ELEMENTARY & INTERMEDIATE ALGEBRA (COLLEGE ALGEBRA I) 1. The area of a rectangle with base b and height h is bh. A rectangular sport goal is 10 ft wide and 8 ft high. Find the area of the opening. 10 ft 8ft 2. Use the intercepts to graph the equation 6x-3y=18 Use the graphing tool to graph the line; use the intercepts when drawing the line if only one intercept exists, use it and another point to draw the line. 3. Find the slope of the line containing the given pair of points. If the slope is undefined, state this (-1,10) and (6,5) 4. Determine whether the order pair (-6,2) is a solution of the following system of equations. Remember to use alphabetical order of variables X+2y=-2 Y=2x + 2 5. Determine whether the given order pair (0,-6) is a solution of the following system of equations. Remember to use alphabetical ordered variables. X-y=6 Y=2x-2 6. Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. x+y=9 x-y=-5 7. Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution state this. 2x-y=-7 X+2y=-1 8. Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set builder notation to write the solution set. If a system has no solution state this. X=-4 Y=2 9. Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set builder notation to write the solution set. If a system has no solution state this. y=4-x 5x+5y=20 10. Translate the problem solution to a system of equations. Do not attempt to solve. The sum of two numbers is 63. The first number is 2/5 of the second number. 11. Translate to a system of equations but do not solve. A nontoxic floor wax can be made from lemon juice and food grade linseed oil. The amount of oil should be twice the amount of lemon juice. How much of each ingredient is needed to make 30 ounces of floor wax? Let X represent the number of ounces of lemon juice and Y the number of ounces of linseed oil. Complete the system of equations 12. Translate to a system of equations but do not solve. A basketball player scored 27 times during one game. He scored a total of 52 points, two for each field goal and one for each free throw. How many field goals did he make? How many free throws? Let X equal the number of field goals, Let Y equal the number of free throws. Complete the system equations 13. Translate to a system of equations but do not solve. One evening 1500 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $25 for covered pavilion seats and $15 for lawn seats. Total receipts were $28, 500. How many of each type of tickets were sold? Let X equal the number of pavilion seat sold; Let Y equal the number lawn seats sold. Complete the system of equations. 14. In a certain year, brand A of heart rate watch cost $36.23 and brand B cost $55.23, A nonprofit community health organization purchased 37 heart rate watches for use at a wellness center. If the organization spent $1587.51 for the watches, how many of each type did they purchase? --The organization purchased? -Heart rate watches of brand A - Heart rate watches of brand B 15. The perimeter of a rectangular field is 360 yd. The length is 40 yd longer than the width. Find the dimensions the smaller of the two sides is__________yd 16. In a certain year, solar and wind energy generation totaled 1018 trillion Btu's. Wind generated 55 Trillion Btu's more than eight times that generated by solar energy. How much was generated by each source? Solar energy generated? Trillion Btu's and Wind energy generated? Trillion Btu's 17. In 2009, a diabetic express company charged $37.75 for a vial of type A insulin and $30.34 for a vial of type B insulin. If a total of $1998.24 was collected for 60 vials of insulin, how many vials of each type were sold? The number of vials of type A insulin sold? The number of vials of type B insulin sold? 18. A store mixes Kentucky bluegrass worth $10 per pound and chewings rescue worth $13 per pound. The mixture is to sell for $11 per pound. Find how much of each should be used to make a 372-pound mixture. How many pounds of the Kentucky bluegrass should be in the mixture? 19. One canned juice drink is 25% orange juice another is 5 % orange juice. How many liters of each should be mixed together in order to get 20 L that is 80% orange juice? How many liters of the 25% orange juice should be in the mixture? 20. Perform the indicated division or state that the expression is undefined 16/-8 21. Graph the equation 16x+4y=8 22. Translate to an equation. Do not solve. Let C and R represent the unknown numbers one less than the product of two numbers is 44 23. Use the distributive law to factor the following. Check by multiplying 24x+12y+48z Factor completely 2 24. Simplify 2 3 93 20 (3|319|) 22 25. Perform the indicated operation and if possible, simplify 80 8 130 13