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1 MTH00 Review Problems for Final Eam - MLC This is not a sample test. These problems are designed to get ou started on our review for the test. Stud the homework from the tetbook and our class notes for a more complete review. Section Use properties of equalit to solve each of the equations. Show our steps. a) = k 1t = 1 c) n = d) 8 = 6. Translate each sentence into an equation, using for the unknown quantit. Solve the equation. a) If nine is added to a number, the result is negative seventeen. The difference of a number and negative twelve is negative five. Section 1.. Use properties of equalit to solve each of the equations. Show our steps. a) 8 = t 8 = 11 c) ( + ) = 8 d) = 6 Section 1.. Solve each equation for the given variable. a) + t = 8 for + t = 8 for t c) 1 + = 1 for Section 1.. Solve each of the inequalities, then graph the solution on a number line. a).+.. c) 1 + Section.1 6. Nacho Dadd s taco stand sells beef burritos. Let b represent the number of burritos purchased and c be the cost, in dollars, for a lunch at Nacho Dadd s. c = b + a) What is the cost for lunch if two burritos are purchased? How man burritos can be purchased for a total lunch cost of $?. A 00 gallon water tank was completel full when it sprang a leak. Let V represent the number of gallons of water remaining in the tank after D das. Use the table to help answer the following questions. a) How much water remains in the tank after 6 das? How man das does it take for the remaining water level to reach 1 gallons? D 6 8 V The graph shows the distance, d, in miles, Phil rode his bike during a cross-countr biccle trip. Let t represent the number of das Phil rode. a) What was Phil s distance after das? How man das did it take Phil to go 00 miles? distance (mi) d time (das) t 8

2 Section. 9. a) Create a scattergram of the table at right. Are the points linearl related? 10. Determine whether or not each ordered pair represents a solution of the equation the equation: = +? (0, ), (1, ), (, 9), (, 1) Section. 11. Find the slope of the line passing through each pair of points. a) (, ) and (6, ) (, ) and (, ) c) (, ) and (, ) d) (, ) and (, ) What is the slope of the line sketched at the right? 1. Find the slope of each line whose equation is given. a) + = + = 1 c) 8 + = d) = 1 Section. 1. Graph each of the equations b hand. a) = + = Section. 1. Find the -intercept and -intercept, and then use the intercept method to graph the equations b hand. Show our work. a) = = 0 Section Find an equation of the line that has the given slope and contains the given point. Write the equation in slope-intercept form. Show our work. a) m =, (, ) m =, (1, ) 1. Find an equation of the line that passes through the two given points. Show our work. Do not use linear regression. a) (, ) and (6, ) (, 8) and ( 1, ) Section. 18. For the given table of values, use a graphing calculator to draw a scatterplot, then use regression to find an equation of the line of best fit. Round decimals to three decimal places. X Y

3 19. The percentage of Fortune 00 companies that offer pensions are shown in the table for various ears. Let be the percentage of Fortune 00 companies that offer pensions at ears after a) Use regression on a calculator to find a linear equation for the line of best fit. Round decimals to two places. Use our regression equation to predict the percentage of companies that offered pensions in 01. c) Use our regression equation to predict the ear that % of the companies offered pensions. Section.8 0. a) Find an equation of a line that contains the point (, ) and is perpendicular to the graph of = 8. Show our work. Find an equation of a line that contains the point (, ) and is parallel to the graph of = 8. Show our work. Section.1 1. Find the solution of the sstem b graphing the equations b hand. Then use intersect on our calculator to check our solution. a) = = + = 10 = 0 Section.. Solve the sstem b substitution. Verif our solution b checking that it satisfies both equations of the sstem. = + 18 = a) = = 1 Section.. Solve the sstem b elimination. Verif our solution b checking that it satisfies both equations of the sstem. a) = = + = 10 = 1 Section.. Set up and solve a sstem of equations to answer each question. a) Sean bought 1 pounds of a grass seed miture for $8.1. The miture was made up of regrass seed that cost $.9 per pound and fescue seed that cost $. per pound. How man pounds of each tpe of grass seed are in the miture. Jolene needs 10 quarts of a % acid solution. She is going to mi two solutions together, solution A, which is 18% acid and solution B, which is 0% acid. How much of each solution does Jolene need? Section.1. Simplif each algebraic epression. a) + + d) ( + )+ 1 Section. 6. Perform the multiplications and combine an like terms. a) t(t + ) ( + ) c) t ear percent 0 6 ( ) d) ( 1)( + + )

4 Section.. Use the rules of eponents to simplif each epression. a) t t 1 m t i m i m t c) 10 6 z Section. 8. Use the rules of eponents to simplif each epression. a) () ( m ) c) t z tz z Section. 9. Use the rules of eponents to simplif each epression. There should be no negative eponents in our answers. a) ( ) c) Section.6 0. Use the conversion table to convert each measurement. Round to two decimal places. Show our work. a) square kilometers into square miles. 0,000 cubic inches into cubic meters. 1. Write each number in scientific notation. a) ,9,000. Write each number in standard notation. a) Perform the indicated operations. Write our answers in scientific notation a) (. 10 )(.8 10 ) Section.1. Factor out the greatest common factor. a) 1t z 8t z 16 + ( ) (.1 10 ) 11 Section.. Factor each trinomial when possible. a) Section. 6. Factor each polnomial completel. a) c) 9 d) 1 foot = 1 inches 1 ard = feet 1 mile = 80 feet 1 inch =. centimeters 1 meter = 100 centimeters 1 meter = 1000 millimeters 1 kilometer = 1000 meters 1 mile = kilometers Section.. Simplif each rational epression. t a) 6t + 9t c) m 6 m +1m + 6

5 Section Solve b factoring. a) ( )( + ) = 0 = 0 c) 8 = + 1 d) + 6 = 16 Section Simplif each of the square roots. Give simplified eact answers, not decimals. a) 8 c) Section Use square roots to solve the equation. Leave answers in simplified eact form. a) 60 = 0 ( + ) = 6 e) = 0 1. Find the missing side length of each triangle. Leave answers as decimals rounded to two places. a) 8 1. Find the distance between the pairs of points. Show our work. a) (, 9) and (1, 6) (, ) and ( 8, 9) Section 6.. Solve b using the quadratic formula. Show our work. a) = 0 0 = 0 c) + 1 = 0 Section 6.. For each equation: Find the verte and four additional points, and graph the equations. a) = ( ) = 6 + Section 6.6. Use a graphing calculator to help ou solve the following equations. Round answers to the nearest thousandth. a).. = = 0 19 ANSWERS: 1. a) = 8 k = 8 c) n = 0 d) t = 16. a) 9 + = 1, = 6 ( 1) =, = 1. a) = t = 1 c) = 16 d) =. a) = 8 t t = 8 c) = 1. a) 6, , c) 6,

6 6. a) $10. a) 1,6 gallons das 8. a) 00 miles das 9. a) Yes 10. (0, ) es, (1, 0) no, (, 9) no, (, 1) es each square is one unit 11. a) m = 6 = = 1 m = ( ) = 8 = c) m = = 0 = 0 d) m = = 0 = undefined 1. m = 1 1. a) m = m = 0 c) m = 8 d) m is undefined 1. a) 1. a) -intercept: (, 0) -intercept: (, 0) -intercept: (0, ) -intercept: (0, ) 16. a) = + 1 = + 1. a) = 11 = 18. = a) = % c) = 6.9, a) = + 1 = 1 1. a) = 1 + = + 1 = = 1 (6, ) No Solution - Inconsistent 6

7 . a) = = 8 = =. a) = = 1 = =. a). lb fescue, 11. lb re. quarts of miture A,. quarts of miture B. a) + 6. a) 10t 1t c) t 10t a) t 18 m 6t+ c) z 8. a) 8m 1 c) 16t 8 z 1 9. a) 1 1 c) 81 d) mi 0. a) km i km = 1.16mi 0,000in i. cm 1m i 1in 100 cm =.m 1. a) a) ,89,000,000. a) a) 1t z ( tz ) 8( + ). a) ( + )( + ) ( + )( ) 6. a) ( + )( ) ( + ) c)( + )( ). a) t t c) m 6 m a) =, = 6, c) =, 6 d) =, 8 9. a) c) 1 0. a) = ± 1 = 1, 11 c) = ± a) = 1.6 = a) a) = =, c) No real-number solution. a) a) =.9,.9 =.19,

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