91Ó°ÊÓ

For the linear function \(f(x)=m x+b, f(-3)=23\) and \(f(2)=-7 .\) Find \(m\) and \(b\).

Graph the solution set of each system of inequalities or indicate that the system has no solution. $$ \left\\{\begin{array}{c} {x^{2}+y^{2} \leq 1} \\ {y-x^{2}>0} \end{array}\right. $$

A modernistic painting consists of triangles, rectangles, and pentagons, all drawn so as to not overlap or share sides. Within each rectangle are drawn 2 red roses and each pentagon contains 5 carnations. How many triangles, rectangles, and pentagons appear in the painting if the painting contains a total of 40 geometric figures, 153 sides of geometric figures, and 72 flowers?

Explain what is meant by the partial fraction decomposition of a rational expression.

Write the linear system whose solution set is {(6, 2)}. Express each equation in the system in slope-intercept form.

Make a rough sketch in a rectangular coordinate system of the graphs representing the equations in each system. The system, whose graphs are a line with positive slope and a parabola whose equation has a positive leading coefficient, has two solutions.

Make a rough sketch in a rectangular coordinate system of the graphs representing the equations in each system. The system, whose graphs are a line with negative slope and a parabola whose equation has a negative leading coefficient, has one solution.

Graph the solution set of each system of inequalities or indicate that the system has no solution. $$ \left\\{\begin{array}{c} {x^{2}+y^{2}<4} \\ {y-x^{2} \geq 0} \end{array}\right. $$

Explain how to find the partial fraction decomposition of a rational expression with distinct linear factors in the denominator.

Write the linear system whose solution set is \(\varnothing .\) Express each equation in the system in slope-intercept form.