Test 1 Review #5. Intermediate Algebra / MAT 135 Fall 2016 Master (Prof. Fleischner)

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1 Test 1 Review #5 Intermediate Algebra / MAT 135 Fall 016 Master (Prof. Fleischner) Student Name/ID: 1. Solve for n. d = m + 9n. Solve for b. r = 5 b + a 3. Solve for C. A = 7 8 B + C ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 1 / 7

2 . Two trains leave stations 0 miles apart at the same time and travel toward each other. One train travels at 70 miles per hour while the other travels at 80 miles per hour. How long will it take for the two trains to meet? Do not do an rounding. hours 5. On Sunda, a local hamburger shop sold a combined total of 0 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How man hamburgers were sold on Sunda? 6. Lisa has a job transporting soft drinks b truck. Her truck is filled with cans that weigh 1 ounces each and bottles that weigh 70 ounces each. There is a combined total of 860 cans and bottles in her truck. Let be the number of 1-ounce cans in her truck. Write an epression for the combined total weight (in ounces) of the cans and bottles in her truck. 7. Three consecutive integers have a sum of 81. Find the integers. 8. Rueben's Coffee Shop makes a blend that is a miture of two tpes of coffee. Tpe A coffee costs Rueben $.30 per pound, and tpe B coffee costs $5.55 per pound. This month's blend used three times as man pounds of tpe B coffee as tpe A, for a total cost of $ How man pounds of tpe A coffee were used? 9. The length of a rectangle is si times its width. If the area of the rectangle is 16 ft, find its perimeter. ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. / 7

3 10. Last ear, Leila invested her mone in two purchases. She purchased a certificate of deposit for $000 that paid % interest per ear and purchased $3000 in corporate bonds paing 6% interest per ear. Answer the questions below. Do not do an rounding. (a) What was the total interest earned at the end of 1 ear? $ (b) What was the percent interest for her total investment? % 11. Two factor plants are making TV panels. Yesterda, Plant A produced 000 fewer panels than Plant B did. Three percent of the panels from Plant A and 5% of the panels from Plant B were defective. How man panels did Plant A produce, if the two plants together produced 130 defective panels? 1. The sets E and F are defined as follows. E = F = > 8 Write E F and E F using interval notation. If the set is empt, write. ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 3 / 7

4 13. Graph the compound inequalit on the number line. 5 or > Solve the compound inequalit and 3 < 8 Graph the solution on the number line Solve the compound inequalit. v 3 < 3 and v + 1 Write the solution in interval notation. If there is no solution, enter. 16. Solve for. + 6 = 1 ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. / 7

5 17. Solve for w. 3w + 6 = 3w Solve for u. 5 u + 7 = Solve for w. w + 1 = Graph the solution to the inequalit on the number line. w < Solve. w 13 5 ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 5 / 7

6 . Graph the solution to the inequalit on the number line Solve Write equations for the horizontal and vertical lines passing through the point 8, 6. horizontal line: vertical line: 5. Rewrite the equation in A + B = C form. Use integers for A, B, and C. + 5 = A line passes through the point, 3 and has a slope of 5. Write an equation in slope-intercept form for this line. ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 6 / 7

7 7. Find an equation for the line below Write an equation of the line below A line passes through the point, 3 and has a slope of 5. Write an equation in point-slope form for this line. ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 7 / 7

8 30. Consider the line =. What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? 31. Consider the line = 7 1. (a) Find the equation of the line that is perpendicular to this line and passes through the point 3,. (b) Find the equation of the line that is parallel to this line and passes through the point 3,. 3. Suppose that the relation T is defined as follows. T =, 0, 9,, 8, Give the domain and range of T. Write our answers using set notation. ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 8 / 7

9 33. For each relation, decide whether or not it is a function. Relation 1 Relation (7, 7), (5, 5), (0, -7), (-7, -7) (0, -3), (9, -3), (3, -9), (-9, -3) Function Not a Function Function Not a Function Relation 3 Relation D om ain Range D om ain Range 1 n star f paper t 0 s Function Function Not a Function Not a Function 3. The functions f and g are defined as follows. f = 3 5 g = 3 3 Find f 3 and g. Simplif our answers as much as possible. T ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 9 / 7

10 35. The graph of the relation T is shown below Give the domain and range of T. Write our answers using set notation. 36. Find the domain of the function. u = + Write our answer using interval notation. 37. For each graph below, state whether it represents a function Function?: Yes No ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 10 / 7

11 Function?: Yes No Function?: Yes No Function?: Yes No - ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 11 / 7

12 Function?: Yes No Function?: Yes No Find the domain of the function. v = 8 Write our answer using interval notation. ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 1 / 7

13 39. Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope of 5.9. See the figure below. With 6 gallons of fuel in its tank, the airplane has a weight of 71. pounds. What is the weight of the plane with 77 gallons of fuel in its tank? Airplane weight in pounds Amount of fuel in gallons 0. Use substitution to solve the sstem. + 5 = 10 = = = Solve the following sstem of equations. 3 8 = = 18. The sum of two numbers is 6 and the difference is 1. What are the numbers? ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 13 / 7

14 3. A chef is going to use a miture of two brands of Italian dressing. The first brand contains 9% vinegar, and the second brand contains 1% vinegar. The chef wants to make 330 milliliters of a dressing that is 13% vinegar. How much of each brand should she use? First brand: milliliters Second brand: milliliters. Solve the following sstem of equations. 7 6 = 9 = A famil has two cars. The first car has a fuel efficienc of 35 miles per gallon of gas and the second has a fuel efficienc of 5 miles per gallon of gas. During one particular week, the two cars went a combined total of 1700 miles, for a total gas consumption of 60 gallons. How man gallons were consumed b each of the two cars that week? First car: Second car: 6. The Nguen famil and the Green famil each used their sprinklers last summer. The water output rate for the Nguen famil's sprinkler was 0 L per hour. The water output rate for the Green famil's sprinkler was 5 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 185 L. How long was each sprinkler used? Nguen famil's sprinkler: Green famil's sprinkler: ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 1 / 7

15 7. Two sstems of equations are given below. For each sstem, choose the best description of its solution. If applicable, give the solution. The sstem has no solution. + = 8 = 8 The sstem has a unique solution:, =, The sstem has infinitel man solutions. The must satisf the following equation: = The sstem has no solution. = + = The sstem has a unique solution:, =, The sstem has infinitel man solutions. The must satisf the following equation: = ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 15 / 7

16 8. Two sstems of equations are given below. For each sstem, choose the best description of its solution. If applicable, give the solution. + 5 = 5 5 = 5 The sstem has no solution. The sstem has a unique solution:, =, The sstem has infinitel man solutions. The must satisf the following equation: = The sstem has no solution. + 3 = 3 3 = 3 The sstem has a unique solution:, =, The sstem has infinitel man solutions. The must satisf the following equation: = 9. One month Deandre rented 5 movies and 3 video games for a total of $7. The net month he rented movies and 1 video games for a total of $81. Find the rental cost for each movie and each video game. 50. For each sstem of linear equations shown below, classif the sstem as "consistent dependent," "consistent independent," or "inconsistent." Then, answer the question about its solutions. L1: = 3 L: + 3 = 6 ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 16 / 7

17 6 L L1 This sstem of equations is: - consistent dependent - consistent independent - inconsistent This means the sstem has: - a unique solution: Solution:, - no solution - infinitel man solutions 1 L1: = L: = L L This sstem of equations is: - consistent dependent - consistent independent - inconsistent This means the sstem has: - a unique solution: Solution:, - no solution - infinitel man solutions ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 17 / 7

18 L1: = + 3 L: = L L This sstem of equations is: - consistent dependent - consistent independent - inconsistent This means the sstem has: - a unique solution: Solution:, - no solution - infinitel man solutions ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 18 / 7

19 Test 1 Review #5 Answers for class Intermediate Algebra / MAT 135 Fall 016 Master 1. n = d m 9. b = r 5 a 3. C = 8 7 A B. 1.6 hours hamburgers 6. total weight (in ounces) = , , 7, pounds 9. 8ft 10. (a) What was the total interest earned at the end of 1 ear? $0 (b) What was the percent interest for her total investment?.% 11. Number of panels produced b Plant A: 1, E F = E F =, 8, ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 19 / 7

20 , = 10, w = u = 8, w = 5, w 8 or w ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 0 / 7

21 3. 8. horizontal line: = 6 vertical line: = = = = = = Slope of a parallel line: 8 3 Slope of a perpendicular line: Equation of perpendicular line: Equation of parallel line: = = domain =, 9, 8 range = 0, ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 1 / 7

22 33. Relation 1 Relation (7, 7), (5, 5), (0, -7), (-7, -7) (0, -3), (9, -3), (3, -9), (-9, -3) Function Not a Function Function Not a Function Relation 3 Relation D om ain Range D om ain Range 1 n star f paper t 0 s Function Function Not a Function Not a Function 3. f 3 = 9 g = domain =,, 0 range = 1, 3,, 36., ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. / 7

23 Function? Yes No Yes No Yes No Function? Yes No Yes No Yes No 38., pounds 0. = 5 = 1. = 7 = 3. Larger number: 9 Smaller number: First brand: 66 milliliters Second brand: 6 milliliters ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 3 / 7

24 . = = 5 5. First car: 0 gallons Second car: 0 gallons 6. Nguen famil's sprinkler: 30 hours Green famil's sprinkler: 5 hours 7. + = 8 = 8 The sstem has no solution. The sstem has a unique solution:, =, The sstem has infinitel man solutions. The must satisf the following equation: = 8 = + = The sstem has no solution. The sstem has a unique solution:, =, The sstem has infinitel man solutions. The must satisf the following equation: = ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. / 7

25 = 5 5 = 5 The sstem has no solution. The sstem has a unique solution:, =, The sstem has infinitel man solutions. The must satisf the following equation: = + 3 = 3 3 = 3 The sstem has no solution. The sstem has a unique solution:, =, The sstem has infinitel man solutions. The must satisf the following equation: = Rental cost for each movie: $1.50 Rental cost for each video game: $ L1: = 3 L: + 3 = 6 6 L L1 This sstem of equations is: - consistent dependent This means the sstem has: - infinitel man solutions ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 5 / 7

26 1 L1: = L: = L L This sstem of equations is: - inconsistent This means the sstem has: - no solution L1: = + 3 L: = L L This sstem of equations is: - consistent independent This means the sstem has: ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 6 / 7

27 - a unique solution: Solution:, 1 ALEKS Test 1 Review #5-05/13/016 08:53 AM EDT - Copright 016 UC Regents and ALEKS Corporation. P. 7 / 7

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