Intermediate Algebra / MAT 135 Spring 2017 Master ( Master Templates)

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1 Test 1 Review #1 Intermediate Algebra / MAT 135 Spring 017 Master ( Master Templates) Student Name/ID: 1. Solve for. = Solve for. = + a b 3. Solve for. a b = L 30. Two trains leave stations miles apart at the same time and travel toward each other. One train travels at 80 miles per hour while the other travels at 70 miles per hour. How long will it take for the two trains to meet? Do not do an rounding. hours 5. A local hamburger shop sold a combined total of hamburgers and cheeseburgers on Tuesda. There were 8 fewer cheeseburgers sold than hamburgers. How man hamburgers were sold on Tuesda? 58 Test 1 Review #1 Page 1 / Copright 01 UC Regents and ALEKS Corporation

2 . TechWiz Electronics makes a profit of for each MP3 plaer sold and for each DVD plaer sold. Last week, TechWiz sold a combined total of Let $35 $18 18 MP3 and DVD plaers. be the number of MP3 plaers TechWiz sold last week. Write an epression for the combined total profit (in dollars) TechWiz made from MP3 and DVD plaers last week. 7. Three consecutive even integers have a sum of. Find the integers. 8. At the movie theatre, child admission is and adult admission is. On Frida, four times as man adult tickets as child tickets were sold, for a total sales of $.10 $9.70 $ How man child tickets were sold that da? 9. The length of a rectangle is three times its width. If the area of the rectangle is 19 in, find its perimeter. $ % $,000 13% 10. An investment firm invested in two companies last ear. The invested in Compan A and made a profit of. The invested in Compan B and made a profit of. Answer the questions below. Do not do an rounding. (a) What was the investment firm's total profit? $ (b) What was the percent profit for their total investment? % 11. Two factor plants are making TV panels. Yesterda, Plant A produced twice as man panels as Plant B. Three percent of the panels from Plant A and % Plant B produce, if the two plants together produced of the panels from Plant B were defective. How man panels did 900 defective panels? Test 1 Review #1 Page / Copright 01 UC Regents and ALEKS Corporation

3 F H 1. The sets and are defined as follows. F = H = < 9 F H F H Write and using interval notation. If the set is empt, write. 13. Graph the compound inequalit on the number line. 0 and Solve the compound inequalit. 3 + or Graph the solution on the number line Solve the compound inequalit. 1 and Write the solution in interval notation. If there is no solution, enter. 3 3 Test 1 Review #1 Page 3 / Copright 01 UC Regents and ALEKS Corporation

4 1. Solve for = Solve for. 5 = Solve for = 9 u 19. Solve for. u + 1 = 5 0. Graph the solution to the inequalit on the number line Test 1 Review #1 Page / Copright 01 UC Regents and ALEKS Corporation

5 1. Solve. + 5 < 1. Graph the solution to the inequalit on the number line. w Solve. u + 5 < 8. Write equations for the horizontal and vertical lines passing through the point. horizontal line: vertical line: 8, 9 5. Rewrite the equation in form. A B Use integers for,, and. A + B = C C = 1 Test 1 Review #1 Page 5 / Copright 01 UC Regents and ALEKS Corporation

6 , 7. A line passes through the point and has a slope of. Write an equation in slope-intercept form for this line. 7. Find an equation for the line below Write an equation of the line below Test 1 Review #1 Page / Copright 01 UC Regents and ALEKS Corporation

7 3, A line passes through the point and has a slope of. Write an equation in point-slope form for this line. = 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? = Consider the line. (a) Find the equation of the line that is perpendicular to this line and passes through the point. 8, (b) Find the equation of the line that is parallel to this line and passes through the point. 8, 3. Suppose that the relation is defined as follows. G G = 3, p, 3, q, 0,,, m G Give the domain and range of. Write our answers using set notation. Test 1 Review #1 Page 7 / Copright 01 UC Regents and ALEKS Corporation

8 33. For each relation, decide whether or not it is a function. Relation 1 Relation (, ), (7, ), (-, k), (, k) (, -9), (, ), (, ), (, -) Function Not a Function Function Not a Function Relation 3 Relation D o m a i n R a n g e D o m a i n R a n g e star 7 7 moon n rock k 5 5 pen Function Function Not a Function Not a Function 3. The functions and are defined as follows. Find and. f Simplif our answers as much as possible. g f = 3 + g = 3 f 7 g 3 Test 1 Review #1 Page 8 / H Copright 01 UC Regents and ALEKS Corporation

9 35. The graph of the relation is shown below. H H Give the domain and range of. Write our answers using set notation. 3. Find the domain of the function. u = 1 Write our answer using interval notation. 37. For each graph below, state whether it represents a function Function?: Yes No Test 1 Review #1 Page 9 / Copright 01 UC Regents and ALEKS Corporation

10 Function?: Yes No Function?: Yes No Function?: Yes No - - Test 1 Review #1 Page 10 / Copright 01 UC Regents and ALEKS Corporation

11 Function?: Yes No Function?: Yes No Find the domain of the function. g = Write our answer using interval notation. Test 1 Review #1 Page 11 / Copright 01 UC Regents and ALEKS Corporation

12 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. See the figure below. With gallons of fuel in its tank, the airplane has a weight of pounds. What is the weight of the plane with gallons of fuel in its tank? Airplane weight in pounds 51 Amount of fuel in gallons 0. Use substitution to solve the sstem. 3 5 = 1 = = = Solve the following sstem of equations. 8 + = 1 11 = A tetbook store sold a combined total of histor and phsics tetbooks in a week. The number of histor tetbooks sold was two times the number of phsics tetbooks sold. How man tetbooks of each tpe were sold? Test 1 Review #1 Page 1 / Copright 01 UC Regents and ALEKS Corporation

13 0% 90% 180 5% 3. A chemical compan makes two brands of antifreeze. The first brand is pure antifreeze, and the second brand is pure antifreeze. In order to obtain gallons of a miture that contains pure antifreeze, how man gallons of each brand of antifreeze must be used? First brand: gallons Second brand: gallons. Solve the following sstem of equations. 3 = = 5. Suppose that there are two tpes of tickets to a show: advance and same-da. Advance tickets cost and same-da tickets cost. For one performance, there were tickets sold in all, and the total amount paid for them was $175 $15 5. How man tickets of each tpe were sold? Number of advance tickets sold: Number of same-da tickets sold: $35. A deliver truck is transporting boes of two sizes: large and small. The combined weight of a large bo and a small bo is pounds. The truck is transporting large boes and small boes. If the truck is carring a total of pounds in boes, how much does each tpe of bo weigh? Large bo: Small bo: Test 1 Review #1 Page 13 / Copright 01 UC Regents and ALEKS Corporation

14 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. + 3 = 0 3 = 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: = Test 1 Review #1 Page 1 / Copright 01 UC Regents and ALEKS Corporation

15 8. 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. 3 + = 3 3 = 3 + 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: = 9. A part rental compan has chairs and tables for rent. The total cost to rent chairs and tables is. The 3 $1 8 $5 total cost to rent chairs and tables is. What is the cost to rent each chair and each table? 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: L: 1 = = 1 3 Test 1 Review #1 Page 15 / Copright 01 UC Regents and ALEKS Corporation

16 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 L1: L: = + 3 = L1 - 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 Test 1 Review #1 Page 1 / Copright 01 UC Regents and ALEKS Corporation

17 L1: L: 5 = = 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 Test 1 Review #1 Page 17 / Copright 01 UC Regents and ALEKS Corporation

18 Test 1 Review #1 Answers for class MAT 135 Spring 017 Master = = a b = L + a.. hours hamburgers. total profit (in dollars) = ,, 7 8. tickets 9. in 10. (a) What was the investment firm's total profit? $000 (b) What was the percent profit for their total investment? 1.5% 11. Number of panels produced b Plant B: 1. F H =, 9 F H =, 9000 Test 1 Review #1 Page 18 / Copright 01 UC Regents and ALEKS Corporation

19 No solution 19. No solution 0. = 8, 8 = No solution Test 1 Review #1 Page 19 / Copright 01 UC Regents and ALEKS Corporation

20 < u < 3. horizontal line: vertical line: = 8 = 5 = 9 = 8 7. = = = Slope of a parallel line: Slope of a perpendicular line: Equation of perpendicular line: Equation of parallel line: 1 = = domain range = 3, 0, = p, q,, m Test 1 Review #1 Page 0 / Copright 01 UC Regents and ALEKS Corporation

21 33. Relation 1 Relation (, ), (7, ), (-, k), (, k) (, -9), (, ), (, ), (, -) Function Not a Function Function Not a Function Relation 3 Relation D o m a i n R a n g e D o m a i n R a n g e star 7 7 moon n rock k 5 5 pen Function Function Not a Function Not a Function 3. f 7 = 19 g 3 = domain range =,, 1 = 1,,, , Test 1 Review #1 Page 1 / Copright 01 UC Regents and ALEKS Corporation

22 Function? Yes No Yes No Yes No Function? Yes No Yes No Yes No 38., 39. pounds = = 3 1. = = 5. Number of histor tetbooks sold: Number of phsics tetbooks sold: 11 Test 1 Review #1 Page / Copright 01 UC Regents and ALEKS Corporation

23 3. 1 First brand: gallons 18 Second brand: gallons. = 8 = 5. Number of advance tickets sold: Number of same-da tickets sold:. Large bo: pounds Small bo: pounds = 0 3 = 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. The sstem has a unique solution:, = 0, 1 The sstem has infinitel man solutions. The must satisf the following equation: = Test 1 Review #1 Page 3 / Copright 01 UC Regents and ALEKS Corporation

24 8. 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: = 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: = 9. Cost to rent each chair: Cost to rent each table: 50. L1: L: 1 = = 1 3 $1.50 $8.5 L L This sstem of equations is: Test 1 Review #1 Page / Copright 01 UC Regents and ALEKS Corporation

25 - inconsistent This means the sstem has: - no solution L1: L: = + 3 = L1 - L - This sstem of equations is: - consistent independent This means the sstem has: - a unique solution: Solution:, 1 L1: L: 5 = = L L This sstem of equations is: Test 1 Review #1 Page 5 / Copright 01 UC Regents and ALEKS Corporation

26 - consistent dependent This means the sstem has: - infinitel man solutions Test 1 Review #1 Page / Copright 01 UC Regents and ALEKS Corporation

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