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Turning 10

December19

tencandlesA significant milestone in the life of our young granddaughter – turning 10. Double digits. Almost a teenager – perhaps could be called a “ten-ager”? (from Wikipedia: “Ten is the base of the decimal system, by far the most common system of  numbers in both spoken and written language. We assume that ten is the most common numerical system simply because we have ten fingers.

Ten is the sum of the first three prime numbers, of the four first numbers (1 + 2 + 3 + 4), of the square of the two first odd numbers and also of the first four factorials (0! + 1! + 2! + 3!). A polygon with ten sides is called a decagon. decagonThe Roman numeral for ten is a cross, X (which looks like two V’s [the Roman numeral for 5] put together); it is thought that the V for five is derived from an open hand (five digits displayed).

Incidentally, the Chinese word numeral for ten, is also a cross: ) . Whichever way you look at it, you have to hand the birthday gift to number 10 – which is kind of appropriate as we celebrate the ultimate giving of a gift (on a cross) this Christmas.
giving a gift

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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