Question

Which system of inequalities is shown in the graph?

Answer 1

Answer:

Option C.

Step-by-step explanation:

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The line passes through the points (1,0) and (0,-2). So, the equation of line is

$y-0=\frac{-2-0}{0-1}(x-1)$

$y=2(x-1)$

$y=2x-2$

It is a solid line and the shaded region lies below the line, so the sign of inequality must be "≤".

First inequality is $y\leq 2x-2$.

The parabola intersect the x-axis at 0 and 3, so the equation of of parabola is

$y=(x-0)(x-3)$

$y=x(x-3)$

$y=x^2-3x$

It is a solid curve and the shaded region lies above the curve, so the sign of inequality must be "≥".

Second inequality is $y\geq x^2-3x$.

Therefore, the correct option is C.

Answer 2

Answer:

actual it’s D

Step-by-step explanation:

APEX