The first five triangular numbers are shown, where n represents the number of dots in the base of the figure, and d (n) represents the total number of dots in the figure. When , there is 1 dot. When , there are 3 dots. When , there are 6 dots. Notice that the total number of dots increases by n each time.

Use induction to prove that .

Kira looked through online census information to determine the overage number of people living in the homes in her city what is true about kira's data collection?

Is there a direction u in which the rate of change of f(x,y)equals=x squared minus 3 xy plus 4 y squaredx2−3xy+4y2 at p(1,2) equals 14? give reasons for your answer. choose the correct answer below. a. no. the given rate of change is smaller than the minimum rate of change. b. no. the given rate of change is larger than the maximum rate of change. c. yes. the given rate of change is larger than the minimum rate of change and smaller than the maximum rate of change.

Solve the following system of equations express your answer as an ordered pair in the format (a,b) with no spaces between the numbers of symbols 5x+2y=22