91Ó°ÊÓ

Match each statement with a translation from the list below. a) \(x+y+z=50\) b) \(x-y-z=-50\) c) \(x-y+z=50\) d) \(x-y-z=50\) The first number minus the second plus the third is \(50 .\)

Match the word or phrase with the most appropriate choice from the list at right. ______ Total profit a) The amount of money that a company takes in b) The sum of fixed costs and variable costs c) The point at which total revenue equals total cost d) What consumers pay per item e) The difference between total revenue and total cost f) What companies spend whether or not a product is produced g) The point at which supply equals demand h) The costs that vary according to the number of items produced

In triangle \(A B C,\) the measure of angle \(B\) is three times that of angle \(A .\) The measure of angle \(C\) is \(20^{\circ}\) more than that of angle \(A .\) Find the angle measures.

In triangle \(A B C,\) the measure of angle \(B\) is twice the measure of angle \(A .\) The measure of angle \(C\) is \(80^{\circ}\) more than that of angle \(A .\) Find the angle measures.

Determine whether the ordered pair is a solution of the given system of equations. Remember to use alphabetical order of variables. $$ \begin{array}{r} {(4,0) ; 2 x+7 y=8} \\ {x-9 y=4} \end{array} $$

Determine whether the ordered pair is a solution of the given system of equations. Remember to use alphabetical order of variables. $$ \begin{array}{r} {(3,-1) ; 3 x-4 y=13} \\ {6 x-8 y=26} \end{array} $$

Determine whether the ordered pair is a solution of the given system of equations. Remember to use alphabetical order of variables. $$ \begin{aligned} (4,-2) ; &-3 x-2 y=-8 \\ 8 &=3 x+2 y \end{aligned} $$

Dana is designing three large perennial flower beds for her yard and is planning to use combinations of three types of flowers. In her traditional cottage-style garden, Dana will include 7 purple coneflower plants, 6 yellow foxglove plants, and 8 white lupine plants at a total cost of 93.31 dollars. The flower bed around her deck will be planted with 12 yellow foxglove plants and 12 white lupine plants at a total cost of 126.00 dollars. A third garden area in a corner of Dana's yard will contain 4 purple coneflower plants, 5 yellow foxglove plants, and 7 white lupine plants at a total cost of 72.82 dollars. What is the price per plant for the coneflowers, the foxgloves, and the lupines?

Find the equilibrium point for the following pairs of demand and supply functions. \(D(p)=7500-25 p\) \(S(p)=6000+5 p\)

Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If \(a\) system has no solution, state this. $$ \begin{aligned} &y=2\\\ &x=-4 \end{aligned} $$