Exam 8: Systems of Equations and Inequalities

Use Inequalities to Describe Limitations in a Situation -An office manager is buying used filing cabinets. Small file cabinets cost $\$ 6$ each and large file cabinets cost $\$ 8$ each, and the manager cannot spend more than $\$ 66$ on file cabinets. A small cabinet takes up 5 square feet of floor space and a large cabinet takes up 9 square feet, and the office has no more than 62 square feet of floor space available for file cabinets. The manager must buy at least 5 file cabinets in order to get free delivery. Let $x =$ the number of small file cabinets bought and $y =$ the number of large file cabinets bought. Write a system of inequalities that describes these constraints.

Solve Nonlinear Systems By Substitution - $x - 2 y = 3$ $x ^ { 2 } - x y = 20$

Write the word or phrase that best completes each statement or answers the question. -The Jillson's have up to $75,000 to invest. They decide that they want to have at least $25,000 invested in stable bonds yielding 6% and that no more than $45,000 should be invested in more volatile bonds yielding 12%. How much should they invest in each type of bond to maximize income if the amount in the more volatile bond should not exceed the amount in the more stable bond? What is the maximum income?

Solve Nonlinear Systems By Substitution - y=-+3 +=5

Systems of Nonlinear Equations in Two Variables 1 Recognize Systems of Nonlinear Equations in Two Variables - $\left\{ \begin{array} { l } x = 3 y + 6 \\3 x - y = 2\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 8 x + 1 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$

Graph a Nonlinear Inequality in Two Variables - $x^{2}+y^{2}>25$

Use Inequalities to Describe Limitations in a Situation -Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 7 hours to make a hat and 4 hours to make an afghan, and she has no more than 70 hours available. She has material for no more than 13 items, and she wants to make at least two afghans. Let $x =$ the number of hats she makes and $\mathrm { y } =$ the number of afghans she makes. Write a system of inequalities that describes these constraints.