Algebra II Module 2
The equation of a line of best fit relating the money earned e at a bake sale to the number of customers c is e = 1.1c + 19. Use the equation to predict the earnings from a bake sale with 80 customers.
$107
Graph the system of linear inequalities. y < −x + 3 y ≥ 2x − 1 Give two ordered pairs that are solutions and two that are not solutions.
(0, 0) and (−4, 1) are solutions. (2, 0) and (5, 1) are not solutions.
Solve the system of equations using a table and a graph. 2x - 1/2y = 4 x + y = 2
(2, 0)
Solve the system of equations using a table and a graph. 2x-1/2y = 4 x+y = 2
(2, 0)
Solve the system of equations using elimination. 6x − 2y = 10 5x − 8 = 2y
(2, 1)
Solve the system of equations using substitution. 2x + y = 3 y = 3x − 7
(2, −1)
Solve the system of equations using substitution. y = 3 − 4x y = 3x − 11
(2, −5)
Graph the system of linear inequalities. y > −x + 3 y ≤ 2x − 1 Give two ordered pairs that are solutions and two that are not solutions.
(3, 2) and (5, 0) are solutions. (0, 0) and (−4, 1) are not solutions.
Solve the system of equations using substitution. 4x + 6y = 10 3y + x = 2
(3, −1/3)
Solve the system of equations using elimination. 4x + y = 9 3x + 2y = −2
(4, −7)
Solve the system of equations using elimination. 7x + 5y = 10 6x + 5y = 5
(5, −5)
Solve the system of equations using elimination. 2x − 3y = −5 6x + 4y = −2
(−1, 1)
Using substitution, identify the ordered pair that is not an element of the solution set of the system of equations. 6x + 3y = 6 2x + y = 2
(−2, 0)
Using substitution, identify the ordered pair that is not an element of the solution set of the system of equations. 3x − y = 2 6x − 2y = 4
(−2, −4)
Nancy needs to earn at least $60 per day. She gets $10 per hour as a babysitter and $20 per hour as a sales person. If she can work at most 5 hours per day, identify the system of inequalities and the corresponding graph that determine when Nancy will be able to meet her goal.
10x + 20y ≥ 60 x + y ≤ 5, small dark green between 3&5 on y
In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 spectators. Tickets cost $15 for students and $25 for adults. Identify the system of inequalities and the corresponding graph that determine whether the charity will reach its goal.
15x + 25y ≥ 3750 x + y ≤ 180, skinny dark green part by 160 on y
A manufacturer makes two types of handmade fancy paper bags: type A and type B. Two designers—a cutter and a finisher—need to work on both kinds of bags. A type A bag requires 2 hours of the cutter's time and 3 hours of the finisher's time. A type B bag requires 3 hours of the cutter's time and 1 hour of the finisher's time. Each month the cutter is available for 108 hours and the finisher is available for 78 hours. The manufacturer gets a profit of $12 for each bag of type A and $9 for each bag of type B. Identify the number of bags of each type to be manufactured to obtain maximum profit.
18 bag A; 24 bag B
Skating school A charges $7 for equipment rental plus $20 per hour for lessons. Skating School B charges $25 for equipment rental plus $12 per hour for lessons. Identify the number of hours for which the equipment rental and fee for lessons is the same for both schools.
2 1/4 hours
Graph the system of linear inequalities. y > 2x + 3 y ≥ 2x − 2
2 shaded areas above the +1 on the x
A furniture company has 400 board ft of teak wood and can sustain up to 450 hours of labor each week. Each chair produced requires 5 ft of wood and 10 hours of labor, and each table requires 20 ft of wood and 15 hours of labor. If a chair yields a profit of $45 and a table yields a profit of $80, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit?
24 chairs; 14 tables
The equation of a line of best fit relating the number of cats c at an animal shelter to the number of dogs d is c = 2.1d − 26. Predict the number of cats at a shelter where there are 30 dogs
37
The equation of a line of best fit relating the number of cats c at an animal shelter to the number of dogs d is c = 2.1d − 26. Predict the number of cats at a shelter where there are 30 dogs.
37
Minimize the objective function P = 5x + 8y for the given constraints. x ≥ 0 y ≥ 0 2x + 3y ≥ 15 3x + 2y ≥ 15
37.5
Identify the graph that shows the feasible region for the following constraints. x ≥ 0 y ≥ 0 x + y ≤ 4 4x + 12y ≤ 24
4 & 2 on y
Maximize the objective function P = 5x + 7y for the given constraints. x ≥ 0 y ≥ 0 2x + 3y ≤ 18 5x + 2y ≤ 23
43
Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system. y < -2x + 1 y ≤ -2/3 + 2
Possible solutions: (−3, −3), (−4, 2)
Identify the solution of the inequality |7p| + 36 > 15 and the graph that represents it.
all real numbers
If 3 basketball game tickets and 4 football game tickets were purchased for $50.25, and if 5 basketball game tickets and 5 football game tickets were purchased for $71.25, what are the costs of basketball game tickets and football game tickets?
basketball game tickets: $6.75; football game tickets: $7.50
At a grocery store, Rick bought 3 bottles of water and 5 heart-healthy frozen meals for $24. Danny bought 4 bottles of water and 4 heart-healthy frozen meals for $22. Identify the cost of a bottle of water and the cost of a heart-healthy frozen meal.
bottle of water: $1.75; frozen meal: $3.75
Classify the system of equations and identify the number of solutions. 3 = 4x + y 2y = 6 − 8x
consistent, dependent; infinite
Classify the system of equations and identify the number of solutions. 3x + y = 4 12x + 4y = 16
consistent, dependent; infinite
independent variable= y
dependent variable= x
Graph the system of linear inequalities. y ≤ x + 5 y ≥ x + 3
fully shaded, dark shade between two lighter ones
Let g(x) be the transformation of f(x) = |x| left 2 units. Identify the rule for g(x) and its graph.
g(x) = |x + 2|, +2 on x
Let g(x) be the transformation of f(x) = |x| so that the vertex is at (1, −3). Identify the rule for g(x) and its graph.
g(x) = |x − 1| − 3, (1, -3)
Let g(x) be the transformation of f(x) = |x| such that the vertex is at (2, 5). Identify the rule for g(x) and its graph.
g(x) = |x − 2| + 5, (2,5)
Let g(x) be the transformation of f(x) = |x| right 2 units. Identify the rule for g(x) and its graph.
g(x) = |x − 2|, +2 on x
Let g(x) be the transformation of f(x) = |x| up 3 units. Identify the rule for g(x) and its graph.
g(x) = |x| + 3, +3 on y
Let g(x) be the indicated transformation of f(x) = |3x| + 4. Stretch the graph of f(x) = |3x| + 4 vertically by a factor of 3 and reflect it across the x-axis. Identify the rule and graph of g(x).
g(x) = −3|3x| − 12, ^ on graph
Let g(x) be the indicated transformation of f(x) = |2x| − 5. Compress the graph of f(x) = |2x| − 5 horizontally by a factor of 1/4 and reflect it across the x-axis. Identify the rule and graph of g(x).
g(x) = −|8x| + 5, ^ on graph
Let g(x) be the indicated transformation of f(x) = |4x| − 5. Compress the graph of f(x) = |4x| − 5 horizontally by a factor of 1/2 and reflect it across the x-axis. Identify the rule and graph of g(x).
g(x) = −|8x| + 5, ^ on graph
Classify the system of equations and identify the number of solutions. 2x + y = 7 y + 5 = −2x
inconsistent; none
Classify the system of equations and identify the number of solutions. 7x + 3y = 10 3y = 9 − 7x
inconsistent; none
Classify the system of equations and identify the number of solutions. 8 + y = 4x 4x − y = −3
inconsistent; none
At a grocery store, Rick bought 4 loaves of bread and 3 gallons of milk for $20. Danny bought 6 loaves of bread and 2 gallons of milk for $25. Identify the cost of a loaf of bread and a gallon of milk.
loaf of bread: $3.50; gallon of milk: $2.00
Solve the equation |2m − 6 | = 10.
m = −2 or m = 8
Identify the solution of the inequality −3|n + 5| ≥ 24 and the graph that represents it.
no solution
Identify the solution set of the inequality 2|f + 4| ≤ −12 and the graph that represents it.
no solution
Solve the equation |p − 8| = 4.
p = 12 or p = 4
Solve the equation |p + 5| = 3.
p = −8 or p = −2
John and Harry went to a stationery shop. John bought 3 pens and 8 notebooks for $20.50. Harry bought 4 pens and 5 notebooks for $16.00. Identify the cost of a pen and the cost of a notebook.
pen: $1.50; notebook: $2.00
Solve the equation |7q| + 3 = 24.
q = 3 or q = −3
The data in the table show how long (in minutes, t) it takes several commuters to drive to work. Find the correlation coefficient and the equation of the line of best fit for the data. Treat the commute distance d as the independent variable.
r ≈ 0.75 t ≈ 0.8d + 11.5
The data in the table show the number of boys b and girls g in several different classes. Find the correlation coefficient and the equation of the line of best fit for the data. Treat the number of girls in the class as the independent variable.
r ≈ −0.18 b ≈ −0.13g + 17.9
Identify the graph that represents the given system of inequalities and the classification of the figure created by the solution region. y ≥ 1/3x - 1 y ≤ -x + 3 x ≥ -1 x ≤ 1
trapezoid
Identify the solution of the inequality |4x + 4| > 8 and the graph that represents it.
x < −3 or x > 1
Identify the solution of the inequality |5x + 10| > 15 and the graph that represents it.
x < −5 or x > 1
Identify the solution of the compound inequality x + 4 > 9 or 2x ≥ 14 and the graph that represents it.
x > 5
Identify the solution of the compound inequality x + 4 ≤ 3 or 4x > 8 and the graph that represents it.
x ≤ −1 or x > 2
Identify the solution of the inequality and the graph that represents it. |4x-4|/2 < 4
x ≥ −1 and x ≤ 3
Identify the solution of the compound inequality −6m −4 < 2m and m − 3 ≤ −4m + 12
−1/2 < m ≤ 3
Identify the solution of the compound inequality −3y < 12 and y − 2 ≤ 4.
−4 < y ≤ 6
