System of Nonlinear Inequalities

A solution to the system of inequalities:           y < -1/2x + 3 and y < (x+1)² is : 

• (0, 6) 

• (-1, 4)

• (2, 1)

• (3, 4)

All are solutions to the given inequalities           { y <-1/2(x-1)²+5 and -5 <y - x   } EXCEPT:

• (0, 0)

• (10, 1)

• (-2, -3)

• (1, 2)

Identify the solutions to the system of inequalities. Select all that apply.

• (0, 0)

• (4, 0)

• (0, 4)

• (-2, 0)

Identify the solutions to the system of quadratic inequalities. Select all that apply.

• {(0, 1)}

• {(1, 0)}

• {(-1, 0)}

• {(0, -1)}

Lisa gives child(x) and adult(y) haircuts in her salon. She charges $10 for a child and $40 for an adult haircut. Her goal is to make at least $1000 per week and work no more than 40 hours. The shaded region of the graph represents the possible combinations of adult and child haircuts that will allow her to meet her goal. Which combination represents her maximum profit?

• 10 adult haircuts and 60 child haircuts

• 20 adult haircuts and 40 child haircuts

• no adult haircuts and 80 child haircuts

• 40 adult haircuts and no child haircuts

Determine the system of inequalities. Select two inequalities.

It requires that each variables to be greater than or equal to zero

• maximization

• minimization

• inequality

• non-negativity constraints

Solve the system of inequalities by graphing.

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Solve the system of inequalities by graphing.

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Tell whether the ordered pair 
(-3, 0) is a solution of the given system.
y ≤ x + 4
y ≥ 2x - 6

• Yes

• No