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 .

Idon’t understand this.. will someone ? will mark brainliest along with 20 points.

14 pointslet x be the seats in the small van and y the seats in the large van. how many seats does the large van have? a company uses two vans to transport worker from a free parking lot to the workplace between 7: 00 and 9: 00a. m. one van has 9 more seats than the other. the smaller van makes two trips every morning while the larger one makes only one trip. the two vans can transport 69 people, maximum. how many seats does the larger van have?

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth