Inequalities
Graphing/Substitution
Linear Combinations
Matrices/Graphing Inequalities
Linear Programming
100
What is 4 < x and x < 8 written as a compound inequality?
4 < x < 8
100
What is a system of equations that results in a graph with infinitely many solutions called?
consistent system
100
Using linear combinations, what variable would be the easiest to eliminate and how would that be done? 2x + y = 1/ 4x + 3y = 9
the y by multiplying the top equation by -3
100
What is the determinant for the matrix 4 \ -5 \ -2 \ 3
2
100
True or false. The boundaries are included in the graph of the solution set of y > 2 / y < 4 - x
False
200
Describe the graph of x < -3 or x >= 2.
Open circle on -3 with arrow to the left and closed circle on 2 with arrow to the right.
200
Solve using substitution: y = 3x + 13/ y = x + 1
(-6, -5)
200
Solve the system using linear combinations. 5w + 4z = -.7 / 8w + 6z = -1.2
(-.3, .2)
200
Do all matrices have inverses? If not, when do you know a matrix does not have an inverse.
no when the determinant is zero
200
True or false. (1, -2) is found in the feasible region for the system 5x > -10 / 3(x + y) < 6 / 6>y - 4x
true
300
What is the solution set for the inequality -20 + 6w <= 40
w <= 10
300
Describe the graph of two lines that produce an inconsistent system.
parallel lines
300
Use linear combinations to solve the system 4x + 5y = -14 / 8x +10y = -20
no solution
300
What is the inverse of the matrix 3 \ -1\ 0 \ -2
1/3 \ -1/6 \ 0 \ -1/2
300
A farm worker can earn $5.00 per hour plus $.30 per bag picking cucumbers at one farm and $5.40 per hour and $.24 per bag at another farm. How many bags of cucumbers must the worker pick daily in order to earn more at the first farm?
more than 53
400
What is the inequality to describe the following situation: In some hospitals, newborns weighing less than 5 pounds are put on special watch.
0 <= x < 5
400
Solve using substitution 2x + y + 2z = 0 / y = 3x + 1/ z = x - 4
(-1,1,0)
400
For what value of k will the system have infinitely many solutions? 12x + 6y = k / 2x + y = 9
k = 54
400
The set of solutions to a system of linear inequalities is called a _________________.
feasible region
400
Some students make necklaces and bracelets in their spare time and sell all that they make. The profit on each necklace is $3.50 and the profit on each bracelet is $2.50. Suppose the vertices of the feasible region are (40, 0), (8, 48), and (0, 50). Use the vertices to determine the maximum profit that can be made from the necklaces and bracelets.
$148 with 8 necklaces and 48 bracelets
500
What is the solution set for the inequality 13 < y + 3(-4y + 8).
y < 1
500
Hotel Oakwood charges $40 a night for two people plus $5 for each additional person. Pine Valley Lodge charges $38 a night for two people plus $6 for each additional person. Write a system of equations for the cost y and x people and solve for how many people will the rate for the two rooms be the same.
4 people
500
At a restaurant, four hamburgers and two orders of fries cost $27.10. Three hamburgers and four orders of fries cost $25.20. If all hamburgers cost the same price and all orders of fries cost the same price, find the cost of each.
hamburgers cost $5.80 fries cost $1.95
500
Solve the system using matrices 4x + 3y = 0 / 2x + y = 6
(9, -12)
500
Jocelyn's Jewelry Store makes rings and pendants. Every week the staff uses at most 500g of metal and spends at most 80 hours making jewelry. It takes 5g of metal to make a ring and 20g to make a pendant. Each ring takes 1.5 hours to make and each pendant takes 1 hour. Translate the constraints into a system of inequalities.
5r + 20p <= 500 / 1.5r + 1p <= 80 / r >= 0 / p >= 0
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