The coordinate plane below represents a city. Points A through F are schools in the city.

Part A: Using the graph above, create a system of inequalities that only contains points D 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 D and E are solutions to the system of inequalities created in Part A. (3 points)

Part C: Timothy can only attend a school in his designated zone. Timothy's zone is defined by y < 3x − 3. Explain how you can identify the schools that Timothy is allowed to attend. (2 points)

Question

akopera1067 akopera1067

12-08-2017
Mathematics

contestada

The coordinate plane below represents a city. Points A through F are schools in the city.

Part A: Using the graph above, create a system of inequalities that only contains points D 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 D and E are solutions to the system of inequalities created in Part A. (3 points)

Part C: Timothy can only attend a school in his designated zone. Timothy's zone is defined by y < 3x − 3. Explain how you can identify the schools that Timothy is allowed to attend. (2 points)

Respuesta :

Otras preguntas

Greg is designing the clock face for a homemade clock. Using the center of the clock face as the origin, he places the label 12 at the point (0, 5). At what poi

Choose the statement from the following choices that best describes the separation of powers. A. Powers and duties of the United States government are divided

what made foreign goods more expensive and northern goods more competitive?

A goal of the Great Peasants’ Revolt was..?

Write the algebraic expression for the quotient of 79 and x

A substance is most likely to diffuse into a cell when (1) it is a large organic food molecule such as protein or starch (2) it is enclosed in an organel

Which of the following statements does NOT describe the Dietary Guidelines? A. Guidelines promote healthy eating habits. B. Guidelines make allowances for d

Which phrase best describes a characteristic of the paintings of French Baroque artist Nicolas Poussin? (Points : 3) the depiction of figures and landscapes f

Which accurately describes a chart developed 20 years after a historical event? effective secondary source document too biased for historical evidence too focus

Why must both Eteocles and Polyneices receive honorable burials, according to Antigone? A. The state requires decent treatment of all bodies. B. The gods requir

meerkat18 meerkat18 · Answer 1 · 2017-08-25T13:04:14+02:00

Part A. The technique on how to find the equation that only applies to point D and E, is to create a line or curve that only includes two of these points. In this case, I created a random parabola that isolates points C and F from the rest of the points. First, we have to find the equation of the parabola through its general forms:

(x - h)² = +/-4a(y-k) or (y - k)² = +/-4a(x - h)

For parabolas drawn like that in the picture, the general form is (x - h)² = +4a(y-k), where the vertex is (h,k) and a is the distance from the vertex to the focus. From the picture, the vertex is at (0,3). Then, we use point D(-2,4) to determine a:

(-2 - 0)² = +4a(4 - 3)
4a = 4

So, the equation of the parabola is:

x² = 4(y - 3)
x² = 4y - 12

Part B. Point D was already verified above. Now for point E(2,4)
x² = 4y - 12
2² ? 4(4) - 12
4 ? 4
4 = 4

Part C. For y < 7x − 4, ignore the equality symbol first and graph the line. Assign random values of x, then you get corresponding values of y. Plot them as shown in the second picture. The line is shown in red. Next, test the equation by choosing a random point. Let's choose the purple point at (4,3).

3 ? 7(4) − 4
3 ? 24
3 < 24

Thus, it applies to the purple point, and all the other areas to that area. The shaded region are all solutions of the inequality. So, Erica is only interested in points E, C and F.