Q:

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 The coordinate plane is belowPart 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.

Accepted Solution

A:
Answer:Part A) The system of inequalities is[tex]x\geq2[/tex]  and  [tex]y\geq2[/tex]Part B) In the procedurePart C) The schools that Natalie is allowed to attend are A,B and DStep-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 regionswe have Points C(2,2), F(3,4)The system of inequalities could be[tex]x\geq2[/tex] -----> inequality AThe solution of the inequality A is the shaded area at the right of the solid line x=2[tex]y\geq2[/tex] -----> inequality BThe solution of the inequality B is the shaded area above of the solid line y=2see 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 thatIf a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalitiesVerify point CC(2,2)    Inequality A[tex]x\geq2[/tex] -----> [tex]2\geq2[/tex] ----> is trueInequality B[tex]y\geq2[/tex] ------> [tex]2\geq2[/tex] ----> is truethereforePoint C is a solution of the system of inequalitiesVerify point DF(3,4)    Inequality A[tex]x\geq2[/tex] -----> [tex]3\geq2[/tex] ----> is trueInequality B[tex]y\geq2[/tex] ------> [tex]4\geq2[/tex] ----> is truethereforePoint D is a solution of the system of inequalitiesPart 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[tex]y < -2x+2[/tex]The solution of the inequality is the shaded area below the dotted line [tex]y=-2x+2[/tex]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 linesee the attached figure N 2thereforeThe schools that Natalie is allowed to attend are A,B and D