Exam 9: Systems of Equations and Inequalities

Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.)

Solve the system by the method of substitution.

Determine which one of the ordered triples below is a solution of the given system of equations.

Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

Find the dimensions of the rectangle meeting the specified conditions. The perimeter is 68 centimeters and the length is 2 centimeters more than the width.

Write the partial fraction decomposition of the rational expression.

Use back-substitution to solve the system of linear equations.

Write the partial fraction decomposition of the improper rational expression.

Write the partial fraction decomposition of the rational expression.

Sketch the graph of the inequality.

An investor has $150,000 to invest in two types of investments. Type A pays 5% annually and type B pays 6% annually. To have a well-balanced portfolio, the investor imposes the following conditions. At least one-third of the total portfolio is to be allocated to type A investments and at least one-third of the portfolio is to be allocated to type B investments. What is the optimal amount that should be invested in each investment?

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.