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

Theorem.
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

factor.
(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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Pythagorean Quadratic
Member
MAT 222 Introduction to Algebra
Instructor Yvette Gonzalez-Smith
August 04, 2013
Pythagorean Quadratic
The PythagoreanTheorem is an equation that allows a person to find the length of a side of a right triangle, as long as the length of the other two sides is known. The theorem basically relates the lengths of three sides of any right triangle. The theorem states that the square of the hypotenuse is the sum of the squares of the legs. It also can help a person to figure out whether or not the triangle is a right triangle or not, as long as the length of the other two sides are given (The PythagoreanTheorem, 1991-2012).
This week’s assignment was found on page 371; it is problem number 98, called “buried treasure”. 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?
Although we were not given a direction for Ahmed’s half of the map, we figure that his and Vanessa’s paces will end up in the same place. I have drawn a diagram on a...

...The PythagoreanTheorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students.
ThePythagoreanTheorem is Pythagoras' most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen. The later discovery that the square root of 2 is irrational and therefore, cannot be expressed as a ratio of two integers, greatly troubled Pythagoras and his followers. They were devout in their belief that any two lengths were integral multiples of some unit length. Many attempts were made to suppress the knowledge that the square root of 2 is irrational. It is even said that the man who divulged the secret was drowned at sea.
The PythagoreanTheorem is a statement about triangles containing a right angle. The PythagoreanTheorem states that:
"The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides."
Figure 1
According to...

... The assignment for the week is on page 371 number 98. We will be using PythagoreanTheorem, quadratic, zero factor, and compound equation, to solve this equation. We will explain step by step to solve how many paces to reach Castle Rock for Ahmed and Vanessa had to accomplish to meet there goal. 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, 2012)?
With the 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, however, we assume that they will end up in the same location. Using a piece of paper, I drew the triangle and it is right triangle. Now I can use the PythagoreanTheorem to help solve for x.
The PythagoreanTheorem is a^2 + b^2 = c^2. Letting a = x, b= 2x+4, and c = 2x + 6.
a^2 + b^2 = c^2 PythagoreanTheorem
x^2 + (2x+4)^2 = (2x+6)^2 Putting the binomials into the PythagoreanTheorem.
x^2 + 4x^2 + 16x +16 = 4x^2 + 24x + 36 Binomials squared. This is 4x^2 on both sides of...

...In mathematics, the Pythagoreantheorem — or Pythagoras' theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
Thetheorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1]
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
The Pythagoreantheorem is named after the Greek mathematician Pythagoras (ca. 570 BC—ca. 495 BC), who by tradition is credited with its discovery and proof,[2][3] although it is often argued that knowledge of the theorem predates him. There is evidence that Babylonian mathematicians understood the formula, although there is little surviving evidence that they used it in a mathematical framework.[4][5]
The theorem has numerous proofs, possibly the most of any mathematical theorem. These are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including...

...PythagoreanTheorem:
Some False Proofs
Even smart people make mistakes. Some mistakes are getting published and thus live for posterity to learn from. I'll list below some fallacious proofs of the Pythagoreantheorem that I came across. Some times the errors are subtle and involve circular reasoning or fact misinterpretation. On occasion, a glaring error is committed in logic and leaves one wondering how it could have avoided being noticed by the authors and editors.
Proof 1
One such error appears in the proof X of the collection by B. F. Yanney and J. A. Calderhead (Am Math Monthly, v.3, n. 6/7 (1896), 169-171.)
Suppose the theorem true. Then AB² = AC² + BC², BC² = CD² + BD², and AC² = AD² + CD². Combining the three we get
AB² = AD² + 2CD² + BD².
But CD² = AD·BD. Therefore,
AB² = AD² + 2AD·BD + BD².
From which
AB = AD + BD,
which is true. The supposition is true.
Critique
By the same token, assume 1 = 2. Then, by symmetry, 2 = 1. By Euclid's Second Common Notion, we may add the the two identities side by side: 3 = 3. Which is true, but does not make the assumption(1 = 2) even one bit less false.
As we know, falsity implies anything, truth in particular.
Proof 2
This proof is by E. S. Loomis (Am Math Monthly, v. 8, n. 11 (1901), 233.)
Let ABC be a right triangle whose sides are tangent to the circle O. Since CD = CF, BE = BF, and AE = AD = r = radius of circle, it is easily shown...

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PythagoreanTheorem
Pythagoras was born in Samos, Greece around 570 BCE. From there he emigrated to Croton, Italy where most of his most important ideas and theories would develop. Early on, Pythagoras founded a society of disciples where he introduced the idea eternal recurrence into Greek thought, and it was Pythagoras’ ambition to reveal the basis of divine order. This is how Pythagoras came to mathematics, and he saw math as a purifier of the soul, and saw numbers in everything. He was convinced that the divine principles of the universe can be expressed in terms of relationships of numbers.
Over 4000 years ago, the Babylonians and the Chinese already knew that a triangle with the sides of 3, 4, and 5 must be a right triangle. They used this knowledge to construct right angles. Pythagoras studied them a bit closer and found that the two shorter sides of the triangles squared and then added together, equal exactly the square of the longest side. And he proved that this doesn't only work for the special triangles, but for any right triangle. This can be written in the form a^2 + b^2 = c^2, and today this is what is known as the PythagoreanTheorem.
The PythagoreanTheorem was one of the first times in human history that people could calculate a length or distance using only outside information. The train of thought used by Pythagoras was the first time the idea of a unset...

...Algebra Week 5 Assignment: Pythagorean Quadratic
Algebra has been around for many years. Some people feel there is no use for algebra in the real world. There are those who feel it is a waste of time because only certain professions really use it. However, algebra is used in many ways which can relate to everyday situations. Algebra truly is a part of our everyday life and there really is no escaping it. This week, we are asked to solve a problem using thePythagoreanTheorem. The PythagoreanTheorem is a relation in geometry among the three sides of a right triangle. The Theorem reveals that the square of the hypotenuse is equal to the sum of the squares of the other two sides. This information can provide useful information and save lots of time and aggravation. People in the construction business find this information quite helpful because it allows them to build a sound structure. Architects and those in the engineering profession also need this information and apply it to their everyday tasks. All three of these situations really do occur daily for many people and it is extremely important to be able to figure these things out.
On page 371 of our text, Elementary and Intermediate Algebra, question #98 tells us, “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...

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PythagoreanTheorem
In mathematics, the Pythagoreantheorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1]
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
These two formulations show two fundamental aspects of this theorem: it is both a statement about areas and about lengths. Tobias Dantzig refers to these as areal and metric interpretations.[2][3] Some proofs of the theorem are based on one interpretation, some upon the other. Thus, Pythagoras' theorem stands with one foot in geometry and the other in algebra, a connection made clear originally byDescartes in his work La Géométrie, and extending today into other branches of mathematics.[4]
The Pythagoreantheorem has been modified to apply outside its original domain. A number...