Using θ-notation, provide asymptotically tight bounds in terms of n for the solution to each of the following recurrences. assume each recurrence has a non-trivial base case of t(n) = θ(1) for all n ≤ n0 where n0 is a suitably large constant. for example, if asked to solve t(n) = 2t(n/2) + n, then your answer should be θ(n log n). you do not need to explain your answers. (a) t(n) = 9t(n/3) + n 2 (b) t(n) = t(n/2) + p n (c) t(n) = 5t(n/2) + n 2 (d) t(n) = t(n/4) + t(3n/4) + n (e) t(n) = t(n/6) + t(2n/3) + n

Factor a^3 - 3 + 3a^2 - a. a) (a - 1)(a + 1)(a + 3) b) (a^2 + 1)(a - 3) c) (a^2 - 3)(a + 1

Solve with work both bert and ernie received an increase in their weekly salaries. bert's salary increased from $520 to $520. ernie's salary went from $580 to $645. find the percent of increase for each salary. what was the larger of the two percents ?

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|