Show that each of these conditional statements is a tautology by using truth tables: (a) ¬p→(p→q)

Write the equation of a line that is perpendicular to the given line and that passes through the given point. –3x – 6y = 17; (6, 3) y = x – 9 y = 2x – 9 y = –2x – 9 y = x + 0 3. is the relationship shown by the data linear? if so, model the data with an equation. x y 1 5 5 10 9 15 13 20 the relationship is linear; y – 5 = (x – 1). the relationship is not linear. the relationship is linear; y – 5 = (x – 1). the relationship is linear; y – 1 = (x – 5). write an equation in point-slope form for the line through the given point with the given slope. (–10, –1); m = y + 10 = (x + 1) y – 1 = (x – 10) y – 1 = (x + 10) y + 1 = (x + 10) 5. write an equation for each translation of . 6.5 units up y + 6.5 = | x | y = | 6.5 x | y = | x | + 6.5 y = | x | – 6.5 6. write an equation for each translation of . 5.5 units right y = | x | + 5.5 y = | x – 5.5 | y = | x | – 5.5 y = | x + 5.5 | 7. which equation translates y = | x | by 8 units to the left? y = | x | – 8 y = | x | + 8 y = | x – 8| y = | x + 8|

On her first stroke, maya hit a golf ball 146 yards, 2 feet, 11 inches. on her second stroke, she hit it 163 yards, 1 foot, 2 inches. how far did the ball go all together? convert the answer to larger units whenever possible.

1. judy took $30 with her to spend on popcorn and drinks for herself and her friends at the movie theater. the price for each bag of popcorn was $5. the price of each drink was half the price of a bag of popcorn. (a) sketch the graph that represents the situation and label the intercepts. use one axis to represent the number of bags of popcorn and the other axis to represent the number of drinks. (b) explain your graph.