Question

Which system of inequalities is graphed below

Answer 1

the closest to this was letter C

hope that helps, God bless!

Answer 2

Option D

Explanation:

Let's explain why the Option D is correct :

• The Parabola equation:
  `$x \leq y^2 - 8$`

This is a parabola equation with vertex at x = -8.

Despite that the "traditional equation" is
`$ y=x^2 + b $` in this case the parabola equation is plotted in the X axis and has a
`$ <= $` sign which indicates that X will take values less and equal than
`$ y^2 -8 $`

The graph of the parabola is attached to the answer.

• The hyperbola equation:
  `$ {x^2 /{3^2}} - {y^2 / {5^2}} > 1 $`

This is a hyperbola equation with center at (0,0) and vertex's : V1=(3;0) and V2=(-3;0)

The two points (0;5) and (0;-5) on the Y axis are not on the hyperbola.

It's similar to the previous case of the parabola, Despite that the "traditional equation" of the Hyperbola :
`$ {x^2 /{a^2}} - {y^2 / {b^2}} = 1 $` in this case the hyperbola equation has a
`$ > $` sign which indicates that hyperbola will take values greater than those who correspond to
`$ {x^2 /{3^2}} - {y^2 / {5^2}} = 1 $`

The graph of the Hyperbola is also attached

Finally we deduce that the D system of inequalities is the correct one.

Also the answer is attached.