Hi, another math problem : a cubic function is definined for x∈r as : f(x)= x³ +x(1-k²) + k , where k is constant. a) show that -k is root of f. b) find, in term of k, the other two roots of f. c) find the set of values of k for which f has exactly one real root. a lot

Anumber cube is rolled and a coin is tossed. the number cube and the coin are fair. what is the probability that the number rolled is less than 4 and the coin toss is tails?

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

When keisha installed a fence along the 200 foot perimeter of her rectangular back yard, she left an opening for a gate.in the diagram below, she used x to represent the length in feet of the gate? what is the value? a. 10 b. 20 c. 25 d. 30