Use a geometric model to factor x^2-6x+8
1 answer:
You might be interested in
You can search in google if you want for the "inscribed quadrilateral conjecture"
and if you want... I can give you a quick proof of it
hmmm in short, if you inscribe a quadrilateral polygon in a circle
it will have 4 angles
each pair of opposite angles, are "supplementary angles", or they add up to 180°
so.. that said in yours, R+P = 180 and Q+O = 180 as well
you only need Q
so
solve for "x"
how big is Q? well, 2x + 4 :)
and if you want... I can give you a quick proof of it
hmmm in short, if you inscribe a quadrilateral polygon in a circle
it will have 4 angles
each pair of opposite angles, are "supplementary angles", or they add up to 180°
so.. that said in yours, R+P = 180 and Q+O = 180 as well
you only need Q
so
solve for "x"
how big is Q? well, 2x + 4 :)
There are a number of ways to approach this problem, including writing all the numbers that match one of the arrangements, such as for sets of 15:
.. 14, 29, 44, 59, 74, 89, 104, 119, 134, 149, 164, 179, 194 (separated by 15)
Modulo 8, these numbers are
.. 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2
This reduces the numbers of interest to those that are 3 modulo 8:
.. 59, 179 (separated by 8*15 = 120)
Looking at these modulo 7, we have
.. 3, 4
pinpointing 179 as the number of spoons in Cheryl's collection.
_____
The attachment shows a solution via graphing calculator. We simply added the absolute values of the differences of the remainders from the desired values and looked for where that sum was zero. This method, too, pointed to 179 as the solution to the problem.
.. 14, 29, 44, 59, 74, 89, 104, 119, 134, 149, 164, 179, 194 (separated by 15)
Modulo 8, these numbers are
.. 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2
This reduces the numbers of interest to those that are 3 modulo 8:
.. 59, 179 (separated by 8*15 = 120)
Looking at these modulo 7, we have
.. 3, 4
pinpointing 179 as the number of spoons in Cheryl's collection.
_____
The attachment shows a solution via graphing calculator. We simply added the absolute values of the differences of the remainders from the desired values and looked for where that sum was zero. This method, too, pointed to 179 as the solution to the problem.