Unit 3 Linear Algebra & Unit 4 Systems of Linear Equations REVIEW. + is equal to 2.
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1 Unit 3 Linear Algebra & Unit 4 Systems of Linear Equations REVIEW 1. The expression 3x + 5y 7x+ 4y is equivalent to which of the following? 1. (1) 4x 9y () 9y 4 x (3) 4x y (4) 10x + 9y. Written without parentheses, the expression 5 ( x 3) ( x 8) + is equal to. (1) 8 x + 31 () 1x 31 (3) 1x + 1 (4) 8x 1 3. Which of the following values of x solves the equation 1.5( x + 3) = 1.05? 3. (1) x = 4.7 () x = 3.7 (3) x = 1.6 (4) x =.3 4. Ellen is charged a flat monthly fee of $10 plus an additional 5 cents per phone call she 4. makes. Which of the following equations gives the dollar cost of her bill, C, as a function of the number of calls she makes, n? (1) C = 10n+ 5 (3) C = 0.5n+ 10 () C = 5n+ 10 (4) C = 10n Which of the following expressions most correctly represents the phrase three less than 5. seven times a number? (1) 7 n 3 () 7( n 3) (3) 3 7n (4) 3( n 7) 6. When ( 5x 9) is subtracted from ( x + 3) the resulting binomial can be written as 6. (1) 3 x 1 () 7x 6 (3) 7x 6 (4) 3x If n +1 represents an even integer, which of the following represents the next smaller 7. consecutive even integer? (1) n () n (3) n 1 (4) n The area of any triangle is given by 1 A= bh. Solved for h this formula is 8. (1) 1 Ab () A 1 (3) (4) b Ab A b
2 9. Which of the following values of x solves the equation 5( x ) ( 3x 9) (1) 11 () 8 (3) 6 (4) =? Maria went to the store and bought 3 pounds of green beans and a loaf of bread that 10. cost $.5. If Maria spent $4.9 in total, which of the following equations could be used to determine the price per pound, p, of the green beans? (1) (3) p = 4.9 () p +.5 = 3( 4.9) (4) 3 p +.5 = 4.9 p + = ( ) 11. The length of a rectangle is 6 more than twice its width, w. Which of the following 11. expressions gives the perimeter of the rectangle in terms of w? (1) 6 w + 1 (3) 4w + 1 () w + 6 (4) 8w Which of the following values of x solves the equation x + =? 1. (1) 9 () 7 (3) - (4) What is the largest integer value that lies in the solution set of the 13. inequality x + 1 5? (1) x = 1 () x = 3 (3) x = 3 (4) x = Two consecutive integers have the property that if twice the smaller is added to the 14. larger the resulting sum is equal to 40. Which of the following represents the larger consecutive integer? (1) 0 () 1 (3) 18 (4) Which of the following is a solution to the system consisting of the linear equations 15. y = 5x and y = 3x+ 6? (1) ( 4, 18) () ( 3, ) (3) ( 1, 9 ) (4) (, 7) 16. If drawn on the same set of axes, at which of the following points would the lines whose equations are y = x+ 7 and y = 3x+ 14 intersect? (1) (, 8) () ( 3, 3 ) (3) ( 0,14 ) (4) ( 10, 4)
3 17. Which of the following equations is not equivalent to 6x+ 3y = 18? 17. (1) x + y = 6 () 6x 3y = 18 (3) 6x+ 6y = 36 (4) 1x+ 6y = The value of x that solves the linear system shown below is which of the following? 18. 3x y = 8 5x+ y= 56 (1) 6 (3) 13 () 8 (4) Two numbers have a sum of 13 and a positive difference of 17. Which of the following 19. represents the larger of the two numbers? (1) 7 () 9 (3) 15 (4) 0 0. Evie goes shopping at the grocery store. She buys five pounds of strawberries and 0. three pounds of apples. In total she spends $18.50 on fruit. If s represents the price per pound of strawberries and a represents the price per pound of apples, which equation below correctly models this scenario? s a (1) s+ a = () 5s+ 3a = (3) + = (4) a+ s = To convert from a temperature in Celsius, C, to a temperature in Fahrenheit, F, a 1. 9 science student will use the formula F = C+ 3. At what temperature would Celsius 5 and Fahrenheit have the same numerical value? (In other words, at what temperature is F = C?) (1) 3 () 50 (3) 40 (4) 5. Which of the following linear systems below would have no solutions? 1. (1) 5x+ 3 y = 7 (3) 6x+ 3 y = 1 x 3y = 14 6x+ 4y = 1 () x+ 9x= 3 (4) 4x 6 y = 1 x 9x= 3 4x+ 6y = 9 3. Solve the equation: ( x ) ( = 8x+ )
4 4. Solve the following equation: ( ) 3x 7= 7x+ 1 5x+ 5. Joseph is selling tickets for the high school musical. Joseph sells s-student tickets for $5 each and n-nonstudent tickets for $7 each. Joseph earns a total of $1031. Write an equation that describes this scenario. 6. Algebraically determine the intersection point of the following two lines: y = 6x 10 y = x Solve the systems of equations below: (a) 3x+ y = 11 y = 4x (b) x+ 5y = 7 3x y = 0
5 8. The sophomore class at Arlington High School is selling tickets to Mr. Arlington. Tickets sold in advance cost $7.50 and tickets sold at the door cost $ If a total of 400 tickets are sold and $ was collected. Determine how many of each type of ticket were sold. 9. Carlos bought six packages of hotdog buns and two packages of hotdogs at the local store and spent $ At the same store, Maria bought three packages of hotdog buns and four packages of hotdogs and spent $ How much did one package of hotdog buns cost? 30. Graph the system of inequalities shown below. Label its solution set S. 1 y x+ 3 and y > x 1 y x
6 31. Graph the system of inequalities shown below. Label its solution set S. x < 4 y 3y x 1 x
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