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Q:
Solve the system by elimination.
Q:
Solve the system by elimination.
Q:
Solve the system by graphing.
Q:
Victoria has been hired by C&M sales to be an account representative. She has been offered two salary options. Option A has a base pay of $880 per week with a commission of $26 for every thousand dollars in sales. Option B has a base pay of $160 per week with a commission of $42 for every thousand dollars in sales. How many thousands of dollars in sales would Victoria need to reach each week in order for the two options to be equal?
Q:
Franklin Meadows is considering opening a lumber business. He estimates that his total expenses will be represented by the formula Mexpenses = 17.1 + 3.8x and that his total sales will be estimated by the formula Msales = 11.4x - 28.5. (Where x is the number of years the business has been operating and M is in $1,000s.) How many years will it take for Franklin's sales to equal his expenses?
Q:
Determine which ordered pairs are solutions to the system of equation.
3x + 3y = 9
-2x - 4y = -8
A) (2, -1)
B) (-2, 1)
C) (2, 1)
D) (2, 2)
Q:
The following graph represents the annual operating expenses and the annual sales (both in $1,000s) for a new graphics business. In what year did sales finally equal expenses?
Q:
Solve this system of equations by sketching the graphs and estimating the solution.
5x + y = -8
3x - 4y = 9
Q:
From the graph shown, identify where y1 > y2. Give your answer in interval form.
Q:
From the graph shown, identify where y1 < y2. Give your answer in interval form.
Q:
Estimate the solutions of the system of equations pictured.
Q:
Estimate the solutions of the system of equations pictured.
Q:
Estimate the solution of the system of equations pictured.
Q:
Estimate the solution of the system pictured. A) B) C) D) and
Q:
Determine whether is a solution to the following system.A) It is a solution.B) It is not a solution.
Q:
Determine whether is a solution to the following system.A) It is not a solution.B) It is a solution.
Q:
Determine whether is a solution to the following system.A) It is not a solution.B) It is a solution.
Q:
Determine whether is a solution to the following system.A) It is not a solution.B) It is a solution.
Q:
Which graph represents your distance from home if you drive casually to work in the morning and then hurry home after work?
A) B) C) D)
Q:
Create the step function from the graph:
Q:
Graph the function
Q:
Graph the function
Q:
Rewrite the following expression without using an absolute value sign.
Q:
Rewrite the following expression without using an absolute value sign.
Q:
Evaluate: |"8 " 1|
Q:
Construct the piecewise linear function for the graph
Q:
Create the graph for the function:
Q:
Create the graph for the function:
Q:
Use the function given to evaluate f("3), for the function:
Q:
Use the function given to evaluate f("1), for the function:
Q:
Use the function given to evaluate for the function
Q:
Use the function given to evaluate for the function
Q:
Find the slope of the line shown.
Q:
Find the slope of the line shown.
Q:
Write the equation of the line perpendicular to and goes through the point (2, 8).
Q:
Write the equation of the line parallel to and goes through the point (3, "2).
Q:
The number of nails required to hold the joint plates of a truss is directly proportional to the pounds of stress on the joint. If a joint carrying 874 pounds of stress requires 23 nails in the plate, how many pounds of stress can be carried by a joint with 35 nails in the plate?
Q:
The number of nails required to hold the joint plates of a truss is directly proportional to the pounds of stress on the joint. If a joint carrying 600 pounds of stress requires 24 nails in the plate, how many nails are required to plate a joint carrying 825 pounds of stress?
Q:
The joint plates of a wooden truss require 1 nail for every 40 pounds of stress on the joint. How many nails would be required in a joint that holds 440 pounds of stress?
Q:
The joint plates of a wooden truss require 1 nail for every 30 pounds of stress on the joint. How many pounds can a joint with 28 nails in the joint plate hold?
Q:
The amount of weight that can be lifted by a simple machine is directly proportional to the the amount of force applied to the machine. If the machine is able to lift 246 pounds when a force of 41 pounds is applied, how much force would need to be applied in order to lift a weight of 894 pounds?
Q:
The amount of weight that can be lifted by a simple machine is directly proportional to the the amount of force applied to the machine. If the machine is able to lift 308.75 pounds when a force of 65 pounds is applied, how many pounds can be lifted when a force of 106 pounds is applied?
Q:
The amount of weight that can be lifted by a simple machine is directly proportional to the the amount of force applied to the machine. If the machine is able to lift 132.25 pounds when a force of 23 pounds is applied, find the equation for this relationship.
Q:
Determine whether the two lines are perpendicular.
and A) They are NOT perpendicular.
B) They are perpendicular.
Q:
Determine whether the two lines are parallel.
and A) They are NOT parallel.
B) They are parallel.
Q:
Find the equation for the line that contains the point (2,2) and is perpendicular to the line .
Write your answer in slope-intercept form.
Q:
Find the equation for the line that contains the point ("2,2) and is parallel to the line y = 1- 7x.
Write your answer in slope-intercept form.
Q:
Find the equation of the line for the following set of conditions.
The line is a horizontal line that passes through the point (9,"6).
Q:
Find the equation of the line for the following set of conditions.
The line is a vertical line that passes through the point ("5,2).
Q:
The distance traveled (in miles), D, is directly proportional to time traveled (in minutes), t.
If you traveled 19.2 miles in 24 minutes, find your distance traveled (in miles) if you've traveled for 53 minutes.
Q:
The distance traveled (in miles), D, is directly proportional to time traveled (in minutes), t.
If you traveled 18 miles in 20 minutes,
A) find a formula that yields D as a function of t.
B) Now use the formula to find your distance traveled (in miles) if you've traveled for 100 minutes.
Q:
The distance traveled (in miles), D, is directly proportional to time traveled (in minutes), t.
If you traveled 16.8 miles in 21 minutes, find a formula that gives D as a function of t.
Q:
y is directly proportional to x and y is 20.8 when x is 4.
A) Find a formula to describe y as a function of x.
B) Use the formula to find y when x is 12.
Q:
y is directly proportional to x and y is 17.5 when x is 5.
Find a formula to describe y as a function of x.
Q:
Put this equation into slope-intercept form.
24x + 4y = 24
Q:
Find the slope of this linear function from the table. x
f(x) 8
-11 16
-5 24
1 32
7 40
13
Q:
Find the slope of this linear function from the table. x
f(x) 3
7 6
19 9
31 12
43 15
55
Q:
Complete the table for the linear function. x
f(x) = 5 + 3x 6 11 16 21 26
Q:
Assuming that the line through the given two points has the given slope m, find the value of t.
(t, 5) and (-8, 2); m = .
Q:
Assuming that the line through the given two points has the given slope m, find the value of t.
(5, 1) and (20, t); m = .
Q:
Find the equation of the line with slope and goes through the point (9, 15).
Write the answer in slope-intercept form.
Q:
Find the equation of the line through the points (5, 8) and (-20, -12).
Write the answer in slope-intercept form.
Q:
Find the equation of the line for the following set of conditions.
The slope is and the line passes through the point (-15, -16).
Write the answer in slope-intercept form, .
Q:
Put the following equation into y = b + mx form.
3x + 4y = -16
Q:
Determine whether the following data is linear. If it is linear, find the function and write your answer in form. If the data is not linear, enter Not Linear. x
y 3
12 5
6 6
0 8
-18 10
-44
Q:
Determine whether the following data is linear. If it is linear, find the function and write your answer in form. If the data is not linear, enter Not Linear. x
y -4
11 -1
5 0
3 3
-3 5
-7
Q:
A house that sold for $35,000 in 1980 sold for $60,500 in 2000.
A) Find the average rate of change of the value of the house per year.
B) If the house continues to increase in value at the same rate, what will be its value in 2016?
Q:
Search and Rescue Teams are often called upon to find lost hikers in remote areas of the Southwest. Members of the search team walk parallel to one another at a fixed distance d between searchers through the area being searched. The team's chance of finding the lost person is related to the distance d of separation. The closer together the searchers are, the better the chances of success. Based on a number of previous searches, the following data was found to be approximately true: If d = 24 ft., P (the probability of success) = 85%. If d = 56 feet, P = 45%.
A) What is the dependent variable?
B) What is the independent variable?
C) Write the equation of the function that relates these two variables.
D) If the team is satisfied with a success rate of 75%, how many feet apart should the searchers be?
Q:
Because of a state budget crisis a publicly supported college is being forced to raise more of its funds from private sources. Their tuition in September 2007 is $6,000; and over the next 5 years they must gradually raise their tuition until it becomes $9,000 in September 2012.
A) Find a linear formula for tuition, T, for any school year, s, during the period of tuition raises. Count school years, s, starting from 2007 as year zero.
B) What is the domain of the function?
C) What is the total tuition for a student starting in September 2008 and finishing in 4 years?
D) How much more would the total tuition be if the student started a year later and finished in 4 years?
Q:
A contractor purchases a piece of equipment for $40,000. The equipment requires an average expenditure of $4.00 per hour for fuel and maintenance, and the operator is paid $13.00 per hour.
A) Write an equation giving the total cost C of operating this equipment for the first t hours, including purchasing it.
B) Assuming that customers are charged $25.00 per hour of machine use, write an equation for the revenue R derived from t hours of use.
C) Use the formula P = R -C to write an equation for the profit, P, derived from the first t hours of use.
D) Find the number of hours this equipment must be used to break even, i.e. make a profit of $0. Round your answer to the nearest hour.
Q:
Jessica works at Acme Manufacturing Company. After 5 years, she was earning $16.00 per hour. After 8 years on the job, she is now earning $20.50 per hour. She has received exactly the same annual raise each year she has been there.
A) Write a linear function describing her hourly wage, w, as a function of years worked, y.
B) What was her beginning hourly wage?
Q:
In 1780, a French balloonist by the name of Jacques Charles discovered that the volume of a fixed amount of gas held at a constant pressure is a linear function of its temperature. In a specific experiment it is observed that if 4 liters of oxygen at 0 Celsius is warmed to 100 Celsius, the volume of the oxygen increases to 5.46 liters.
A) Determine v, the volume of oxygen (in liters) as a function of t, its temperature (in degrees Celsius). Write your answer in slope-intercept form.
B) What is the volume of 4 liters of oxygen at 80 degrees Celsius?
C) What temperature (in degrees Celsius) is required to cause a volume of 4.2 liters?
Round all values to 4 decimal places.
Q:
As a diver descends into the ocean, the pressure increases linearly with the depth (i.e. pressure is a linear function of depth). At the surface (a depth of 0 feet) the pressure is 15 pounds per square inch. At a depth of 33 feet below the surface the pressure is 30 pounds per square inch.
A) Find a formula for the linear function that expresses pressure, P, in terms of depth, d.
Write your answer in slope-intercept form and round values to 2 decimal places, if necessary.
B) Use the function from part A to determine the pressure when the diver is 21 feet below the surface.
Round your answer to 2 decimal places, if necessary.
C) Use the function from part A to determine how deep can the diver go if the highest safe for his equipment and experience is 69 pounds per square inch.
Round your answer to 2 decimal places, if necessary.
Q:
A company has fixed costs of $24,000 per month and variable costs of $5.10 per unit manufactured. (Fixed costs are those that occur regardless of the level of production. Variable costs depend on the number of units manufactured.)
A) Find a formula that describes the total monthly costs, C, for the company as a function of the number of units manufactured, x.
Write your answer in slope-intercept form, .
B) If the company manufactures 600 units what will their monthly costs be?
C) If the company has $27,570 available to cover the monthly costs, how many units can the company manufacture?
Q:
When the price is $220, a company makes 1017 bicycles available for market. For each $4 increase in price, 17 more bicycles are made available.
Let x denote the number of bicycles available for market and p the price.
A) Find an equation that expresses x in terms of p.
Write your answer in slope-intercept form, .
B) How many bicycle will be available if the price of bicycles is set at $200?
C) What price (in dollars) should be set if 1187 bicycles are made available?
Q:
A small business purchases a piece of equipment for $1440. After 9 years, the equipment will be outdated and have no value.
A) Write an equation giving the value V of the equipment as a function of t, the years since purchased.
B) State the domain of the function. Write your answer in interval notation.
Q:
When a large airliner approaches an airport, it begins its descent from about 100 miles away and takes about 20 minutes to descend from an altitude of 36000 feet. Assume that the airliner's distance to the airport is a linear function of the time, t (minutes), since it began its descent.
A) Express as a function of t (minutes). Write your answer in slope-intercept form.
B) Now find the airliner's altitude, A, as a function of the airliner's distance from the airport, d. Write your answer in slope-intercept form.
Q:
By analyzing sales figures, the accountant for the Johnson Stereo Company knows that 275 units of a CD player can be sold each month when the price is $195 per unit. The figures also show that for each $20 hike in price, 11 fewer units are sold monthly. Let x denote the number of units sold per month and p the price per unit. Find an equation that expresses x in terms of p.
Write your answer in slope-intercept form, . Round values to 2 decimal places.
Q:
Find a linear equation that describes the statement.At the age of 7 a person is 47 inches tall and at the age of 11 the person is 55 inches tall.Write your answer in slope-intercept form, , in terms of height, h, and age, a.
Q:
Find a linear equation that describes the statement.A cat is born (age 0) weighing 3.8 ounces and at 8 years of age the cat weighs 148.6 ounces.Write your answer in slope-intercept form, , in terms of weight, w, and age, a.