Exam 8: Systems of Equations and Inequalities

Solve the problem. -The equation of a line passing through two distinct points is given by Use the determinant to write an equation for the line passing through (-3, -9)and(5, 2). Express the lineʹs equation in standard form.

Find the value of the determinant. -

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

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of feasible points. -z = x + 6y. Find maximum.

Perform the indicated operation(s), whenever possible. -Let and Find A - B.

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Write the word or phrase that best completes each statement or answers the question. -Meisha has $25,000 that she wants to invest. She invests it in accounts paying 12%, 7%, and 6% simpleinterest. The account paying 12% is a higher-risk account, so she wants the amount in that account to behalf of the amount she has in the account paying 6% simple interest. If her annual interest is $1945, howmuch is invested at each rate?

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Write the word or phrase that best completes each statement or answers the question. -In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 27 feetahead of the third-place runner. Assuming that each runner maintains a constant speed throughout therace, by how many feet does the second-place runner beat the third-place runner? (5280 feet in 1 mile.)

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Perform the row operation(s)on the given augmented matrix. -

Solve the system of equations. -

Solve the system of equations. If the system has no solution, say that it is inconsistent. -

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours toprepare, 2 hours to paint, and 9 hours to fire. A tree takes 14 hours to prepare, 3 hours to paint, and 4hours to fire. A sleigh takes 4 hours to prepare, 16 hours to paint, and 7 hours to fire. If the workshop has113 hours for preparation time, 64 hours for painting, and 101 hours for firing, how many of each can bemade?

Graph the inequality. -

Use a graphing utility to find the inverse, if it exists, of the matrix. Round answers to two decimal places. -

Perform the indicated operation(s), whenever possible. -Let Find A - B.

Write the word or phrase that best completes each statement or answers the question. -

Solve the system of equations using substitution. -

Solve the system of equations using substitution. -