what is the algorithm in this pattern of numbers
1
11
21
121
111211
311221
13212211
111312112221

in each row it counts how many numbers are there individually.

Explanation:

for example in the first row there is the number 1

so, in the second row its says that there is one 1

in the third, it explains that in the previous row there is two 1's. in line four, it says 121 that explains the previous line, there is one 2 and one 1. And it goes on and on. so, for instance, in the last line, 111312112221, it explains that in the previous row, there is one 1, one 3, one 2, one 1, two 2's and two one's

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.