Question 1 of 10 Select the point that is a solution to the system of inequalities. y y>x^2-4

Question

asked Jul 24, 2023 30.3k views

1 Answer

Sola · Answer 1 · 2023-07-29T12:49:53+0000

Answer:

a) (1,2)

Explanation:

$y < x^2 + 3\\y > x^2 - 4$

a.

$2 < 1^2 + 3\\2 > 1^2 - 4$

$2 < 1 + 3\\2 > 1 - 4$

$2 < 4\\2 > -3$

Both equations are true

b.

$0 < 4^2 + 3\\0 > 4^2 - 4$

$0 < 16 + 3\\0 > 16 - 4$

$0 < 19\\0 > 12$

Both equations are false

c.

$-4 < -2^2 + 3\\-4 > -2^2 - 4$

$-4 < 4 + 3\\-4 > 4 - 4$

$-4 < 7\\-4 > 0$

Only one equation is true (-4 < 7)

d.

$4 < 0^2 + 3\\4 > 0^2 - 4$

$4 < 0 + 3\\4 > 0 - 4$

$4 < 3\\4 > - 4$

Only one equation is true (4 > -4)

Therefore, our final answer is a) (1,2)

Hope this helps!