1. hannah gives clues about her 6 digit secret number:
clue 1: it is the same number if you read it from right to left.
clue 2: the number is a multiple of 9
clue 3: cross of the first and last digits. the only prime factor of the remaining four digit number is 11.
what is hannah's 6 digit number?
2. the only way that 10 can be written as the sum of four different counting numbers is 1+2+3+4. in how many different ways can 15 be written be written as the sum of 4 different counting numbers? assume the order does not matter.

1.  This is a rule which helps a person identify if a number is divisible by nine.
There is no specific answer to why this is observed but I believe that is just how multiples of nine and three behave!

It is the same with the multiples of three as well!

By the way the 6 digit number could be 513315
thanks, hope that helps!!

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12