(Solved): 15. Simplify the following Boolean expressions using a Karnaugh table: a) \( S=\bar{A} \bar{B} C+A ...

15. Simplify the following Boolean expressions using a Karnaugh table: a) \( S=\bar{A} \bar{B} C+A B \bar{C}+A \bar{B} C+\bar{A} \bar{B} \bar{C} \) b) \( S=A B \bar{C}+A \bar{B} C+A \bar{B} \bar{C}+\bar{A} B \bar{C} \) c) \( S=A \bar{B} \bar{C} D+\bar{A} B \bar{C} \bar{D}+A B C \bar{D}+\bar{A} \bar{B} \bar{C} D+\bar{A} B C \bar{D} \) d) \( S=A B \bar{C} \bar{D}+A B \bar{C} D+A B C D+A B C \bar{D}+A \bar{B} \bar{C} \bar{D} \) 16. For each line, identify the slope and the \( y \)-intercept. Then determine if the lines are perpendicular, parallel, or neither. a) Line 1: \( y=5-4 x \) b) Line 1: \( y=-4 x+5 \) Line 2: \( y=2 x-8 \) c) Line 1: \( y=2 x-4 \) Line 2: \( y=2 x+3 \) d) Line 1: \( x=-3 \) Line 2: \( y=2 x+8 \) Line 2: \( x=15 \) 17. Given the points \( P 1(2,3) \) and \( P 2(4,-2) \) determine: a) The slope of the line passing through the two points b) The point-slope form of the line c) The slope-intercept form of the line d) What is the \( y \)-intercept of the line? 18. Line 1: \( 2 y+4 x=2 \) Find the equation of the line that is a) parallel to line 1 and contains point \( P(2,3) \) b) perpendicular to line 1 and contains point \( P(1,7) \) 19. A computer repair shop charges \( \$ 50 \) for the visit, and \( \$ 2 \$ \) per hour to assess and fix your computer. a) Determine the two unknown variables. b) Determine the linear equation for the cost of a repair. c) If your computer takes 3 hours to repair, how much will it cost? d) If they charge you \( \$ 175 \) to fix your computer, how long did they work on your computer.