Aparallelogram has side lengths of 13 and 17 and an angle that measures 64°. law of cosines: a2 = b2 + c2 – 2bccos(a) what is x, the length of the diagonal, to the nearest whole number? 16 18 19 21

What is the effect on the graph of the function f(x) = x2 when f(x) is changed to f(x) − 4?

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?

Crickets can jump with a vertical velocity of up to 14 ft/s. which equation models the height of such a jump, in feet, after t seconds? h(t) = –16t2 + v0t + h0 h(t) = –16t2 + v0t + 14 h(t) = –16t2 + 14t h(t) = –16t2 + 14t + 14 what is the maximum height the cricket reaches? round to the nearest thousandth. h = feet