Assume the statement is true for n= k. Prove that it must be true for n=k+1, therefore proving it true for all natural numbers, n. Hint: Since the total number of dots increases by n each time, prove that d(k) + (k + 1) = d (k+1).​

Atriangle with all sides of equal length is a/an triangle. a. right b. scalene c. equilateral d. isosceles

Ascientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. each replicated organism also replicates at the same rate. at hour one, there is one organism. at hour two, there are five more organisms. how many total organisms are there at hour seven? 2,801 19,531 19,607 97.655

Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 4 p plus 4 x plus 2 pxequals56. suppose also that p and x are both functions of time, measured in days. find the rate at which x is changing when xequals2, pequals6, and startfraction dp over dt endfraction equals1.5.