Dalia Isabel Gonzalez rocha math1010spring2016-90 3 WeBWorK assignment number WBWK-06 is due : 02/22/2016 at 11:59pm MST. THOUGHT: \"Do not worry about your problems in mathematics. I assure you, mine are greater still.\" Einstein This set is on transformations of functions and systems of equations. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble guring out your error, you should consult the book, or ask a fellow student, one of the TA's or your professor for help. Don't spend a lot of time guessing - it's not very efcient or effective. Give 4 or 5 signicant digits for (oating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 ^ 3 instead of 8, sin(3 pi/2)instead of -1, e ^ (ln(2)) instead of 2, (2 + tan(3)) (4 sin(5)) ^ 6 7/8 instead of 27620.3413, etc. Here's the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. 1. (2 pts) As a warm-up solve the following linear system: 2x x +3y y 5. (2 pts) Solve the system = 1 = 3 x + 4y 3x + 12y The solution of this system is x= and y = . Hint: Subtract twice the second equation from the rst, or add three times the second equation to the rst. If the system has innitely many solutions, express your answer in the form x = x and y as a function of x Your answer is x= y= 2. (2 pts) The solution of the linear system x 3x is x= and y = +y y = 1, = 3. = 7 = 1 6. (2 pts) Solve the system using elimination . 3. (2 pts) Use the elimination method to nd all solutions of the system 8x 9y= 44 9x y= 86 x= 5x + 2y = 9, 7x + 3y = 12. y= Your answer is x= y= 7. (2 pts) Use the elimination method to nd all solutions of the system 4. (2 pts) Use the substitution method to solve the system 5x + 2y = 16, 7x + 3y = 23. x + y = 0, 4x 3y = 2. Your answer is: If there is more than one point, type the points separated by a comma (i.e.: (1,2),(3,4)). If the system has no solution, type none in the answer blank. Your answer is: If there is more than one point, type the points separated by a comma (i.e.: (1,2),(3,4)). If the system has no solution, type none in the answer blank. 8. (1 pt) Match each question with its answer. 1 If there are innitely many solutions, enter x in the answer blank for x and enter a formula for y in terms of x in the answer blank for y. If there are no solutions, leave the answer blanks for x and y empty. ? 1. y = x+4 x+y 2 = 0 ? 2. x= y = 1x+1 2 y = 4x+2 3 y= ? 3. y = 2x 1 4x 2y = 2 11. (1 pt) Solve the system using the substitution or elimination method A. Unique solutions B. No solutions C. Innite solution 9. (1 pt) A linear system may have a unique solution, no solution, or innitely many solutions. Indicate the type of the system for the following examples by U , N , or I , respectively. 1. 2x + 3y 2x + 3y 2. = 5 = 10 3. 2x + 3y 2x + 4y How many solutions are there to this system? = 5 = 6 2x + 3y 4x + 6y 2x 6y = 17, 3x + 9y = 24. = 5 = 6 Hint: The issues are discussed here. If you can't tell the nature system by inspection try to solve the system and see what happens. A. None B. Exactly 1 C. Exactly 2 D. Exactly 3 E. Innitely many F. None of the above If there is one solution, give its coordinates in the answer spaces below. If there are innitely many solutions, enter x in the answer blank for x and enter a formula for y in terms of x in the answer blank for y. If there are no solutions, leave the answer blanks for x and y empty. 10. (2 pts) Solve the system . 2x + y = 2, 4x + 3y = 14. How many solutions are there to this system? A. None B. Exactly 1 C. Exactly 2 D. Exactly 3 E. Innitely many F. None of the above x= y= 12. (1 pt) Case 1 If there is one solution, give its coordinates in the answer spaces below. 2 Case 3 Case 2 Match each question with its answer. ? 1. Unique solution ? 2. No solutions ? 3. Innite solutions A. Case 1 B. Case 2 C. Case 3 13. (2 pts) Solve and write as an ordered pair. 2x (x, y) = ( , 3y = 4 4x + 2y = 2 ) 14. (1 pt) The coffee variety Arabica yields about 700 kg of coffee beans per hectare, while Robusta yields about 1200 kg per hectare. Suppose that a plantation has a hectares of Arabica and r hectares of Robusta. Write an equation relating a and r if the plantation yields 40000 kg of coffee. Do not enter any commas or units in your answer. 3 19. (2 pts) A cash register contains only ve dollar and ten dollar bills. It contains twice as many ve's as ten's and the total amount of money in the cash register is 560 dollars. How many ten's are in the cash register? 15. (2 pts) Bork (B) got 18 on quiz 0 and improves by 2 points each week. Brenda (R) got 15 on quiz 0 and improves by 3 each week. Write an equation for each. Let x= quiz number. B= 20. (2 pts) After robbing a bank in Dodge City, a robber gallops off at 12 mi/h. 20 minutes later, the marshal leaves to pursue the robber at 15 mi/h. How long (in hours) does it take from when the marshal starts to when he catches up to the robber? Enter your answer as a decimal rounded to three decimal places. R= On which quiz will they have equal scores? 16. (2 pts) You need to do your laundry. The Laundry Fairy will give you all of her quarters, if you solve her riddle: 21. (2 pts) Two cyclists, 48 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist? \"I have $ 5.00 in nickels and quarters. The total number of coins is 56. How many quarters do I have?\" Write an equation about the number of coins using n and q as variables. (n= nickels, q= quarters) 22. (2 pts) This exercise concerns with modeling with linear equations. = 56 Write an equation about the amount of money. It should also contain n and q. One positive number is one-fth of another number. The difference between the two numbers is 304, nd the numbers. = 5.00 The two numbers in increasing order are Now solve. How many nickels? How many quarters? and 23. (2 pts) A manufacturer has 2200 units in stock. The product is now selling at $9 per unit. Next month the unit price will increase by $0.50. The manufacturer wants the total revenue received from the sale of the 2200 units to be no less than $20350. What is the number of units that can be sold this month? n= q= Answer: At most units 24. (2 pts) REVIEW: One day, a deli sold a total of 40 hamburgers and hot dogs. The revenue from these sales was $157.22. The hamburgers were $4.27 each and the hot dogs cost $3.30 each. a) Write a mathematical expression for the number of burgers, x, and the number of hot dogs, y, sold that day. Answer: b) Write a mathematical expression for the amount of revenue from this day's sales. Use x for the number of burgers and y for the number of hot dogs. Answer: 17. (2 pts) Seven years ago, I was eleven times as old as my daughter. Now I am four times as old as she is. My age is . 18. (1 pt) Find two positive integers whose sum is 48, and whose sum also equals twice their difference. The smaller integer is and the larger is . Hint: Set up and solve a linear system. 4 c) How many hot dogs did the store sell that day? (Include the word hot dogs in your answer). Answer: 25. (2 pts) A truck can be rented from Basic Rental for $65.00 a day plus $0.20 per mile. Continental charges $47.00 per day plus $0.40 per mile to rent the same truck. a) Write an expression to calculate the cost of renting and driving a truck from Basic Rental. Let x be the number of miles driven. Cost = b) Write an expression to calculate the cost of renting and driving a truck from Continental. Let x be the number of miles driven. Cost = c) How many miles must be driven in a day to make the rental cost for Basic Rental a better deal than Continental's? Note: Enter your answer as, More than mmm miles in a day - do not put a period at the end of the phrase. Answer: 26. (2 pts) The tuition cost for part-time students taking C credits at Stonewall College is given by 500 + 300C dollars. (b) If the tuition cost is $3200, how many credits are taken? 27. (1 pt) You buy a saguaro cactus 9 feet high and it grows at a rate of 0.4 inches each year. Express its height h, in inches, as a function of time t, in years, since the purchase. Enter your answer as an equation with h on the left side, and an expression involving t on the right. 28. (1 pt) The temperature of the soil is 25 C at the surface and decreases by 0.07 C for each centimeter below the surface. Express temperature T , in degrees Celsius, as a function of depth d, in centimeters, below the surface. Enter your answer as an equation with T on the left side, and an expression involving d on the right. 29. (2 pts) Suppose f (t) = (a) Evaluate f (10). f (10) = (a) Find the tuition cost for 11 credits. Do not use dollar signs or commas in your answer. $ (b) Solve f (t) = 3. t= Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America 5 7t + 5 . 7