1) 3r² – 2r=-9
Quadratic formula

Solving the equation using quadratic formula we get:

Step-by-step explanation:

We need to solve the equation using quadratic formula.

The quadratic formula is:

For the given equation:

We can write it as:

We have a = 3, b= -2 and c=9

Putting values in quadratic formula and finding value of r

So, solving the equation using quadratic formula we get:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is