5 > -3 - 4 ⇒ 5 > -7 which is true

For point F(-3, -3): -3 > 3(-3) - 4 ⇒ -3 > -9 - 4 ⇒ -3 > -13 which is true

Therefore, the farms in which chicken can be raised are the farms at point A, D, E and F.

.Take that exam and got 100% .The exam was 05.13 Segment One Exam Part 3.I really hope this helps you.And please give me the brainliest