Math 0310 Final Exam Review Problems

Transcription

1 Math 0310 Final Exam Review Prblems Slve the fllwing equatins. 1. 4dd + 2 = h 5 = (18 xx) + 2(xx 1) = 4(xx + 2) yy 3 4 = 1 2 yy aa = 2.24aa 5.42 Slve the fllwing wrd prblems. 6. The perimeter f a triangle is 78 in. The lengths f the sides are represented by three cnsecutive integers. Find the lengths f the sides f the triangle. 7. The smallest angle f a triangle is 2 mre than 1 f the largest angle. The middle angle is 4 2 less than the largest angle. Find the measure f each angle. 8. A carpenter uses a special saw t cut an angle n a piece f framing. If the angles are cmplementary and ne angle is 10 mre than the ther, find the measure f each angle. 9. Slve the inequality; graph the slutin set and express the answer in set builder ntatin and interval ntatin. 3ww 4 > Slve the inequality; graph the slutin set and express the answer in set builder ntatin and interval ntatin. 2xx 7 5

2 11. Use the slpe-intercept frm t graph the line f the equatin. yy = 1 4 xx Find the slpe f the line passing thrugh the given pints ( 12, 3) and ( 4, 2). 13. Identify the slpe and the y-intercept f the line represented by the equatin xx + 5yy = Use the pint-slpe frmula t write an equatin in standard frm given slpe is 6 and the line passes thrugh the pint ( 7, 8). 15. Find the x- and y-intercepts f the graph f the equatin. 8yy 3xx = Determine if the equatins represent parallel lines, perpendicular lines, r neither. ll 1 : 3xx + 2yy = 8 ll 2 : 12yy = 8xx 24

3 17. When the given equatin is graphed, determine if the line frmed is a hrizntal line, vertical line, r slanted line. 6yy 2 = Slve the inequality by graphing. 4xx 8 2yy 19. Slve the inequality by graphing. 4xx < 12

4 20. Find the equatin f the line thrugh the pint (2, 6) that is perpendicular t the line 7x 4y = 12. Use nly the pint-slpe frmula [yy yy 1 = mm(xx xx 1 )] t write the equatin in slpe intercept frm and identify the fllwing: mm = mm = xx 1 = yy 1 = 21. Classify the fllwing systems f equatins selecting ne respnse frm each categry (type f system and type f slutin). a. Cnsistent Dependent Cnsistent Independent Incnsistent One Unique Slutin Infinitely Many Slutins N Slutin b. Cnsistent Dependent Cnsistent Independent Incnsistent One Unique Slutin Infinitely Many Slutins N Slutin c. Cnsistent Dependent Cnsistent Independent Incnsistent One Unique Slutin Infinitely Many Slutins N Slutin

5 22. Slve the fllwing system f equatins using the Graphing Methd. 3xx + yy = 6 xx 2yy = Slve the fllwing system f equatins using the Substitutin Methd. 2xx + 3yy = 21 yy = 3xx Slve the fllwing system f equatins using the Additin/Eliminatin Methd. 3xx 4yy = 5 4xx 3yy = 5

6 25. Slve the fllwing system f equatins using any methd. xx + 2yy = 4 2xx + 4yy = Slve the fllwing system f equatins using any methd. xx 2yy = 2 3xx + 6yy = A televisin and DVD player cst a ttal f $1002. The cst f the televisin is tw times the cst f the DVD player. Find the cst f each item. 28. A jet travels 5240 miles against a jetstream in 8 hurs and 6680 miles with the jetstream in the same amunt f time. What is the rate f the jet in still air and what is the rate f the jetstream? Descriptin Object s speed ± Mther Nature s speed Rate Time = Distance 29. Suppse that there are tw types f tickets t a shw: advance and same-day. The cmbined cst f ne advance ticket and ne same-day ticket is $65. Fr ne perfrmance, 35 advance tickets and 20 same-day tickets were sld. The ttal amunt paid fr the tickets was $1900. What was the price f each kind f ticket?

7 30. A scientist has tw slutins, which she has labeled Slutin A and Slutin B. Each cntains salt. She knws that Slutin A is 40% salt and Slutin B is 65% salt. She wants t btain 60 unces f a mixture that is 50% salt. Hw many unces f each slutin shuld she use? Descriptin Amunt f item Strength f Substance = Value Perfrm the indicated peratin and simplify when needed. 31. qq3 qq 12 qq qq xx4 yy 3 4xxyy (3uu 5 vv 2 ) (7yy 2 11yy 6) (8yy 2 + 3yy 4) 36. (q + 8)(6q - 1) 37. (b 4)(b + 4) yy3 10yy 2 5yy 39. (2tt 2 + tt 10) (tt 2) 40. (5aa aa 22) (5aa 3)

8 Slutins: 1. d=1 2. h=18 3. x=6 4. y= a= in, 26 in, 27 in 7. 22, 78, and ww ww > , ( {xx xx 6} (, 6] ] mm = mm = 1 5 yy iiiiiiiiiiiiiiiiii: (0, 15) 14. 6xx + yy = xx iiiiiiiiiiiiiiiiii: (2, 0) yy iiiiiiiiiiiiiiiiii: (0, 3 4 ) 16. mm 1 = 3 2 and mm 2 = 2 3 The lines are neither; because their slpes are nt the same and therefre nt parallel. And, their slpes are nt ppsite reciprcals and therefre nt perpendicular.

9 17. yy = yy 2xx xx > 3

10 20. yy = 4 34 xx + r yy = 4 xx mm = 7 4 mm = 4 7 xx 1 = 2 yy 1 = a) Cnsistent Independent, One Unique Slutin b) Incnsistent, N Slutin c) Cnsistent Dependent, Infinitely Many Slutins 22. Slutin: (2,0) 23. Slutin: (3, 5) 24. Slutin: (5, 5) 25. N Slutin 26. Infinitely Many Slutins; the slutin is the set f all pints satisfying the equatin: yy = 1 xx i.e. (xx, yy) yy = 1 xx 1 r {(xx, yy) xx 2yy = 2} r {(xx, yy) yy = 3xx + 6yy = 6} Cst f televisin: $668, Cst f DVD player: $ Descriptin Against a jetstream With a jetstream Object s speed ± Mther Nature s speed Time = Distance Rate x y 8 hrs. = 5240 x+y 8 hrs. = 6680 Rate f the jet in still air: 745 mph, Rate f the jetstream: 90 mph 29. Advance ticket: $40, Same-day ticket: $25

11 30. Descriptin Slutin A Slutin B Mixture Amunt f Strength f Substance = Value item x 40% = 0.40x y 65% = 0.65y 50 50% = 30 Slutin A: 36 unces, Slutin B: 24 unces 31. qq xx6 yy uu15 27vv x yy 2 14yy qq qq bb yy 2 2yy 39. 2t aa aa 3