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Algebra II Test 5
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Terms in this set (24)
Which of the following best describes a system of two equations where the lines intersect?
consistent
Which of the following best describes a system of two equations where the lines are parallel?
inconsistent
How many solutions does a system of two equations have if the lines are coincident?
infinite
Which of the following best describes the solutions to a system of inequalities that continue infinitely in one direction?
unbounded region
In a linear programming problem, if an optimal objective value exists, where in the feasible solution region will the optimal objective value be located?
at a vertex of the feasible solution region
Which of the following points satisfies the inequality 5x - 3y > (or =) -6?
(2, - 3)
Solve by elimination. 2x - 6y = 5 and 3x + 6y = 5
(2, - 1/6)
Solve by elimination. 2x + 3y = 9 and x - 2y = -6
(0,3)
Solve by substitution. 2x + y = 10 and 3x - 2y = 1
(3,4)
Solve by substitution. x - y = -2 and 3x - 4y = -8
(0,2)
Elementary Row Operations: Perform the elementary row operations on the given system of equations and write the resulting system. x + y - z = 8 (Eq1) 2x - y + 3z = 9 (Eq2) x + 2y + z = 5 (Eq3) ***(Eq1) <> (Eq2)
(Eq1) 2x - y + 3z = 9 (Eq2) x + y - z = 8 (Eq3) x + 2y + z = 5
Elementary Row Operations: Perform the elementary row operations on the given system of equations and write the resulting system. x + y - z = 8 (Eq1) 2x - y + 3z = 9 (Eq2) x + 2y + z = 5 (Eq3) ***2(Eq2) + (Eq3)> (Eq3)
(Eq1) x + y - z = 8 (Eq2) 2x - y + 3z = 9 (Eq3) 5x + 7z = 23
Solve the three variable system of equations. - 3x + 7y + 6z = -20 and x - 3y + 2z = - 6 and - 2x + 5y + 5z = -16
(3, 1, -3)
Graph the two variable inequality. 4x - y < or = 4
graph not shown
Graph the two variable inequality. y > x(2) + 3
graph not shown
Write the vertex of the intersection region of the system of inequalities of the given graph.
(2,2) (Pic not shown)
State if the intersection region of the system is bounded or unbounded.
unbounded (pic not shown)
A school library is planning to add a reference section to their collection. the library can add no more than 20 books, and the librarian decided that the school could use a maximum of 16 dictionaries and a maximum of 9 thesauruses. Dictionaries cost $15, and thesauruses cost $10. Write the objective function. Represent cost as C, dictionaries as x, and thesauruses as y.
C = 15x + 10y
A school library is planning to add a reference section to their collection. the library can add no more than 20 books, and the librarian decided that the school could use a maximum of 16 dictionaries and a maximum of 9 thesauruses. Dictionaries cost $15, and thesauruses cost $10. List the three constraints (not including x > or = 0 and y > or = 0.)
x + y < or = 20 x < or = 16 y < or = 9
A farmer's market manger needs to purchase points of blueberries and pints of strawberries. His display for berries can hold no more than 50 pints. his customers buy no more than 25 pints of blueberries and no more than 40 pints of strawberries. He is able to sell blueberries for $3 per pint and strawberries for $5 per pint. In the graph on your test x represents blueberries and y represents strawberries. ***What is the name of the shaded region in the graph?
Feasible solution region
A farmer's market manger needs to purchase points of blueberries and pints of strawberries. His display for berries can hold no more than 50 pints. his customers buy no more than 25 pints of blueberries and no more than 40 pints of strawberries. He is able to sell blueberries for $3 per pint and strawberries for $5 per pint. In the graph on your test x represents blueberries and y represents strawberries. ***What are the vertices?
(0,0), (10,40), (25,25), (0,40), and (25,0)
A farmer's market manger needs to purchase points of blueberries and pints of strawberries. His display for berries can hold no more than 50 pints. his customers buy no more than 25 pints of blueberries and no more than 40 pints of strawberries. He is able to sell blueberries for $3 per pint and strawberries for $5 per pint. In the graph on your test x represents blueberries and y represents strawberries. ***What is the objective function?
P = 3x + 5y
A farmer's market manger needs to purchase points of blueberries and pints of strawberries. His display for berries can hold no more than 50 pints. his customers buy no more than 25 pints of blueberries and no more than 40 pints of strawberries. He is able to sell blueberries for $3 per pint and strawberries for $5 per pint. In the graph on your test x represents blueberries and y represents strawberries. ***What is the optimal value of profit?
$230
A farmer's market manger needs to purchase points of blueberries and pints of strawberries. His display for berries can hold no more than 50 pints. his customers buy no more than 25 pints of blueberries and no more than 40 pints of strawberries. He is able to sell blueberries for $3 per pint and strawberries for $5 per pint. In the graph on your test x represents blueberries and y represents strawberries. ***How many pints of blueberries and strawberries should the manager purchase in order to optimize his profit?
Blueberries: 10 pints Strawberries: 40 pints
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