Use the binomial theorem to prove the following equalities for any natural number n ∈ n. it is enough in each case to specify x and y in the binomial theorem and show that this results in the given equality. (i’ve written the left-hand sides in two ways–in summation notation and written out in full.) (a) (hammack §3.4 #5 ) xn k=0 n k = n 0 + n 1 + · · · + n n = 2n (b) (hammack §3.4 #7 ) xn k=0 3 k n k = n 0 + 3 n 1 + 32 n 2 + · · · + 3n n n

First, put the equation of the line given into slope-intercept form by solving for y. You get y = 2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00