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Ierofanga [76]
3 years ago
6

2. Which of the following systems of inequalities represents the graph?

Mathematics
2 answers:
Rom4ik [11]3 years ago
8 0

Answer:

Option: D is the correct answer.

D)  –2x + y ≥ 4

         x + y < 2

Step-by-step explanation:

We are asked to find the linear inequality that represents the following graph.

Clearly from the graph we could observe that one line is dotted and the other is solid line.

i.e. one inequality is strict while the other is a inequality with equality sign.

<u>Dashed line:</u>

It passes through (0,2) and  (2,0).

Hence, the equation of line is:

y-2=\dfrac{0-2}{2-0}\times (x-0)\\\\\y-2=\dfrac{-2}{2}\times x\\\\y-2=-x\\\\x+y=2

As the shaded region is towards the origin.

Hence, the inequality will be:

x+y<2.

<u>Solid line:</u>

The line passes through (-2,0) and (0,4).

hence equation of line is:

y-0=\dfrac{4-0}{0-(-2)}\times (x+2)\\\\

i.e

y=\dfrac{4}{2}\times (x+2)\\\\y=2\times (x+2)\\\\y=2x+4\\\\-2x+y=4

Now, as the shaded region is away from the origin hence the inequality which will be used is:

-2x+y\geq 4

Hence, option: D is the correct answer.

D.   –2x + y ≥ 4

       x + y < 2

Irina18 [472]3 years ago
5 0

Answer:

D.–2x + y ≥ 4

x + y < 2

<3

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Answer:

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Step-by-step explanation:

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d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} which for x_1=0 and y_1 = 0 transforms as  d=\sqrt{(x_2)^2 + (y_2)^2}. The first point we are looking for is connected to the origin and therefore, its components will form a right triangle in which, the Pythagoras theorem holds, see the first attached figure. Then, x_2, y_2 and 10 are a Pythagorean triple. From this, x_2= 6 or  x_2=8 while y_2= 6 or y_2=8. This leads us with the set of coordinates:

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