For each positive integer n, p (n) is defined to be the product of the digits of n. for example, p (724) = 56, since 7 × 2 × 4 = 56. which of the following statements must be true? i. p(10n) = p(n) ii. p(n + 1) > p(n) iii. p(2n) = 2p(n)

  none of the above

Step-by-step explanation:

Consider the following:

  p(129) = 1·2·9 = 18

  p(10·129) = p(1290) = 1·2·9·0 = 0 . . . . . statement I is not true

  p(129+1) = p(130) = 1·3·0 = 0 . . . . . . . . . statement II is not true

  p(2·129) = p(258) = 2·5·8 = 80 . . . . . . . statement III is not true

None of the offered statements must be true.

Statement I must be true if p(n) is the product of the non-zero digits of n.

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

step-by-step explanation: