Pythagorean Theorem

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The assignment for this week is on page 371 number 98. Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is x? (Dugoploski) With that information we know that Vanessa must walk North x paces, then 2x + 4 paces to the East. We do not know which direction Ahmed must go, but assume that they will end up in the same location. Using a piece of paper I drew the triangle and it is a right triangle. Now I can use the Pythagorean Theorem to help solve for x. The Pythagorean Theorem is a^2+b^2=c^2. Letting a = x, b = 2x+4, and c = 2x+6 a^2+b^2=c^2 Pythagorean Theorem x^2+〖(2x+4)〗^2=〖(2x+6)〗^2 Putting the binomials into the Pythagorean

x^2+〖4x〗^2+16x+16=〖4x〗^2+24x+36 Binomials squared. x^2+16x+16=24x+36 Subtract 〖4x〗^2 out x^2+16x-24x+16-36=0 Subtracted 24x+36 to the other side x^2-8x-20=0 Now I have a quadratic equation with a zero

(x-10)(x+2)=0 Coefficient of x^2 is 1. Put a x inside two sets of parenthesis. Use the trial and error method to find two factors of -20 that add up to -8. My first choice was -5, 2 or 5, -2. Which did not work. So I tried 10, -2 and -10, 2.

x - 10 = 0 or x + 2 = 0 compound equation x = 10 or x = -2 possible answers You cannot use one of these answers because it is a negative number. You cannot have negative...
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