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Studienführer > College Algebra

Solutions

Solutions to Try Its

1. x=5x=-5 2. x=3x=-3 3. x=103x=\frac{10}{3} 4. x=1x=1 5. x=717x=-\frac{7}{17}. Excluded values are x=12x=-\frac{1}{2} and x=13x=-\frac{1}{3}. 6. x=13x=\frac{1}{3} 7. m=23m=-\frac{2}{3} 8. y=4x3y=4x - 3 9. x+3y=2x+3y=2 10. Horizontal line: y=2y=2 11. Parallel lines: equations are written in slope-intercept form. Coordinate plane with the x-axis ranging from negative 5 to 5 and the y-axis ranging from negative 1 to 6. Two functions are graphed on the same plot: y = x/2 plus 5 and y = x/2 plus 2. The lines do not cross. 12. y=5x+3y=5x+3

Solutions to Odd-Numbered Exercises

1. It means they have the same slope. 3. The exponent of the xx variable is 1. It is called a first-degree equation. 5. If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator). 7. x=2x=2 9. x=27x=\frac{2}{7} 11. x=6x=6 13. x=3x=3 15. x=14x=-14 17. x4x\ne -4; x=3x=-3 19. x1x\ne 1; when we solve this we get x=1x=1, which is excluded, therefore NO solution 21. x0x\ne 0; x=52x=\frac{-5}{2} 23. y=45x+145y=\frac{-4}{5}x+\frac{14}{5} 25. y=34x+2y=\frac{-3}{4}x+2 27. y=12x+52y=\frac{1}{2}x+\frac{5}{2} 29. y=3x5y=-3x - 5 31. y=7y=7 33. y=4y=-4 35. 8x+5y=78x+5y=7 37. Parallel Coordinate plane with the x and y axes ranging from negative 10 to 10. The functions 3 times x minus 2 times y = 5 and 6 times y minus 9 times x = 6 are graphed on the same plot. The lines do not cross. 39. Perpendicular Coordinate plane with the x and y axes ranging from negative 10 to 10. The function y = negative 3 and the line x = 4 are graphed on the same plot. These lines cross at a 90 degree angle. 41. m=97m=\frac{-9}{7} 43. m=32m=\frac{3}{2} 45. m1=13, m2=3; Perpendicular{m}_{1}=\frac{-1}{3},\text{ }{m}_{2}=3;\text{ }\text{Perpendicular} 47. y=0.245x45.662y=0.245x - 45.662. Answers may vary. ymin=50, ymax=40{y}_{\text{min}}=-50,\text{ }{y}_{\text{max}}=-40 49. y=2.333x+6.667y=-2.333x+6.667. Answers may vary. ymin=10,ymax=10{y}_{\mathrm{min}}=-10, {y}_{\mathrm{max}}=10 51. y=ABx+CBy=\frac{-A}{B}x+\frac{C}{B} 53. Yes, they are perpendicular.
The slope for (1,1) to (0,4) is 3.The slope for (1,1) to (2,0) is 13.The slope for (2,0) to (3,3) is 3.The slope for (0,4) to (3,3) is 13\begin{array}{l}\text{The slope for }\left(-1,1\right)\text{ to }\left(0,4\right)\text{ is }3.\\ \text{The slope for }\left(-1,1\right)\text{ to }\left(2,0\right)\text{ is }\frac{-1}{3}.\\ \text{The slope for }\left(2,0\right)\text{ to }\left(3,3\right)\text{ is }3.\\ \text{The slope for }\left(0,4\right)\text{ to }\left(3,3\right)\text{ is }\frac{-1}{3}\end{array}.
55. 30 ft 57. $57.50 59. 220 mi

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