MATH SOLVE

4 months ago

Q:
# PLEASE NEEED HEELPPPart A: Using the graph above, create a system of inequalities that only contains points A and E 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 A and E are solutions to the system of inequalities created in Part A. (3 points)Part C: Chickens can only be raised in the area defined by y < −2x + 4. Explain how you can identify farms in which chickens can be raised. (2 points)

Accepted Solution

A:

there are many systems of equation that will satisfy the requirement for Part A.

an example is y≤(1/4)x-3 and y≥(-1/2)x-6

y≥(-1/2)x-6 goes through the point (0,-6) and (-2, -5), the shaded area is above the line. all the points fall in the shaded area, but

y≤(1/4)x-3 goes through the points (0,-3) and (4,-2), the shaded area is below the line, only A and E are in the shaded area.

only A and E satisfy both inequality, in the overlapping shaded area.

Part B. to verify, put the coordinates of A (-3,-4) and E(5,-4) in both inequalities to see if they will make the inequalities true.

for y≤(1/4)x-3: -4≤(1/4)(-3)-3

-4≤-3&3/4 This is valid.

For y≥(-1/2)x-6: -4≥(-1/2)(-3)-6

-4≥-4&1/3 this is valid as well. So Yes, A satisfies both inequalities.

Do the same for point E (5,-4)

Part C: the line y<-2x+4 is a dotted line going through (0,4) and (-2,0)

the shaded area is below the line

farms A, B, and D are in this shaded area.

an example is y≤(1/4)x-3 and y≥(-1/2)x-6

y≥(-1/2)x-6 goes through the point (0,-6) and (-2, -5), the shaded area is above the line. all the points fall in the shaded area, but

y≤(1/4)x-3 goes through the points (0,-3) and (4,-2), the shaded area is below the line, only A and E are in the shaded area.

only A and E satisfy both inequality, in the overlapping shaded area.

Part B. to verify, put the coordinates of A (-3,-4) and E(5,-4) in both inequalities to see if they will make the inequalities true.

for y≤(1/4)x-3: -4≤(1/4)(-3)-3

-4≤-3&3/4 This is valid.

For y≥(-1/2)x-6: -4≥(-1/2)(-3)-6

-4≥-4&1/3 this is valid as well. So Yes, A satisfies both inequalities.

Do the same for point E (5,-4)

Part C: the line y<-2x+4 is a dotted line going through (0,4) and (-2,0)

the shaded area is below the line

farms A, B, and D are in this shaded area.