# Buried Treasure: Case Study Quiz

*Register to read the introduction…*If Ahmed used string and tied it to the Castle Rock point and labeled it as point “A” on paper it would be basically 2x + 6 paces. With this being the radius you will know that it is the same anyway you fit this from the circle. So to find the Treasure we will use “C”. Vanessa will use her compass to find north from Castle Rock. From there she will walk “X” paces in a straight line northward. At the end of her distance she will call this point “B”. Vanessa will now turn 90 degrees to the right and will walk 2x+4 paces east until she is at point “C”. We have now acquired a line segment which we will call AB which is basically the line from A to B, the line segment from B to C is considered BC. However, the lines AB and BC intersect to form a perpendicular angel, and we will use line AC as Ahmed’s route. The end state of the line segments if one was to draw them out would equal a triangle. With the face that Vanessa had turned in a 90 degree angle that makes this triangle a right angle ABC. Lines AB and BC are to be considered as the legs and we will think of AC as the

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The formula is written like this, (a + 1)(b + 1)….(z + 1) where a, b, …., z are considered to be the exponents of prime number. So looking at 225 we know that it has prime numbers 2 and 5 with a exponent of 2 next to the 2. So using our formula we will now use (2 + 1)(1 + 1) = (3)(2) = 6. Now when we’re looking at this there are many different possibilities of factors of 20. When looking at the term 20 of quadratic equation we can see that it could be ±1, ±2, ±4, ±5, ±10, and ±20. So now when we input our information into the equation we will use the formula of (ax + b)(cx + d) = 0. We will now use a as 1 and c as -1 and use our possibilities for b and d. I try to be as easy as possible in math so I will choose 4 and 5 as our b and d. We will now rewrite the formula to (1x + 4)(1x + 5) = 0, however when we use our FOIL method we will notice that it turns out to be x2 + 5x + 4x + 20 = x2 + 9x + 20 = 0 which in no shape or form is the same as x2 – 8x – 20 = 0 because of the negative numbers and the middle does not match. We will continue to input numbers into b and d to create the equation to match x2 – 8x – 20 = 0. With this being said we must also keep in mind that a and c will be multiplied to equal positive 1 and that the middle will create the sum of ad and bc to create a -8. We will also have to remember that b and d when multiplied will have to be the same