Write your answer in the simplest radical form

6±2√3

Step-by-step explanation:

We can use the quadratic equation to solve x²-12x+24=0. The special quadratic formula (used when the x term has an even coeffcient, in this case it does) is (-b'±√(b'²-ac))/a where in this case a=1, b= -6, and c=24.

Plugging these in, we get {-(-6)^2±√[(-6)²-1*24]}/1. When we simplify, we get 6±√(36-24) → 6±√12 → 6±2√3. Hope this helps!

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

hi! i think the answer is 1/2 : )