||||O Equations and InequalitiesSolving a decimal word problem using a linear inequality with the variabl...Goran is choosing between two exercise routines.In Routine #1, he does only running, burning 18.5 calories per minute.In Routine #2, he burns 22 calories walking. He then runs at a rate that burns 16.3 calories per minute.For what amounts of time spent running will Routine #1 burn more calories than Routine #2?Use t for the number of minutes spent running, and solve your inequality for t.0<0020X>O OSOS

Answered: Image /qna-images/answer/9e63c0a4-80a7-436c-94af-ce85f531876d.jpg

Answered: Goran is choosing between two exercise…

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter3: Graphs And Functions

Section3.4: Graph Linear Inequalities In Two Variables

Problem 279E: The doctor tells Laura she needs to exercise enough to burn 500 calories each day. She prefers to...

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Shanthie needs to earn at least $500 a week during her summer break to pay for college. She works two jobs. One as a swimming instructor that pays $10an hour and the other as an intern in a law office for$25 hour. How many hours does Shanthie need to work at each job to earn at least $500 per week? (a) Let x be the number of hours she works teaching swimming and let y be the number of hours she worksas an intern. Write an inequality that would model thissituation. (b) Graph the inequality. (c) Find three ordered pairs (x,y) that would be solutions to the inequality. Then, explain what that means for Shanthie.
Harrison works two part time jobs. One at a gas station that pays $11 an hour and the other is IT troubleshooting for $16.50 an hour. Between the two jobs, Harrison wants to earn at least $330 a week. How many hours does Harrison need to work at each job to earn at least $330? (a) Let x be the number of hours he works at the gas station and let y be the number of (hours he works troubleshooting. Write an inequality that would model this situation. (b) Graph the inequality. (c) Find three ordered pairs (x, y) that would be solutions to the inequality. Then, explain what that means for Harrison.
Veronica works two part time jobs in order to earn enough money to meet her obligations of at least $280 a week. Her job at the day spa pays $10 an hour and her administrative assistant job on campus pays $17.50 an hour. How many hours does Veronica need to work at each job to earn at least $280? (a) Let x be the number of hours she works at the day spa and let y be the number of hours she works as administrative assistant. Write an inequality that would model this situation. (b) Graph the inequality. (c) Find three ordered pairs (x, y) that would be solutions to the inequality. Then, explain what that means for Veronica
Hugh works two part time jobs. One at a grocery store that pays $10 an hour and the other is babysitting for $13 hour. Between the two jobs, Hugh wants to earn at least $260 a week. How many hours does Hugh need to work at each job to earn at least $260? (a) Let x be the number of hours he works at the grocery store and let y be the number of hours he works babysitting. Write an inequality that would model this situation. (b) Graph the inequality. (c) Find three ordered pairs (x, y) that would be solutions to the inequality. Then, explain what that means for Hugh.
The doctor tells Laura she needs to exercise enough to burn 500 calories each day. She prefers to either run or bike and burns 15 calories per minute while running and 10 calories a minute while biking. (a) If x is the number of minutes that Laura runs and y is the number minutes she bikes, find the inequality that models the situation. (b) Graph the inequality. (c) List three solutions to the inequality. What optionsdo the solutions provide Laura?
Atsushi he needs to exercise enough to burn 600 calories each day. He prefers to either run or bike and burns 20 calories per minute while running and 15 calories a minute while biking. (a) If x is the number of minutes that Atsushi runs and yis the number minutes he bikes, find the inequality that models the situation. (b) Graph the inequality. (c) List three solutions to the inequality. What options do the solutions provide Atsushi?
Armando’s workouts consist of kickboxing and swimming. While kickboxing, he burns 10 calories per minute and he burns 7 calories a minute while swimming. He wants to burn 600 calories each day. (a) If x is the number of minutes that Armando will kickbox and y is the number minutes he will swim, find the inequality that will help Armando create a workout for today. (b) Graph the inequality. (c) List three solutions to the inequality. What options do the solutions provide Armando?
Height and Weight For a healthy person who is 4 feet 10 inches tall, the recommended minimum weight is about 91 pounds and increases by about 3.6 pounds for each additional inch of height. The recommended maximum weight is about 115 pounds and increases by about 4.5 pounds for each additional inch of height. (a) Let x be the number of inches by which a person’s height exceeds 4 feet 10 inches and let y be the person’s weight (in pounds). Write a system of inequalities that describes the possible values of x and y for a healthy person. (b) Use a graphing utility to graph the system of inequalities from part (a). (c) What is the recommended weight range for a healthy person who is 6 feet tall?
Biology Each day, an average adult moose can process about 32 kilograms of terrestrial vegetation (twigs and leaves) and aquatic vegetation. From this food, it needs to obtain about 1.9 grams of sodium and 11,000 calories of energy. Aquatic vegetation has about 0.15 gram of sodium per kilogram and about 193 calories of energy per kilogram, whereas terrestrial vegetation has minimal sodium and about four times as much energy as aquatic vegetation. Write and graph a system of inequalities that describes the amounts t and a of terrestrial and aquatic vegetation, respectively, for the daily diet of an average adult moose.
Graph the linear inequality: 2xy3 .
Blood Pressure A person’s blood pressure is measured with two numbers. The systolic blood pressure measures the pressure of the blood on the arteries as the heart beats. The diastolic blood pressure measures the pressure while the heart is resting. (a) Let x be your systolic blood pressure. Researchand then write the compound inequality that shows you what a normal systolic blood pressure should be for someone your age. (b) Let y be your diastolic blood pressure. Researchand then write the compound inequality that shows you what a normal diastolic blood pressure should be for someone your age.
The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8,000. (a) Find the cost function C when x energy drinks aremanufactured. (b) Find the revenue function R when x drinks are sold. (c) Show the break-even point by graphing both the Revenue and Cost functions on the same grid. (d) Find the break-even point. Interpret what the breakeven point means.

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