Write the corresponding linear inequality for the amount that lynnah w...

Write the corresponding linear inequality for the amount that lynnah wants to earn. The Natural Fertilizer Company,using the following data Express the solution i Solve the linear programming problem by the method of corners A linear inequality is an inequality in one variable that can be written in one of the following forms where a, b, and c are real numbers and a ≠ 0 a ≠ 0: Solve the inequality 6 y ≤ 11 y + 17 , 6 y ≤ 11 y + 17 , graph the solution on the number line, and write the solution in interval notation His brother earns ?3,300 per month The company has 125 hours of labor and 45 board-ft Given that my age is an integer number of years, what is the smallest my age could be? KJ investment partners is starting a new derivative fund containing a mix of bonds, home loans, auto loans and personal loans Solve the inequality , graph the solution on the number line, and write the solution in interval notation How has your attitude towards solving word problems changed as a result of working through this chapter? Explain Pro Graph the system of linear inequalities 2x+3y\leq -9 and 2x-3y\geq -3 The average weight of the 25 people on the water taxi when it sank was 168 pounds per person How many guests can attend if Adele and Walter want the total cost to be no more than ?12,500? Shower budget Penny is planning a baby shower for her daughter-in-law They can earn the rest of the money they need by having a car wash Determine (in The cost of a long distance call is $0 His speed going upstream is two miles per hour slower than his speed going downstream How do you find the individual masses? You also know their displacement Solution Solve the inequality 9 y + 2 ( y + 6 ) > 5 y − 24 9 y + 2 ( y + 6 ) > 5 y − 24, graph the solution on the number line, and write the solution in interval notation To d What numbers are greater than two but less than five? Are you thinking say, We can represent all the numbers between two and five with the inequality We can show on the number line by shading all the numbers between two and five What is the most that can be invested at 6% in order to make at least $1500 interest in one year? Solve the following inequality If the average weight of a student is assumed to be 140 pounds, what is the maximum number of students who could safely be on the stage? Maximum Weight on a Boat In 2004, a water taxi sank in Baltimore harbor and five people drowned If there are 12 children, what is the total number of people on the hike? Marla’s breakfast was 525 calories 2y + 3 / 4 - y / 2 = 5 Solve the following inequality for x Charmaine is choosing between two exercise routines Picture frame A sells for $20 each, and picture frame B sells for $25 each His monthly expenses are ?1,600 00 and so An economics class formed a company to sell school supplies The advertising budget is limited to $8,000 per month What is the maximum number of packs she can buy? Daniel wants to surprise his girlfriend with a birthday party at her favorite restaurant How much should the tip be? Reza was very sick and lost 15% of his original weight The first option has an initial fee of $50 and then charges $30 per month [6, \infty) \\ E Admission i Reese wants to organize a party and decides to save money for it 00 each and purple balloons cost $0 The perimeter is 40 feet It will cost them $110 for registration, $375 for transportation and food, and $42 per person for the hotel The Fun Zone charges $19 per child How long can you talk without spending more than $5? (Write and solve an equation He got a ?100 gift card to the art supply store and wants to use it to buy canvases (2,6] \\ D A sample of 36 of these c Expedition Outfitters manufactures a variety of specialty clothing for hiking, skiing, and mountain climbing Dawn won a mini-grant of $4,000 to buy tablet computers for her classroom Find the measures of all three angles Write and solve an inequality to find the minimum number of yards she must mow to make a profit of at Diana is earning money by mowing lawns For how many ordered pairs of positive integers (x,y) is 2x + 3y ( 6? List the ordered pairs and show/explain It costs him $10 He pays his uncle 2% interest on the ?4,500 he borrowed from him, and he pays the bank 11 Her speed on the flat road was three miles per hour faster than her speed going uphill 08 per therm 25 less than he paid to go to a concert it should satisfy all of the inequalities in the system The fruit juice costs ?6 5% annual interest and the rest in a certificate of deposit that pays 1 What is the maximum number of text messages Kiyoshi can use so the phone bill is no more than $56 Edusin walks at least 3 miles a day 80 per month plus $2 Anne has dollars -3 \le \frac{x^2 + 8}{x^2 - 8} \le 3 His budget for the party is $500 the graph of the solution set of a system of linear inequalities in two variables of the two linear inequalities in the system Everything you need to prepare for an important exam! K-12 tests, GED math test, basic math tests, geometry tests, algebra tests At 6:30, Devon left her house and rode her bike on the flat road until 7:30 9, \ 36 \frac{9}{5}x - \frac{7}{6} \geq -\frac{6}{5}x \boxed{\space} Given is an LP Model Max Z = 0 The measure of the third angle is 14 more than the measure of the smallest angle They plan to rent a car from a company that charges $75 a week plus $0 Her coach recommends that gymnasts wh Waccovia Bank is in the process of devising a loan policy that involves a maximum of $12 million in funds What is the smallest po A car rental company offers two plans for renting a car He has $189 in savings and can earn $35 for each lawn he mows Solve the conjunction -2 less than or equal to a + 3 less than 8 His monthly expenses are ?2,272 The perimeter is 96 inches state the solutions exactly and in set notation: 4\cos\left(\theta-\dfrac{\pi}{4}\right)+9\geq11 Solve the inequality and sketch the solution on the real number line How many hours will it take them to be 375 miles apart? Kyle rowed his boat upstream for 50 minutes 75 Let f(x) = -4cos x and g(x) = 2cos x + 3 for 0 less than or equal to x less than 2 pi , is a small manufacturer of golf equipment and supplies When graphing y -6 should the region below line y = -6 be shaded or should the region above the line y = -6 be shaded? Nikki noticed that if she stacked her dollar bills in stacks of 6 - she had 3 left over, stacks of 8 - 7 left over, and stacks of 4 - 4 left over Find Kyle’s upstream and downstream speeds Tracy had left Nashville and drove 4 hours towards Chicago, at a speed one mile per hour faster than Louellen’s speed How much did she earn last week? Janet gets paid ?24 per hour The investor has decided to use three vehicles for generating income: municipal bonds, a certificate of deposit (CD), and a money market account He has $1,810 in savings What would Andre’s total sales need to be for his pay to be at least as high as the average pay for this job? Nataly is considering two job offers Each bed requires 6 hours of carpentry and 4 hour of varnishing Just like some equations are identities and some are contradictions, inequalities may be identities or contradictions, too Consider the equation: f(x)=\sqrt{4x-6}-\sqrt{5x-6} \\ a) Find the domain of the function f(x) Do not plot the nonnegativity constraints A salad contains ham and chicken How many of each ticket were sold? Tickets for a basketball game cost ?2 for students and ?5 for adults If false, give a counterexample: "A system of two linear inequalities has either no points or infinitely many points in its solution Northern Illinois University, Master of Science, Cur SUNY College at Oneonta, Bachelor of Science, Childhood Education { x + y greater than or equal to 2 and x + y less than or equal to 8 and 2 x + y less than or equal to 10 and x greater than o Kyle plans to invest $8,500, part at 6% simple interest and the rest at 7% simple interest \left\{\begin{matrix} x \geq 0\\ y \geq 0 \\ 2x + \frac{5}{2}y \leq 11 \\ 4y + 2x < 13 \end{matrix}\right What are the possible values of that number? Describe the linear programming situation for this system of inequalities The Albuquerque bus heads west on the I-40 at a speed of 72 miles per hour, and the Oklahoma City bus heads east on the I-40 at a speed of 78 miles per hour He has $840 in savings, and he earns $45 per hour for tutoring She charges ?2 2 hours towards Nashville The number of ?10 bills is one less than twice the number of ?5 bills The total amount Joan paid for - Brainly y A coordinate system is placed at the center of a town with the positive x-axis pointing east, and the positive y-axis pointing north Silver balloons cost $1 50 per wedding invitation Each pack of juice boxes costs ?2 How many guests can attend if Adele and Walter want the total cost to be no more than ?12,500? Shower Budget Penny is planning a baby shower for her daughter-in-law \\ b) Solve analytically: -2= f(x) \\ 2 He has decided that the money invested in bonds must be at least twice as much as that in stocks y < -2x + 1 \\ y \leq \frac{1}{5}x - 1 G Writing and using linear inequalities to model real-world situations (WORD problems) Flashcards | Quizlet Oh no! It looks like your browser needs an update Company B charges $35 per month plus $0 The cost is ?9850 for up to 100 guests, plus ?38 for each additional guest They would like to sell at least 20 notebooks and 50 pens per week, with a goal of earning at least $150 per week Her monthly expenses are $3,745 There is ?450 budgeted for the convention in the student government savings account Nga and Lauren bought a chest at a flea market for ?50 24 for each additional minute He left at 3:45 and had heavy traffic until 5:30 How many miles can Renee drive so that her monthly car expenses are no more than ?250? Costa is an accountant What is the maximum number of tablets Dawn can buy? Angie has ?20 to spend on juice boxes for her son’s preschool picnic What would her total sales need to be for her salary on the second offer be higher than the first? Jake’s water bill is $24 Write the answer in interval notation The Northwest Flower Company owns a greenhouse, which furnishes roses and carnations to florist's in Oregon, Washington, and Idaho - \frac{4}{3}(x - 2)^{-\frac{4}{3}} + \frac{8}{9}x(x - 2)^{-\frac{7}{3}} \geq 0 A How many text messages can she send/receive and keep her monthly phone bill no more than ?50? Sergio and Lizeth have a very tight vacation budget John Steinbeck has an income of $80 per week, all of which he spends on grapes (G) and tortillas (T) B) Write an English statement to describe the set Write an inequality that can be used to calculate the minimum number of TJ's Daniel can spend no more than $40 at the fair Each milkshake costs the same integer amount of cents Find the length and the width If he charges ?60 per job, how many jobs must he do to earn a profit of at least ?4,000 a month? Caleb has a pet sitting business (10,0) d They want the monthly rent to be no more than $2,360 In Plan B, there is no monthly fee, but the cust Which of the following statements are TRUE (Choose ALL the true statements, choosing incorrect statements will incur negative marking) a) A good spreadsheet design is where the final values of con Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now 60 per hour (2,2) c If there are 87 children, what is the total number of people at the concert? One number is eleven more than another Fuel x costs $2 per gallon and fuel y costs $3 per gallon What is the highest rent Emma will qualify for? Solution Alan is loading a pallet with boxes that each weighs 45 pounds What is the maximum number of ccf Jake can use if he wants his bill to be no more than $60? Kiyoshi’s phone plan costs $17 She will also have a favor for each of the guests, and each favor will cost $720 per text message Join Here! Basic Arithmetic : Linear Equations with Money Study concepts, example questions & explanations for Basic Arithmetic 6 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept Example Questions You loan a friend at a annual simple interest rate 04 per gallon and the soda costs ?4 (3, 3/4) c We substitute the point into the linear inequalities Most inequalities will take more than one step to solve The number of ?0 1 / {x - 3} less than or equal to 9 / {4 x + 3} Solve the inequality and graph the solution on the real number line Aft A) Graph the solution set for the inequality 4x - 3y greater than 9 solve for f(x) greater than g(x) on (0,2 pi) For what amount of total sales will Keshad’s monthly pay be higher than his brother’s monthly pay? Kimuyen needs to earn ?4,150 per month in order to pay all her expenses Landry only has time to ride 4 rides We follow the same steps we used in the general strategy for solving linear equations, but make sure to pay close attention when we multiply or divide to isolate the variable In Plan A, the customer pays a monthly fee of $13 and then an additional 6 cents per minute of use How much should she invest in each account if she wants to earn 4 of wood available each day Raisins cost ?3 Koji has ?5,502 in his savings account 00 on milkshakes 5% of his total sales The total budget is $960 per week But the money invested in bon Solve the following linear inequalities Solve the following system of linear inequalities: \left\{\begin{matrix} y > x - 4\\ y < 2x + 10 \end{matrix}\right If she has five more dimes than quarters, how many of each coin does she have? At a concert, ?1,600 in tickets were sold His monthly expenses are $2,272 This eliminates negative coefficients and so we don’t have to multiply or divide by a negative—which means we don’t have to remember to reverse the inequality sign 2 Her monthly expenses are ?650 The original price of the freezer was ?695 This was 35% of her total calories for the day If the Solve the inequality He charges ?175 per car His total income last year was more than $70,000 (use the variable E) b) Solve the inequality 8 p + 3 ( p − 12 ) > 7 p − 28 , 8 p + 3 ( p − 12 ) > 7 p − 28 , graph the solution on the number line, and write the solution in interval notation How much should his total sales be for his variable pay option to exceed the fixed amount of ?925? Tiffany just graduated from college and her new job will pay her ?20,000 per year plus 2% of all sales How many units can she take to have a maximum cost of $1,365? Arleen got a $20 gift card for the coffee shop How many aprons must she sell next month if she wants to earn at least ?1,000? Ryan charges his neighbors ?17 Set Weenies and Buns is a food processing plant that manufactures hot dogs and hot dog buns Her monthly expenses are ?3,745 Solve each inequality, graph the solution on the number line, and write the solution in interval notation I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law She also works as a tutor for $7 per hour How much fruit juice and how much soda should she use so that the punch costs ?5 How many “cut & styles” must she do to save at least ?1,200 per month? Noe installs and configures software on home computers One point is awarded for each correct answer, and one-third of a point is deducted for each incorrect answer If her rent is $300 every 4 weeks, what is her net profit in 4 weeks? Samuel bakes cakes and earns $5 profit from each cake Write and graph a system of linear inequalities to represent this situation How many invitations must she write to earn a profit of at least ?2,800 per month? Caleb has a pet sitting business They grind their own flour for the hot dog buns at a maximum rate of 200 pounds per week Kinetic by OpenStax offers access to innovative study tools designed to help you maximize your learning potential If their sum is increased by seventeen, the result is 90 The restaurant charges ?950 for up to 25 guests, plus ?31 25 for each game Her monthly expenses are $3,150 How many children can she have at the party and stay within her budget? Carlos is looking at apartments with three of his friends ) A package has a fixed girth of 53 inches ) Plot the five corner poin Determine whether the following statement is true or false The cost is ?9,850 for up to 100 guests, plus ?38 for each additional guest 2 hours Adult tickets were ?9 each and children’s tickets were ?4 each What is the minimum Kimuyen’s total sales must be in order for her to pay all her expenses? Andre has been offered an entry-level job He finds this formula: Maximum total length of all fish in pond (cm) = \frac{25 \pi LW}{4}, where π = 3 For what amount of total sales will Keshad’s monthly pay be higher than his brother’s monthly pay? Kimuyen needs to earn $4,150 per month in order to pay all her expenses {3 x} / {x - 1} less than or equal to x / {x + 4} + 3 The set of all points on the real number line that represents the solution set of an inequality is the ________ of the inequality Join our Discord to connect with other students 24/7, any time, night or day This month, he worked 10 days The tablets she would like to buy cost ?254 What is the maximum number of ccf Jake can use if he wants his bill to be no more than ?60? Kiyoshi’s phone plan costs ?17 It took him 30 minutes to row back downstream His expenses for buying software, renting an office, and advertising are ?6,000 ph II If Mark only has to spend on a car wash, for how long can he wash his car? Jamie makes $60 a day, 5 days a week She wants to be able to put at least ?1,200 per month into her savings account order to open her own salon How many lawns must he mow to have enough money to pay for the trip? Alonzo works as a car detailer 50 How many boxes can he safely load onto the pallet? The elevator in Yehire’s apartment building has a sign that says the maximum weight is 2100 pounds 99 per month plus ?5 The cell phone rates may compare usage of minutes or usage of text m Andrew is having an irrigation system installed in his yard How many hours must she tutor to have enough money for the party? Maximum load on a stage In 2014, a high school stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical production How many people can Kellen have at the shower if she wants the maximum cost to be $1,500? Moshde runs a hairstyling business from her house Tran has $24,000 to invest, some in bonds and the rest in stocks Her monthly expenses are $3745 One heads east at a speed of 428 miles per hour How many units can she take to have a maximum cost of ?1,365? Arleen got a ?20 gift card for the coffee shop State whether the equation is an identity, a contradiction, or a conditional equation Write each statement as a linear inequality in two variables She charges $88 per necklace Learn more dentify the relation symbol to be used in the expression: "How many candies and bubble gums can you buy if you have at least ₱20?" Identify the linear inequality for this situation: Bill has 90 feet of fencing materials 95 for each additional guest She will put some of it into a fund that pays 4 The measure of the smallest angle in a right triangle is less than the measure of the next larger angle A student must have an average of 92 on four tests to receive an A in the course Solve the inequality 1 3 a − 1 8 a > 5 24 a ​ + 3 4 , 1 3 a − 1 8 a > 5 24 a ​ + 3 4 , graph the solution on the number line, and write the solution in interval notation There were 9 times as many white cars as yellow cars Tammy is choosing between two exercise routines 80 a month plus $0 It will cost him $198 for airfare, $56 for local transportation, and $45 per day for food How many therms can Rameen use if he wants his heating bill to be a maximum of ?87 If he charges $60 per job, how many jobs must he do to earn a profit of at least $4,000 a month? Solution Caleb has a pet sitting business 50 fee for every minu A phone company offers two monthly charge plans (1) 2x + 5y < 30 (2) x + y < 12 (3) 3x + 2y < 36 (4) x, y > 0 Explain what information is presented in this model How much money did he receive this month? Northern Illinois University, Bachelor of Science, Elementary Education How far from the base of the antenna can he attach the wire? A sidewalk in front of Kathy’s house is in the shape of a rectangle four feet wide by 45 feet long Wh Diane is going to rent a truck for one day To ensure the best experience, please update your browser The first job would pay her $83,000 per year What was the original price of the crib? Winston deposited ?3,294 in a bank account with interest rate 2 Her monthly income will be $5,625 She charges $115 per four-person meal What is the most that he can invest at 6% and still be guaranteed at least $535 in interest per year? Given this linear programming model: Max Z = 10x + 16y (profit) s Solve the inequality: (3x - 7)/(x + 2) less than or equal to 1 39 in pennies and nickels How many miles can they travel during the week and still keep within their ?200 budget? Rameen’s heating bill is ?5 How much money does Koji have in his checking account? The bill for Dino’s lunch was ?19 To make part X, machine A is needed for 4 hours and machine B is needed for 2 hours How many miles can they travel and still keep within their $200 budget? Solution Taleisha’s phone plan costs her $28 Company B charges $1200 plus $17 per sprinkler head Then she started riding uphill and rode until 8:00 How many driveways must he shovel to have enough money to pay for the trip? Mona is planning her son’s birthday party and has a budget of ?285 How many calories did she have that day? Melinda deposited ?5,985 in a bank account with an interest rate of 1 The party will cost her $1,520 for food and drinks and $150 for the photographer The notation for inequalities on a number line and in interval notation use similar symbols to express the endpoints of intervals His budget for the party is ?500 She charges ?45 for a haircut and style If he wants to earn not less than ₱200 how many of each guavas and atis does he needs to sell? By using the intercepts (3,0) and (0,3) write the equation of the line then determine the relation symbol to be used Company A charges $120 and allows unlimited mileage What should the maximum number of people of this weight have been? Wedding budget Adele and Walter found the perfect venue for their wedding reception He will need to pay ?120 for application fees, ?950 for security deposit, and first and last months’ rent at ?1,140 per month -3 less than or equal to (x^2 + 8)/(x^2 - 8) less than or equal to 3 Solve the following linear programming problem graphically: 1 How much money did Samuel earn this week? It costs $8 to enter the carnival, and then each ride costs $2 to ride The company has decided to begin production on two new parkas designed for use in extre County Credit Union (CCU) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans What is the maximum number of people Daniel can have at the party? Taleisha’s phone plan costs her ?28 Each gallon of Color A requires 4 units of yellow dye and 1 A manufacturing company produces mango juice and yoghurt with a contribution of MK8 and MK10 per unit respectively Solve the inequality, graph the solution on the number line, and write the solution in interval notation The restaurant charges $950 for up to 25 guests, plus $31 See (Figure) In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation Considering the following inequality, -x (x + 4)^2(x - 3)^3(x + 1) less than 0, sketch and solve graphically Alan is loading a pallet with boxes that each weighs 45 pounds Anthony drove from New York City to Baltimore, a distance of 192 miles The width of a rectangle is 45 centimeters I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process How many white cars did Rafael count? Given that (x + 1)(2x - 8) less than 0, the solution set of the inequality is: (a) (-1, 8) (b) (-1, 4) (c) [-1, 4] (d) [-1, 8] Mr How fast was Aaron’s friend driving? Describe how you have used two topics from this chapter in your life outside of your math class during the past month He rented shoes for $5 C) Write the answer Anna is going to make and sell bread Justify your answer (use the variable G) c) There is $450 budgeted for the convention in the student government savings account He calculates that he needs to save at least $420 in 9 weeks (2,6) B 60? Marlon’s TV plan costs ?49 The sale price was 40% of the original price f(6) \\3 What is the length? The length of a rectangle is 12 cm more than the width Three-fourths of the people at a concert are children The two types of biscuits require the followi Solve the inequality and show the graph of the solution in this case on a number line: 3(1 - x) less than 2(x + 4) List all vertices for the following system of constraints Dawn won a mini-grant of ?4,000 to buy tablet computers for her classroom She will make a profit of A sequence is defined by un = 71-7n/2 Banana bread is made with 4 cups of flour and 1 cup of sugar The company has 120 work hours per day for manuf Given inequality system x ? 4 y 0, y ? 5 Which of the following points is NOT part of the solution set for the system? a 0 International License, except where otherwise noted The company wants to know how many ounces of oats and rice it should incl Graph the equation 3^3 x + 15^3 y less than or equal to 60 realistically on a graph with a scale of 2 The company offered him ?48,000 per year plus 3 41 stamps she bought was five more than the number of ?0 Her favorite iced drink costs ?3 Type of loan I At a large nursery, a border for a rectangular garden is being built The production process requires carpentry and varnishing 5 predict the y value when x =-1 The pallet can safely support no more than 900 pounds How many sprinkler heads will Calculate the PIBP and PISP for a deal [0 Find the dimensions of the rectangular box of maximum volume that can be inscribed in the ellipsoid: \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} + \dfrac{z^2}{c^2} = 1 For several competitions she received the following "All round" scores: 37 Adult tickets cost ?10 each and children’s tickets cost ?6 each Company A charges 90 dollars and allows unlimited mileage (2,-1) Choose all correct answers f(-2) \\2 Brenda has ?500 in savings and can earn ?15 an hour babysitting How long could the original scarf have been? Mickey went to Donald Dee's to buy 75 milkshakes for his party ​ If you were an employee, would you consider working on your rest day, on a special holiday, or legal holiday? Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here 49 per first-run movie Shade the region on a graph bounded by the graphs of f and g between the Par Inc It takes Elsa 2 hours to drive the same distance What is the maximum number of times he can go to the driving range next month? Joni sells kitchen aprons online for $32 Figure 2 She would like to invite 40 guests t Find out how many units you have left, after this term, to achieve your college goal and estimate the number of units you can take each term in college 8% annual interest Her monthly expenses are ?3,150 There are two companies she can choose from, and they have the following prices She will also have a favor for each of the guests, and each favor will cost ?7 He charges ?32 per hour She wants to be able to put at least $1,200 per month into her savings account order to open her own salon The stage could support a maximum of 12,750 pounds His solution was k is greater then or equal to did he make? D How do you solve the inequality (k/3) - 14 is strictly less than -5 and graph the solution on a number line? Solve the linear equation Safety A child’s height, h, must be at least 57 inches for the child to safely ride in the front seat of a car How much interest was earned in 2 years? Dotty bought a freezer on sale for ?486 Find the solution of the following, and graph the solution, and find the interval notation: 2x^2-5x-3 geq 0 10 per mile Plan B: $40 per day with free unlimited mileage How many miles would you need to drive for plan B Sarah must maintain a balance of at least $500 in her checking account to avoid finance charges How many hours must he work in order to earn a profit of at least $800 per month? Brenda’s best friend is having a destination wedding and the event will last 3 days A loaf of Irish soda bread is made with 2 cups flour and 1/4 cup sugar 30x + 0 12 per minute Write this as an inequality Her monthly income will be ?5,265 In Routine #1, she burns 24 calories walking How many invitations must she write to earn a profit of at least $2,800 per month? Solution Caleb has a pet sitting business The distance is 300 miles and the bus travels at a steady rate of 60 miles per hour How many first-run movies can he watch if he wants to keep his monthly bill to be a maximum of ?100? Kellen wants to rent a banquet room in a restaurant for her cousin’s baby shower x 1, y 0 , 3x + y 5 the answer is unbounded XYZ chemical company is producing two products A and B Central Connecticut State University, Masters, Special Education Assume also that the Deli has on hand each day A fitness club offers two membership options Learn more You can work a total of no more then 41 hours each week at your two jobs How many necklaces must she sell if she wants to make a profit of at least $1,650? Five student government officers want to go to the state convention What is the maximum she can spend for each costume? Frank found a rental car deal online for ?49 per week plus ?0 If the number of adult tickets was 30 less than twice the number of children’s tickets, how many of each kind were sold? Kim is making eight gallons of punch from fruit juice and soda She has ?792 in savings 20 on renting the meeting room Francie has ?4 Three years later, she repaid the ?4,500 plus ?243 interest Describe the solution set using interval notation and by graphing He charges ?125 per job What is the maximum number of times he can go to the driving range next month? Ryan charges his neighbors $17 Join Here! Find all values of x in the interval (0, 2\pi) that satisfy the inequality 45 per pound and nuts cost ?7 Find Gabe’s speed and Elsa’s speed The estimated rate of return on each of these derivatives is 10% for b Use the equation y = 5 + square root x to answer the following question How many “cut & styles” must she do to save at least $1,200 per month? Noe installs and configures software on home computers Elevators The total weight, w, of an elevator’s passengers can be no more than 1,200 pounds 99 micron high 5B less than or equal to 200 c) A,B greater than or equal to 0 You have been hired by a cell phone company to create two rate plans for customers, one that benefits customers with high usage The distance is 187 miles and the trip took 2 B) Determine if the point (1, -3) is in the solution set 1 / 2 (8 x + 1) greater than or equal to 3 x + 5 / 2 Solve the inequality in terms of intervals and illustrate the solution set on the real number line Define the variabl For a constant real number k, the inequality x less than k represents the half-plane to the (left/right) of the (horizontal/vertical) line x = k 55 for a bucket of balls each time he goes The history club wants to spend less than $107 What is the maximum number of lollipops Anne can buy? How much money does she have left over (round to the nearest whole cent)? Mark has taken his car down to his local car wash Again, be careful with the signs when multiplying or dividing by a negative 3\right ] In order to make it worth the move, Briana needs to have an annual salary of at least ?66,500 She has $792 in savings Solve the inequality and sketch the solution on the real number line She will use basic tiles that cost ?8 per square foot and decorator tiles that cost ?20 per square foot Solution Solve the inequality 1 4 x − 1 12 x > 1 6 x + 7 8 1 4 x − 1 12 x > 1 6 x + 7 8, graph the solution on the number line, and write the solution in interval notation 5% How much money does he spend at the carnival? Bill receives a monthly stipend of $500 If the average weight of a student is assumed to be 140 pounds, what is the maximum number of students who could safely be on the stage? Maximum weight on a boat In 2004, a water taxi sank in Baltimore harbor and five people drowned The second would pay her $66,500 plus 15% of her total sales (2,-1) Identify the feasible region for the following set of constraints: a) 2A - 1B less than or equal to 0 b) -1A + 1 How many text messages can she send/receive and keep her monthly phone bill no more than $50? Solution Sergio and Lizeth have a very tight vacation budget If they charge ?5 per car, how many cars must they wash in order to have enough money to pay for the trip? Cesar is planning a four-day trip to visit his friend at a college in another state Company B has An Omaha electronics firm has received a shipment of 200 special components designed to maintain a constant power output of 64 watts, with a standard deviation of 4 watts 6 The sum of 3 consecutive odd integers is between 21 and 39 06 buying stamps Write the solution set in interval notation How many hours must she tutor to have enough money for the party? Everyday Math Maximum Load on a Stage In 2014, a high school stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical production B) Graph the region of the plan A math professor scores all tests with a maximum of 100 points 31 for the 1st minute and $0 The solution is all the numbers to the right of 2: Always remember to change the direction of the inequality when dividing or multiplying by a negative number A painter has exactly 32 units of yellow dye and 54 units of green dye The tablets she would like to buy cost $254 The inequality 10x+5y≥200 describes the situation: Pete sells guavas and atis for ₱10 and ₱5 each, respectively How many cars must he wash next summer if his goal is to earn at least ?1,500? Keshad gets paid ?2,400 per month plus 6% of his sales Her monthly expenses are $960 Tickets are $7 each He wants to fence a rectangular plot of land He has ?840 in savings, and he earns ?45 per hour for tutoring 90y s How many jobs must he work in order to make a profit of at least $2,400? Katherine is a personal chef The production are as follows: Solve the model using the graphical method She charges $15 per yard How much did Jaime borrow to buy the refrigerator? Zack bought a printer for his office that was on sale for ?380 How many first-run movies can he watch if he wants to keep his monthly bill to be a maximum of $100? Kellen wants to rent a banquet room in a restaurant for her cousin’s baby shower Louellen and Tracy met at a restaurant on the road between Chicago and Nashville He wants to earn at least $7,000 next month He also works a part-time job, earning $30 a day How many of each did she buy? Marquese is making 10 pounds of trail mix from raisins and nuts The Fun Zone charges ?19 per child He plans to mix as many gallons of Color A and B Coplanar points lie on the same plane Elsa’s speed is seven miles per hour faster than Gabe’s speed How many aprons must she sell next month if she wants to earn at least $1,000? Ryan charges his neighbors $17 Traffic was light for the rest of the drive, and he arrived at 7:30 Each minute of radio advertising costs $12 and each minute of TV A small company will be introducing a new line of lightweight bicycle frames to be made from special aluminum and steel alloys The number of students was three less than 10 times the number of adults Joaquim earns a salary of $4,000 per month plus a 6% commission on all of his sales If admission into the fair is $10 and the rides cost $1 Always remember to change the direction of the inequality when dividing or multiplying by a negative number How many tax returns must he do if he wants to make a profit of at least ?8,000? Jenna is planning a 5-day resort vacation with three of her friends His monthly expenses are $1,600 Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and r Suppose that f(x)=-x-5 and g(x)=x-11 Is this an acceptable number of terms until you meet your goal? What are some ways you could accelerate this process? Intermediate Algebra by OSCRiceUniversity is licensed under a Creative Commons Attribution 4 95 per pound The proceeds will be donated to a local alcohol information center 1 How far is it from home plate to second base, as shown? The length of a rectangle is two feet more than five times the width They want the monthly rent to be no more than $2360 What was the rate of interest? Jaime’s refrigerator loan statement said he would pay ?1,026 in interest for a 4-year loan at 13 What was his original weight? Dolores bought a crib on sale for ?350 63 Graph y greater than or equal to 2x + 1 3 The width of a rectangle is three more than twice the length 05% annual interest on the total amount? Enrique borrowed ?23,500 to buy a car What is the maximum number of canvases he can buy with his gift card? Briana has been offered a sales job in another city Find Devon’s speed on the flat road and riding uphill The largest angle is the sum of the other angles If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip? Cesar is planning a four-day trip to visit his friend at a college in another state If the result is a false statement, we have a contradiction Solve the inequality using algebra and a number line How many hours must she work in order to have enough money for her vacation? Four-fifths of the people on a hike are children 79 Letting (x1, x2) You are going to invest $20,000 part at 6% and part at 8%, for one year " A business manufactures two parts, X and Y The cord-type drill requires 1 hour to make, and the cordless model requires 2 hours Which numbers are solutions of the inequality 4x - 2 > 6? (Select all that apply) a x^3 + 3x less than 4x^2 His monthly expenses are ?1,100 If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip? Cesar is planning a 4-day trip to visit his friend at a college in another state The College of Saint Rose, Bachelors, Spanish Write a system of inequalities that shows the various numbers of hours you can work at each job If her current balance is $794, write an inequality to determine how many times she can withdraw $25 Write a system of inequalities to express the exterior of the triangle ABD if A=(-2,7), B=(4,0), and C=(1,-3) After how many years will he owe you just in interest? A lollipop costs The student receives 89, 86, and 90 on three tests His speed in light traffic was four miles per hour more than twice his speed in heavy traffic Child tickets cost ?19 each and adult tickets cost ?40 each y > -2x + 1 \\ y \leq \frac{1}{5}x - 1 H The cost is $9850 for up to 100 guests, plus $38 for each additional guest 99 per month plus $5 20 per ccf (hundred cubic feet) of water Which of the following are solutions of the system? a 42 per month plus ?1 He charges $175 per car -5 b 5, X] for a linear risk tolerance decision maker with p=72 and \eta=0 In Routine 2, she burns 26 calories walking She then runs at a rate that burns 10 Write your answer in interval notation Let y = the amount spent Given that F(x)= - 4 cos x , g(x) = 2 cos x + 3 for 0 less than or equal to x less than or equal to 2 pi Bonita has ?2 5 calories per minute 6(x - 3) - 5x \geq 15 \\a) (-\infty, 33\\b)(33, \infty)\\c)18, \infty)\\d) 33, \infty) How do you write an inequality and solve given "eight times a number minus twenty seven is no more than the negative of that number plus eighteen"? Eight of the entries have been deleted from the computer output that follows The restaurant charges $350 for the banquet room plus $32 What is the maximum number of tablets Dawn can buy? Solution Angie has $20 to spend on juice boxes for her son’s preschool picnic (a) Solve f(x) > 0 How many hours must she tutor to have enough money for the party? Everyday Math Maximum load on a stage In 2014, a high school stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical production Do you feel this is an appropriate number of hours? Is this the appropriate phone plan for you? Find out how many units you have left, after this term, to achieve your college goal and estimate the number of units you can take each term in college She expects to pay ?350 airfare, ?375 for food and entertainment and ?60 a night for her share of a hotel room What is the maximum number of times he can go to the driving range next month? Joni sells kitchen aprons online for ?32 How many questions does Tami Consider the following linear programming problem: M i n i m i z e 20 X + 30 Y S u b j e c t o : 2 X + 4 Y ? 800 6 X + 3 Y ? 300 X , Y ? 0 What is the optimum solution to this problem (X,Y)? (400, Write an inequality to describe the given situation: Sandy is buying a balloon bouquet One cake was so beautiful, that the customer tipped Samuel an extra $25 How much did he pay for the concert? Elissa earned ?152 How much should his total sales be for his variable pay option to exceed the fixed amount of $925? Solution Tiffany just graduated from college and her new job will pay her $20,000 per year plus 2% of all sales 55 microns wide and 0 What average interest rate does he pay on the total ?23,500? (Round your answer to the nearest tenth of a percent How many guests can attend if Penny wants the total cost to be no more than ?1,500? Find your last month’s phone bill and the hourly salary you are paid at your job She heard that this is of what Adam is paid How many cars must he wash next summer if his goal is to earn at least $1,500? Keshad gets paid $2,400 per month plus 6% of his sales 80 per month plus ?2 She expects to pay $350 airfare, $375 for food and entertainment and $60 a night for her share of a hotel room How many text messages can she use and keep her monthly phone bill no more than ?50? Rameen’s heating bill is ?5 Type 1 and Type 2 items generate $3 and $5 profit for each unit sold respectively (0, 2/11) b We can clear fractions in inequalities much as we did in equations Assume that the company produces 100 pound sacks of 35-20-20 fertilizer for lawns and 100 pound sacks of 14-13-12 fertilizer for gardens, wh What do you need to know to graph the linear inequalities -3x-5y-15 Given the equation y=-4x+2 How many boxes can he safely load onto the pallet? Dawn won a mini-grant of $4,000 to buy tablet computers for her classroom What combinat The phone company has two plans for cell phones The notation for inequalities on a number line and in interval notation use the same symbols to express the endpoints of intervals 6% The second would pay her ?66,500 plus 15% of her total sales How many hours must he work in order to earn a profit of at least ?800 per month? Elliot has a landscape maintenance business y < -2x + 1 \\ y \geq \frac{1}{5} - 1 J If the result is a true statement, we have an identity 95 and 0 List three solutions in the shaded region Solve the inequality, graph the solution on the number line, and write the solution in interval notation: Solve the inequality, graph the solution on the number line, and write the solution in interval notation: When solving inequalities, it is usually easiest to collect the variables on the side where the coefficient of the variable is largest It will cost her ?279 for airfare, ?300 for food and entertainment, and ?65 per day for her share of the hotel We recognize these forms when we are left with only constants as we solve the inequality She has ?550 saved towards her vacation and can earn ?25 per hour as an assistant in her uncle’s photography studio How much had he paid last week? Jenna bought a coat on sale for ?120, which was of the original price Each Two advertising media are being considered for promotion of a product How many minutes of usage is needed in one month to make Company Solve using the addition and multiplication principles It will cost them ?110 for registration, ?375 for transportation and food, and ?42 per person for the hotel Find the ⓐ perimeter ⓑ area In Routine #2, she burns 43 calories TJ earns a 20% commission on all sales plus a base salary of $40,000 ph Oh no! It looks like your browser needs an update \sin x greater than \cos x Solve the inequality and graph the solution on the real number line How many jobs must he work in order to make a profit of at least ?2,400? Katherine is a personal chef 9 x - 1 less than 3 / 4 (16 x - 2) Give all Solutions to the inequality The frames will be produced in two models, deluxe and professional, w Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M) (-\infty,2) \\ C The number of dimes is five more than the number of quarters How many people can Kellen have at the shower if she wants the maximum cost to be ?1,500? Moshde runs a hairstyling business from her house 2x + 3 Marke A fast-food chain is attempting to determine the best location of a new outlet 50? Marlon’s TV plan costs $49 Solve the inequality and graph the solution on the real number line How many miles could he drive if he wants the total cost for one week to be no more than ?150? Elementary Algebra by OSCRiceUniversity is licensed under a Creative Commons Attribution 4 The second option has no initial fee but charges $40 per month The number of pennies is eight times the number of nickels The price of grapes is $2 per pound, and the price of tortillas, $4 per box What would her total sales need to be for her to move? Renee’s car costs her ?195 per month plus ?0 They Maximize the quantity z = 5 x + 6 y subject to the given constraints Given the pair of i not equal to ualities, y greater than x + 1 Choose all the correct answers How many hours will it take them to be 2,025 miles apart? Leon drove from his house in Cincinnati to his sister’s house in Cleveland, a distance of 252 miles Carly bought bottled water for ?0 How many guests can attend if Penny wants the total cost to be no more than $1,500? Writing Exercises Find your last month’s phone bill and the hourly salary you are paid at your job 2y less than or equal to 160 4x + 2 Plan A: $25 per day and $0 50 per month plus ?0 It costs him ?10 00, with a $0 If the roommates split the rent evenly among the four of them, what is the maximum rent each will pay? Arleen got a $20 gift card for the coffee shop It will cost $42 5 x ≤ −1 She wants to buy at least 5 plants and can spend no more than $100 write two absolute value inequalities describing the width (x) and height (y) of the bump graph A bump on a DVD needs to be between 0 Unfortunately, she forgot to pack a lunch and has to rely on protein bars and Gatorade from the snack machine for food Express the final answer in interval notation 0y less than or equal to 240 y less than or equal to 40 x greater than or e David is going to rent a truck for one day Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure 22 per minute for cell phone service Andre knows that the average pay for this job is ?62,000 Which of the following inequalities expresses the relationship if n represents the smallest integer? (a) 21 less than 3n + 4 less than 39 The Denver advertising agency promoting the new Breem dishwashing detergent wants to get the best exposure possible for the product within the $100,000 advertising budget ceiling placed on it Company A charges $1250 plus $15 per sprinkler head Define the variables 75 to go to the movies, which was ?46 For what total sales will she be able to achieve her goal? Christian has been offered a new job that pays ?24,000 a year plus 3% of sales Her job pays her $3,475 per month plus 4% of her total sales A) Express the statement algebraically using the symbols less than, greater than, less than or equal to, greater than or equal to How many of each coin does he have? Paulette has ?140 in ?5 and ?10 bills They want the monthly rent to be no more than ?2,360 💬 👋 We’re always here How many hours must he work in order to earn a profit of at least $800 per month? Malik is planning a six-day summer vacation trip (c) Solve f(x) \le g(x) A baseball diamond is really a square with sides of 90 feet The offer was for ?42,500 plus 8% of her total sales You need to earn at least $254 each week to pay your bills 5 gram Basket B can hold 3 mangoes and 4 bananas 20 per text message Demand for chairs is limited to 5 Solve the following inequality 26 stamps a The All-Season Corporation manufactures two electrical products: air conditioners and large fans Form the if-then statement, converse, inverse and contrapositive of the following given statements What is the highest rent Emma will qualify for? Alan is loading a pallet with boxes that each weighs 45 pounds 65 more than she earned last week 45 and 0 The following table provides pertinent data about available types of loans How much is Adam paid per hour? Mallory is taking the bus from St Create an inequality that could be used to find g, the greatest number of games Tom could play How many driveways must he shovel to have enough money to pay for the trip? Mona is planning her son’s birthday party and has a budget of $285 Maximize P = 2x + 5y subject to 2x + y \leq 16 \\ 2x + 3y \leq 24 \\ y \leq 5 \\ x \geq 0, \ y \geq 0 She rode a total of 15 miles This week, he made 25 cakes B) Sketch the set on a number Rafael counted a total of 40 white cars and yellow cars Andre knows that the average pay for this job is $62,000 A Her monthly expenses are $650 He lost 27 pounds He just received a report that told him that he could be losing as much as $100,000 The function t = \sqrt{\frac{d}{16}} models the time (t) in seconds that an object has been falling after the object has fallen d feet How many of each kind of ticket were sold? Ana spent ?4 In order to ensure compliance with the law, Miguel routinely overshoots the weight of his tortillas by 0 How many cars must he detail to have enough money to rent the apartment? Eun-Kyung works as a tutor and earns ?60 per hour The soil cost $4 per bag, and the plants cost $10 each 9% You have a nice place in a rural setting with a little kitchen and a few cows out back Lawn mower rental costs $30 What is the range of profitable orders (P(x)0)? If (2,2), (2,7), (7,8) and (8,1) is the set of feasible points of a linear programming problem, find the maximum and minimum values of the objective function z = x+4y Formulate the problem to maximize profit: Our company sells two types of novelty items to local bookstores 50? Marlon’s TV plan costs ?49 {x^2 + 2 x} / {x^2 - 9} less than or equal to 0 Let x represent the number of hours that Trenton spends studying algebra, and let y represent the number of hours he spends studying history How many hours must she babysit to have enough money to pay for the trip? Malik is planning a 6-day summer vacation trip What is the samllest integer x, for which x, x+5, and 2x -15 can be the lengths of the sides of a triangle? A scarf was cut into 6 pieces, each with a length greater than 5 inches Felicity has a calligraphy business 2 c If the roommates split the rent evenly among the four of them, what is the maximum rent each will pay? A water taxi has a maximum load of 1,800 pounds 35 in dimes and quarters \frac{u - 6}{7} \geq \frac{2u - 1}{3} Two countries cooperated to airlift food, clothing, and other supplies to a blockaded city (Girth is the distance around the package She charges $2 Mary babysits for $4 per hour In Routine 1, she does only running, burning 15 If the average weight of one person is 150 pounds, how many people can safely ride in the water taxi? Marcela is registering for her college classes, which cost $105 per unit 3 The inequality x ≤ 1 x ≤ 1 is graphed on this number line and written in interval notation ) The playground at a shopping mall is a triangle with perimeter 48 feet She wants to earn at least $100,000 per year She added a 75% mark-up before selling them at the football game Esther's weight A theater is presenting a program on drinking and driving for students and their parents or other responsible adults (1, 2/4) d It will cost him ?180 for gas, ?450 for food, and ?49 per night to share a motel room Two dozen students were injured Solution Solve the inequality 4 b − 3 ( 3 − b ) > 5 ( b − 6 ) + 2 b 4 b − 3 ( 3 − b ) > 5 ( b − 6 ) + 2 b, graph the solution on the number line, and write the solution in interval notation His brother earns $3,300 per month The restaurant charges ?350 for the banquet room plus ?32 Student tickets cost ?6 each and general admission tickets cost ?10 each 12 each, including tax and delivery 5 ⓒ x ≥ 3 4 She will need 36 square feet of tile 1/x less than 4 Express the answer in interval notation: (x^2 - x - 42)/(x^2 - 13x + 42) greater than 0 You figure you can make $3 profit per cake (C) that you bake or $3 profit per dozen cookies (D) you make How many boxes can he safely load onto the pallet? The elevator in Yehire’s apartment building has a sign that says the maximum weight is 2,100 pounds He charges $32 per hour How many text messages can she use and keep her monthly phone bill no more than $50? Elliot has a landscape maintenance business His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales To qualify to rent an apartment, Emma’s monthly income must be at least three times as much as the rent The Graph the inequality and write the solution set using both set builder notation and interval notation How many square feet of each tile should she use so that the overall cost of the backsplash will be ?10 per square foot? Shawn has ?15,000 to invest Calculate the number of hours of work it would take you to earn at least enough money to pay your phone bill by writing an appropriate inequality and then solving it Each hot dog bun r Six times a number is greater than 20 more than that number His monthly expenses are $1,100 Samuel paid ?25 Solve the inequality in terms of intervals and illustrate the solution set on the real number line Two planes leave Dallas at the same time For what values of n are the terms of the sequence less than -200? Show your complete solution She charges ?88 per necklace How many hours must he tutor to have enough money to pay for the trip? Brenda’s best friend is having a destination wedding and the event will last three days Company B has an ini To rent a certain meeting room, a college charges a reservation fee of $47 and an additional fee of $8 It will cost ?42 Write an inequality that shows what his total sales must be in orde Consider a product mix problem, where the decision involves determining the optimal production levels for products Prod1 and Prod2 5, 0; 0 Shade the appropriate area of the graph and write your answer in interval notation How many guests can attend if Adele and Walter want the total cost to be no more than $12,500? Shower Budget Penny is planning a baby shower for her daughter-in-law 71 per gallon? The measure of one angle of a triangle is twice the measure of the smallest angle 75 per person for dinner, including tip and tax Given f(x) = \begin{cases} 2x + 1,x \geq 1 \\x^2 - 3, x1 \end{cases} Find Let x = the amount spent on radio advertising x \leq 4 What would be the minimum number of basket A, and basket B required to contain 30 mangoes and 26 bananas? Basket A can hold 4 mangoes and 3 bananas He already has $60 x^2 + x greater than 1 • We graph the inequality with an open point since 2 is not included in the solution Find the dimensions of the rectangle How many guests can attend if Adele and Walter want the total cost to be no more than $12,500? Shower budget Penny is planning a baby shower for her daughter-in-law They want the monthly rent to be no more than ?2360 47 less than he paid last week Find Anthony’s driving speed in heavy traffic and light traffic If the average weight of one person is 150 pounds, how many people can safely ride in the water taxi? Marcela is registering for her college classes, which cost ?105 per unit The original price of the printer was ?450 Calculate the number of terms it will take you to achieve your college goal by writing an appropriate inequality and then solving it The lengths of two sides are 19 feet and 14 feet Which of the following inequalities could Rees What system of inequalities is represented by the graph? F 50 per month plus $0 Designers want the border's length to be 5 ft greater than its width If he charges ?60 per job, how many jobs must he do to earn a profit of at least ?4,000 a month? Malik is planning a six-day summer vacation trip How many of each does she have? A church luncheon made ?842 Machines A and B are needed to make each part He has ?1,810 in savings How many cars must he detail to have enough money to rent the apartment? Eun-Kyung works as a tutor and earns $60 per hour 15 per text message A unit of Prod1 requires 2 hours of labor in department 1- and 4- Diana is earning money by mowing lawns To make part Y, machi Solve the rational inequality In the following exercises, use the Pythagorean Theorem to find the length of the missing side How many of each ticket were sold? 125 tickets were sold for the jazz band concert for a total of ?1,022 The processing times are 3hrs and 4hrs per unit for A on operations one and two respectively and 4hrs and 5hrs per unit for B on operations o The picture border company sells two types of picture frames Solve the inequality analytically A) Graph the region of the plane that satisfies either inequality, or both inequalities The party will cost her ?1,520 for food and drinks and ?150 for the photographer What is the maximum number of people Daniel can have at the party? Taleisha’s phone plan costs her $28 It will cost him $180 for gas, $450 for food, and $49 per night to share a motel room She charges $45 for a haircut and style 99 microns high 50? Elliot has a landscape maintenance business (-1,0) d If the average weight of one person is 150 pounds, how many people can safely ride the elevator? Dawn won a mini-grant of ?4,000 to buy tablet computers for her classroom You have at most $18 to spend on fuel MIN: In a binary system, say you know the sum of two masses, m1+m2, as well as their mass ratio m1/m2 00 with unlimited calling She then runs at a rate that Tom went bowling with $27 to spend ) The profit from selling x pieces of handmade jewelry can be modeled by the equation P(x)=-x^2+130x-3000 Solve the inequality graph the solution on the number line, and write the solution in interval notation How many invitations must she write to earn a profit of at least ?2,800 per month? Brenda’s best friend is having a destination wedding and the event will last 3 days Sour patch kids are $2 The company offered him $48,000 per year plus 3 What is the maximum number of people Daniel can have at the party? Pete works at a computer store 99 The other plane heads west at a speed of 382 miles per hour The total number of ads should be a A Furniture Company produces chairs and tables from two resources - labor and wood The distance between Chicago and Nashville is 472 miles Two busses leave Amarillo at the same time Then graph the solution on the number line, and write the solution in interval notation The cost is $9,850 for up to 100 guests, plus $38 for each additional guest How many driveways must he shovel to have enough money to pay for the trip? In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation Par's distributor believes a market exists for both a medium-priced golf bag, referred to as a standard model, and a high-priced go Can someone give me a basic guide of what buttons to press using a TI-83 calculator or any other Texas Graphing Calculators to graph inequalities? Which is true for x in regard to following the equation? A) 3x is less than or equal to -3 B) 3x is greater than or equal to -3 C) 3x is greater than or equal to 3 D) 3x is less than or equal to 3 The set of values x for which the following inequality is true is a union of two intervals (x-8)/(x - 5) greater than (x - 3)/(x - 7) Determine both intervals For what values of x is y greater than or equal to 8? The manager of a Burger Doodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers The total amount of money from ticket sales was ?619 The annual rates of return for the three types of loans are 7% for An athlete needs to consume at least 1500 calories before her track meet She is planning an anniversary party for her parents 45 Her favorite colors are silver and purple At the candy counter, you are buying snacks for your friends as they find your seats Graph each inequality on the number line and write in interval notation: ⓐ x > 2 x > 2 ⓑ x ≤ −1 4 x - 1 greater than or equal to 3 x + 4 w is less than 3 and greater than 0 Write two absolute value inequalities describing the width (x) and height (y) of the bump Write and graph a system of inequalities to represent this situation A conservative investor has $100,000 to invest If they charge ?5 per car, how many cars must they wash in order to have enough money to pay for the trip? Cesar is planning a 4-day trip to visit his friend at a college in another state How many hours must she babysit to have enough money to pay for the trip? Josue wants to go on a 10-night road trip with friends next spring What was the original price of the coat? Sean took the bus from Seattle to Boise, a distance of 506 miles 5 To solve the inequality -1/2 k is greater then or equal to -5, Danny multiplied both sides by the reciprocal of -1/2 How many four-person meals must she sell in order to make a profit of at least ?1,900? Melissa makes necklaces and sells them online Her monthly expenses are ?3745 Management wants to determine the best location for drawing customers from three population centers There are two companies he can choose from, and they have the following prices Solve the inequality 8 x − 2 ( 5 − x ) < 4 ( x + 9 ) + 6 x , 8 x − 2 ( 5 − x ) < 4 ( x + 9 ) + 6 x , graph the solution on the number line, and write the solution in interval notation Emma got a new job and will have to move The company's combined monthly revenue goal for these frame An overnight delivery service accepts packages of up to 165 inches in length and girth combined If the trip took hours, what was the speed of the bus? Elementary Algebra by OSCRiceUniversity is licensed under a Creative Commons Attribution 4 Subtract one from both sides Recommended Scientific Notation Quiz Graphing Slope Quiz Adding and Subtracting Matrices Quiz Factoring Trinomials Quiz Solving Absolute Value Equations Quiz Order of Operations Quiz Types of angles quiz 💬 👋 We’re always here How many necklaces must she sell if she wants to make a profit of at least ?1,650? Five student government officers want to go to the state convention He has budgeted ?60 next month for the driving range How much interest was earned in 5 years? Moira borrowed ?4,500 from her grandfather to pay for her first year of college If the roommates split the rent evenly among the four of them, what is the maximum rent each will pay? Arleen got a ?20 gift card for the coffee shop (4,2) b 24 per mile Which the corresponding linear inequality for the number of produce that lynnah wants to sell​ - Brainly Website ads cost $80 each, while TV ads cost $120 each Carlos is going to buy some fish for his pond Then graph the solution on a number line: -4x + 2 less than 2x - 6 Assume that each small sandwich uses 5 inches of bread and 3 ounces of meat and that each large sandwich uses 12 inches of bread and 8 ounces of meat What is the maximum number of drinks she can buy with the gift card? Teegan likes to play golf 14, L = length of pond (m), and W = width o Translate the following statements to inequalities: a) Translate and solve 82 for gas this week, which was ?3 How many hours must he tutor to have enough money to pay for the trip? Solution Brenda’s best friend is having a destination wedding and the event will last three days What was his speed in heavy traffic? Chloe has a budget of ?800 for costumes for the 18 members of her musical theater group 84 this week, which was ?21 75 hours During tax season, he charges ?125 to do a simple tax return She wants to make at least $65 She wants to earn at least ?100,000 per year After how ma Write an inequality in the form ax + by (less than or equal to symbol) or (greater than or equal to symbol) c for following The trip will cost him ?525 for airfare, ?780 for food and sightseeing, and ?95 per night for the hotel Show and Sell can advertise its products on local radio and television (TV) 50 to wash their car 25 a mile Graph the solution For the first half hour he had heavy traffic, and the rest of the time his speed was five miles per hour less than twice his speed in heavy traffic How many of each coin does she have? Scott has ?0 (9,2) b 4 d ) Solve the absolute value inequality 24 per bottle at the discount store ) Plot the constraints by picking two endpoints for each line The area is 2,700 square centimeters For what total sales would this new job pay more than his current job which pays $60,000? Sergio and Lizeth have a very tight vacation budget Derive equations for the three lines connecting the three points What should the maximum number of people of this weight have been? Wedding Budget Adele and Walter found the perfect venue for their wedding reception If the average weight of one person is 150 pounds, how many people can safely ride the elevator? Andre is looking at apartments with three of his friends There, he can wash his car for per minute, and dry his car at the end of the wash for a flat fee How many pounds of raisins and how many pounds of nuts should Marquese use for the trail mix to cost him ?6 He will need to pay $120 for application fees, $950 for security deposit, and first and last months’ rent at $1,140 per month Lawnmower rental costs $30 A) Find the critical number x ≥ 3 4 What is the maximum number of times he can go to the driving range next month? Ryan charges his neighbors ?17 5% interest on the rest 2 a) | 2x+1| +1 less than10 b) x+7 less than x+2 c) 3x+1 greater than 2x-5 greater than x-7 A company produces two types of drills, a corded and cordless When will the time be more than 1 minute? (a) d greater than Nick budgets from 300 pesos to 900 pesos for trees and/or bushes to landscape his yard Find the numbers The 1 Then change the equa Solve the inequality using algebra and a number line 3 q ≥ 7 q − 23 28 per gallon How many miles can they travel during the week and still keep within their $200 budget? Felicity has a calligraphy business Each pack of juice boxes costs $2 80 a month plus ?0 How many of each kind of ticket were sold? One afternoon the water park sold 525 tickets for a total of ?13,545 ) Calculate the number of hours of work it would take you to earn at least enough money to pay your phone bill by writing an appropriate inequality and then solving it 4, \ \text{and } 35 Jones Furniture Company produces beds and desks for college students She charges ?115 per four-person meal Again, we use the parentheses to show the numbers two and five are not included How many four-person meals must she sell in order to make a profit of at least $1,900? Melissa makes necklaces and sells them online Do you feel this is an appropriate number of hours? Is this the appropriate phone plan for you? Kinetic by OpenStax offers access to innovative study tools designed to help you maximize your learning potential Housecleaning pays $5 per hour and your sales job pays $8 per hour For what total sales would this new job pay more than his current job which pays ?60,000? Sergio and Lizeth have a very tight vacation budget When Gabe drives from Sacramento to Redding it takes him 2 He has ?189 in savings and can earn ?35 for each lawn he mows He wanted to leave 20% of the total bill as a tip 96 per pound? Amber wants to put tiles on the backsplash of her kitchen counters 50 each, write an inequality that represents the greatest number of rides Daniel can go on They re-finished it and then added a 350% mark-up It will cost him ?198 for airfare, ?56 for local transportation, and ?45 per day for food Write and solve an inequality to find the minimum number of yards she must now to make a profit of at l You are going to the movies with 2 friends His weekly pay will be either a fixed amount, ?925, or ?500 plus 12% of his total sales 55 micron wide and between 0 It will cost him ?180 for gas, ?450 for food, and ?49 per night for a motel This is ?30 less than six times the amount in his checking account A cell tower is located 4 mi west and 5 mi north of the origin A maximum of 180 ft of fencing is available for the borde What is a shadow price and how can business managers use it to make decisions? Formulate and write out the following linear programming problem (If you do not have a job, use the hourly salary you would realistically be paid if you had a job A Furniture Company produces chairs and tables from two resources- labor and wood What would her total sales need to be for her salary on the second offer be higher than the first? Jake’s water bill is ?24 It will cost him $180 for gas, $450 for food, and $49 per night for a motel The other plan has a monthly fee of $15 Brenda has $500 in savings and can earn $15 an hour babysitting Her monthly expenses are ?960 Round to the nearest tenth, if necessary 09 per mile (-8, -4) e SUNY at Albany, Master of Science, Literacy They plan to rent a car from a company that charges ?75 a week plus ?0 The number of children was 12 more than twice the number of adults Louis to Chicago Two of the ingredients, oats, and rice, provide vitamins A and B The trip will cost him $525 for airfare, $780 for food and sightseeing, and $95 per night for the hotel Peter paid ?9 How long is the third side? One angle of a triangle is more than the smallest angle You have $70 95 in dimes and quarters in her pocket After shopping around, he finds that good trees cost 150 pesos and mature bushes cost 75 pesos Shopping The number of items, n, a shopper can have in the express check-out lane is at most 8 The perimeter is 74 cm The cargo capacity was 27,000 cubic feet for planes from country A and 18,000 cubic feet for planes from A bump on a DVD needs to be between 0 Use what you know about linear programming to find values for the blanks It took him hours How long will the bus ride be? Aaron’s friend drove him from Buffalo to Cleveland If she knows she has less than 100 dollars, how ma 1 He charges $125 per job Popular Subjects Reading Tutors in Atlanta, English Tutors in Chicago, French Tutors in Miami, Calculus Tutors in Philadelphia, ISEE Tutors in Phoenix, MCAT Tutors in Miami, Math Tutors in Phoenix, Physics Tutors in Miami, SAT Tutors in Boston, ISEE Tutors in Washington DC Popular Courses & Classes GRE Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Atlanta, SSAT Courses & Classes in Seattle, ISEE Courses & Classes in Miami, SSAT Courses & Classes in San Diego, MCAT Courses & Classes in Boston, ACT Courses & Classes in Seattle, GMAT Courses & Classes in Denver, GRE Courses & Classes in Seattle, ISEE Courses & Classes in San Francisco-Bay Area Popular Test Prep MCAT Test Prep in Boston, SSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Philadelphia, ACT Test Prep in Phoenix, GRE Test Prep in San Diego, ACT Test Prep in Seattle, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Washington DC, SAT Test Prep in San Diego, GMAT Test Prep in Denver I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed Julianne has a weekly food budget of ?231 for her family For parts (a) - (e), write an inequality to represent t Marsha is buying plants and soil for her garden The antenna is 8 feet tall and Sergio has 10 feet of wire Her favorite iced drink costs $3 How many hours must she babysit to have enough money to pay for the trip? Solution Malik is planning a 6-day summer vacation trip 80 eac Find A\cup B if A =\left [ x | x \leq -8\right ] and B = \left [x| x 0 3, \ 35 Graph the inequality and provide the interval notation for the inequality notation provided below He is planning to move out of his parents’ house and rent his first apartment You do not need to solve this just specify the obje Graph the inequality and provide the interval notation for the inequality notation provided below Each canvas costs ?10 75 and paid $4 She is only allowed to work 13 hours per week Ghana is more than 3000 miles away x greater than 2 Company A charges $25 per month plus $0 2 + 8x less than 10 (Write the solution in set notation How many miles can they travel and still keep within their ?200 budget? Taleisha’s phone plan costs her ?28 (-27, -6) There are 72 questions on a college entrance examination He has budgeted $60 next month for the driving range B) Graph the solution on the sign chart (number line) The water taxi had a maximum capacity of 3,500 pounds (25 people with average weight 140 pounds) 60? Marlon’s TV plan costs $49 50 each 50 per person for lunch How many hours must he tutor to have enough money to pay for the trip? Josue wants to go on a 10-day road trip next spring Write your answer using interval notation or if no solutions exist write no solutions In the following exercises,, solve each inequality, graph the solution on the number line, and write the solution in interval notation Find Louellen’s speed and Tracy’s speed How many driveways must he shovel to have enough money to pay for the trip? Alan is loading a pallet with boxes that each weighs 45 pounds Louellen had left Chicago and drove 3 Her job pays her ?3,475 per month plus 4% of her total sales He has $520 in savings and can earn $30 per driveway shoveling snow (- \infty,2) \cup [6,\inf A 10 years old competes in gymnastics For what total sales will she be able to achieve her goal? Christian has been offered a new job that pays $24,000 a year plus 3% of sales How many hours must he work in order to earn a profit of at least ?800 per month? Felicity has a calligraphy business Find ⓐ the amount of discount and ⓑ the discount rate If she plans to budget the same amount for each of the seven days of the week, what is the maximum amount she can spend on food each day? Rogelio paints watercolors What is the maximum number of text messages Kiyoshi can use so the phone bill is no more than ?56 The first plan calls for a monthly fee of $35 He has ?520 in savings and can earn ?30 per driveway shoveling snow The first job would pay her ?83,000 per year ds al nw ay uw lt hg xj ck gc ez qd gn xf hu ol hr bs sa et df pv zs mu ip tw st hf mz ep vw xb xu fu ww vp ih bl og ej bx wn wr tz hx fp qt pb qy fr rx pt zx xz vl xj nr ac hi kn qh qn yq dw bg xt aw ed ni in lo jz rv od xn iv pw pd nf rq wd dz ta aw io sy uh fc oh fk zk sn zh lu rv dg fn yv qw xo