Respuesta :

Answer:

C on edge

Step-by-step explanation:

the guy above is correct

The graph that represents the given inequalities is required.

The required graph is attached.

The inequalities are

[tex]x^2+9y^2<81[/tex]

[tex]y^2+2<x[/tex]

Converting to general forms

Ellipse

[tex]\dfrac{x^2}{9^2}+\dfrac{9y^2}{9^2}<1\\\Rightarrow \dfrac{x^2}{9^2}+\dfrac{y^2}{3^2}<1[/tex]

So,

[tex]a=\pm9[/tex]

[tex]b=\pm3[/tex]

The vertices of the major axes are [tex](9,0)[/tex] and [tex](-9,0)[/tex]

The vertices of minor axes are [tex](0,3)[/tex] and [tex](0,-3)[/tex]

The center lies on the origin.

Since, the sign of the inequality is [tex]<[/tex] the shaded region will be inside the ellipse excluding the ellipse.

Parabola

[tex]x>1(y-0)^2+2[/tex]

So,

Vertex of parabola = [tex](2,0)[/tex]

Since, the square term is [tex]y^2[/tex] the axis of symmetry is the [tex]x[/tex] axis.

The parabola will open towards the positive x axis.

The shaded region is the area in the parabola excluding the parabola due to the [tex]>[/tex] sign.

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