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MAT221 Introduction to Algebra Pythagorean Quadratic

Week five of this class has been a complete challenge for me, from start to finish. Trying to master everything that we have been taught over the five weeks has truly been a test. I know there are benefits to knowing these principals, however, it stresses me to think about having to use it in real life circumstances.

This problem involves using the Pythagorean Theorem to find distance between several points in our textbook (Dugopolski, 2012). 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?

We need to look at the equation so we can know how far Ahmed will have to walk, which is 2x+6 paces from Castle Rock. Even though Vanessa’s half of the map does not indicate in which direction the 2x + 4 paces should go, it can be assumed that her’s and Ahmed’s paces should end up in the same place. When sketched on scratch paper, a right triangle is formed with 2x + 6 being the length of the hypotenuse, and x and 2x + 4 being the legs of the triangle. When a right triangle is involved, the Pythagorean Theorem helps solve for x.

The Pyhagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse c, these length have the relationship of a2 + b2 =c2. Let a = x, and b = 2x + 6, so that c = 2x + 4 Then, putting these measurements into the Theorem, the equation becomes: x2 + (2x + 6)2 = (2x + 4)2 The binomials into the Pythagorean Theorem. x2 + 4x2 + 16x + 16 = 4x2 + 24x + 36 The binomials squared. Notice there…...

...Type [pic] 8.7 Factoring Special Cases 8.8 Factoring by Grouping (4 Terms Only) Rational Expressions and Equations 11.1 Simplifying Rational Expressions 11.2 Multiplying and Dividing Rational Expressions 11.3 Dividing Polynomials 11.4 Adding and Subtracting Rational Expressions 11.5 Solving Rational Expressions Quadratic Equations and Functions 9.1 Exploring Quadratic Graphs 9.2 Quadratic Functions 9.3 Finding and Estimating Square Roots 10.1 Simplifying Radicals 9.4 Solving Quadratic Equations 9.5 Factoring to Solve Quadratic Equations 9.7 Using the Quadratic Formula 9.8 Using the Discriminant California Content Standards 10.0, 11.0 2.0, 10.0, 12.0, 13.0, 15.0 2.0, 14.0, 17.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.1, 25.3 4th Quarter Review for State Testing 2.5 Equations and Problem Solving 2.6 Mixture Problems and Work Problems Radical Expressions and Equations 10.2 The Pythagorean Theorem 10.2.1 Distance Formula (Supplemented) 10.2.2 Midpoint Formula (Supplemented) 10.3 Operations and Radical Expressions 10.4 Solving Radical Equations 10.5 Graphing Square Root Functions Graphs and Functions 4.2 Relations and Functions 4.3 Function Rules, Tables, and ......

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...Pythagorean Theorem: Finding Treasure Patricia Diggs MAT 221 Introduction to Algebra Instructor Bridget Simmons May 12, 2013 Pythagorean Theorem: Finding Treasure In this paper I will attempt to use the Pythagorean Theorem to solve the problem which reads 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 they can find x and save a lot of digging. What is x? The Pythagorean Theorem states that in every right triangle with legs the length a and b and hypotenuse c, these lengths have the relationship of a2 + b2=c2. a=x b=(2x+4)2 c=(2x+6)2 this is the binomials we will insert into our equation x2+(2x+4)2=(2x+6)2 the binomials into the Pythagorean Theorem x2+4x2+16x+16=24x36 the binomial squared. The 4x2can be subtracted out first x2+16x+16=24x+36 now subtract 24x from both sides x2+-8x+16=36 now subtract 36 from both sides x2-8x-20=0 this is a quadratic equation to solve by factoring and using the zero factor. (x- )(x+ ) the coefficient of x2 is one (1). We can start with a pair of parenthesis with an x each. We have to......

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...Pythagorean Quadratic Diane Todd MAT 221 Introduction to Algebra Instructor Alicia Davis September 29, 2013 Treasure hunts have always been a big deal in our home. Having raised five boys, anything to do with an adventure was exciting. Actually, this past June I planned one of my grandsons birthday parties around the theme of pirates and treasure hunting. I had never considered the math that went behind the maps in which I made up. Needless to say, when I saw the question entitled “buried treasure” in our math book, it brought back numerous memories. 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? Even though Ahmed’s half of the map does not tell him which direction the 2x + 6 paces should go, Ahmed can assume that his and Vanessa’s paces should end up in the same place. If I sketch out this scenario on paper, I see that I have a right triangle with 2x + 6 being the length of the hypotenuse, and 2x + 4 being the legs of the triangle. I now can use the Pythagorean Theorem to solve for x. The Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse of c,......

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...Running head: Pythagorean Quadratic Pythagorean Quadratic Sharlee M. Walker MAT 221 Instructor Xiaolong Yao December 2, 2013 Pythagorean Quadratic Ahmed’s half of the map doesn’t indicate which direction the 2x + 6 paces should go, we can assume that his and Vanessa’s paces should end up in the same place. I did this out on scratch piece of paper and I saw that it forms a right triangle with 2x + 6 being the length of the hypotenuse, and x and 2x + 4 being the legs of the triangle. Now I know how I can use the Pythagorean Theorem to solve for x. The Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse c, these lengths have the formula of a2 + b2 = c2. Let a = x, and b = 2x + 4, so that c = 2x + 6. Then, by putting these measurements into the Theorem equation we have x2 + (2x + 4)2 = (2x + 6)2. The binomials into the Pythagorean Thermo x2 + 4x2 + 16x + 16 = 4x2 + 24x + 36 are the binomials squared. Then 4x2 on both sides of the equation which can be (-4x2 -4x2) subtracted out first leaving the equation to be x2 + 16x + 16 = 24x + 36. Next we should subtract 16x from both sides of equation, which then leaves us with: x2 +16 = 8x + 36. The next step would then be to subtract 36 from both sides to get a result of. x2 -20= 8x. Finally we need to subtract 8x from both sides to get x2 – 8x...

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...Running Head: PYTHAGOREAN QUADRATIC Running head should use a shortened version of the title if the title is long! All capital letters for the title and the words Running and Head should be capitalized as well. 1 Pythagorean Quadratic (full title; centered horizontally & vertically) First Name Last Name MAT 221 Dr. xxxxxxxxxxx xxxxxxxxx Date PYTHAGOREAN QUADRATIC 2 Pythagorean Quadratic Be sure to have a centered title on page 1 of your papers!! [The introductory paragraph must be written by each individual student and the content will vary depending on what the student decides to focus on in the general information of the topic. YOUR INTRODUCTION SHOULD CONNECT MATH CONCEPTS AND REAL-WORLD APPLICATIONS. DO NOT INCLUDE THE DIRECTIONS IN THE INTRO! The following paragraph is not an introduction to the paper but rather the beginning of the assignment.] Here is a treasure hunting problem very similar to the one in the textbook (Dugopolski, 2012). This problem involves using the Pythagorean Theorem to find distance between several points. Spanky has half of a treasure map, which indicates treasure is buried 2x + 9 paces from Leaning Rock. Buckwheat has the other half of the treasure map, which says that to find the treasure one must walk x paces to the north from Leaning Rock and then 2x + 6 paces east. Spanky and Buckwheat found that with both bits of information they can solve for x and save themselves a lot of digging. How many paces is x? Even though......

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...ground instruction, ﬁrst-time jumpers can be ready to make a solo jump. Without the assistance of oxygen, skydivers can jump from as high as 14,000 feet and reach speeds of more than 100 miles per hour as they fall toward the earth. Jumpers usually open their parachutes between 2000 and 3000 feet and then gradually glide down to their landing area. If the jump and the parachute are handled correctly, the landing can be as gentle as jumping off two steps. Making a jump and ﬂoating to earth are only part of the sport of skydiving. For 5 5.1 Factoring Out Common Factors Special Products and Grouping Factoring the Trinomial ax2 bx c with a 1 Factoring the Trinomial ax2 bx c with a 1 Difference and Sum of Cubes and a Strategy Solving Quadratic Equations by Factoring 5.2 Chapter 5.3 5.4 5.5 5.6 example, in an activity called “relative work skydiving,” a team of as many as 920 free-falling skydivers join together to make geometrically shaped formations. In a related exercise called “canopy relative work,” the team members form geometric patterns after their parachutes or canopies have opened. This kind of skydiving takes skill and practice, and teams are not always successful in their attempts. The amount of time a skydiver has for a free fall depends on the height of the jump and how much the skydiver uses the air to slow the fall. In Exercises 85 and 86 of Section 5.6 we ﬁnd the amount of time that it takes a skydiver to fall from a given......

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...Pythagorean Quadratic Treasure Hunters Pythagorean Quadratic Treasure Hunters Introduction to Algebra Treasure Hunters Ahmed and Vanessa both have possession of one half of a complete treasure map. Ahmed’s map shows the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa’s map shows the treasure buried at x paces to the north and 2x + 4 paces to the east. When the two combine information, the location of the buried treasure is going to be a lot easier to find and they can share in the booty loot that they discover. Castle Rock is the lowest left point of the hypotenuse and at the bottom of the left leg and the treasure is at the furthest right point of the right leg. To factor the equation we start with the following, X2+(2x + 4)2 = (2x+6)2 Using the Pythagorean Theorem, a2+2ab+b2 i get a compound X2 +(4x216x+16)=4x2+24x+36 equation. It is then necessary to simplify using the quadratic 5x2+16x+16=4x2+24x+36 equation ax2-bx+c=0 so that I can factor. (x2+2)(x-10)=0 everything is set to zero for the zero factor X = 10 solve for x Plugging the x value for a, b, and c to the legs or the hypotenuse and what this does is it gives me the equation of how many paces it is to the treasure A= 10 B=2(10)+4 = 20+4 = 24 C=2x+6 = 2(10)+6 = 26 In conclusion, castle rock is located at the bottom left of a right hand triangle, and the treasure is 26 paces northeast of......

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...Buried Treasure Allen Raikes MAT 221 DR. Steven Flanders Ahmed and Vanessa has a treasure that needs to be located. It’s up to me and to help find it, I will do that by using the Pythagorean quadratic. On page 371 we learned that the Ahmed has a half of the map and Vanessa has the other half. Ahmed half in say the treasure is buried in the desert 2x+6 paces from Castle Rock and Vanessa half says that when she gets to Castle Rock to walk x paces to the north, and then walk 2x+4 paces to the east. So with all the information I have I need to find x. the Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse c, which have of a relationship of a2+b2=c2. In this problem I will let a=x, and b= 2x+4, and c=2x+6. So know it time to put the measurements into the Theorem equation; 1) X2+ (2x+4)2=(2x+6)2 this is the Pythagorean Theorem 2) X2+4x2+16x+16 = 4x2+ 24x+36 are the binomials squared 3) 4x2 & 4x2 on both sides can be subtracted out. 4) X2+16x+16 = 24x +36 subtract 16x from both sides 5) X2+16 = 8x+36 now subtract 36 from both sides 6) X2-20 = 8x 7) X2-8x-20=0 this is the quadratic equation to solve by factoring using the zero factor. 8) (x-)(x+) Since the coefficient of x2 is 1 we have to start with pair of () is the 20 in negative there will be one + and one – in the binomials. 9) -2, 10: -10,2: -5,4; -4, -5 10) Looks I’m going to use -10 and 2......

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...A Treasure Hunt at Castle Rock using Pythagorean Quadratic June Tye-Patterson Math 221: Introduction to Algebra Instructor: Shenita Talton 07-13-2014 A Treasure Hunt at Castle Rock using Pythagorean Quadratic For this week assignment we are given a word problem and the use of the Pythagorean Theorem to solve it. We will be helping Ahmed and Vanessa, who both have a half of a map, find buried treasure in the desert somewhere around a place named Castle Rock. Ahmed map says the treasure is 2x+6 paces from Castle rock, whereas, Vanessa map says in order to find the treasure, go to Castle Rock, walk x paces to the north and then walk 2x+4 paces to the east. In order to discover the location of the treasure, we need to factor down the three quadratic expressions by putting the measurements into the Pythagorean Theorem. The first thing we need to do is to write an equation by inserting the binomials into the Pythagorean Theorem, which also states that every right triangle with legs of length have the relationship of a^2+b^2=c^2 x^2+ (2x+4)^2=(2x+6)^2 The binomials into the Pythagorean Theorem. x^2(2x+4) (2x+4)=(2x+6) (2x+6) The equation squared. x^2 4x+8x+8x+16=4x^2+12x+12x+36 Equation FOILED or distributed. x^2+4x^2=5x^2 First two terms......

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...Real World Quadratic Functions Christine Sandoval MAT222: Intermediate Algebra (ACR1438C) Instructor: Yvette Gonzalez-Smith October 10, 2014 Real World Quadratic Functions In some types of business being able to solve real world quadratic functions are very important. When we think about the quadratic curves I would point to curves known as the circle, ellipse, hyperbola and parabola (Dugopolski, 2012). I at first thought this was something that came about during my time but these actual quadratic curves came about during the ancient Greek times but they now have more real world applicability than one would think. Quadratic equations described the orbits where the planets moved round the Sun but also furthered advances in astronomy (Budd & Sangwin, 2004). A long time ago Galileo found some type of link between quadratic equations and acceleration (2004). I would believe that being able to solve real world quadratic problems are important in business because we should be able to show a return on investment or profit. We need to be able to analyze the accounts payable and receivable to determine how the business looks. Quadratic functions are not only used in business they are used in science and engineering just to name a couple of areas. Our task today is not only to show how important it is to understand quadratic functions but also to explain how important they are in business. When we think about quadratic functions we may think about the u-shape of the......

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...particularly renowned is the Pythagorean Theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides of any right triangle. While most people have heard of or even used the Pythagorean Theorem, many know little of the man who proved it. Pythagoras was born in 570 BC in Samos, Greece. His father, Mnesarchus, was a merchant from Tyre who traveled abroad. It is rumored that Pythagoras traveled with his father during his early years and was introduced to several influential teachers, including Thales who was a famous Greek philosopher. Several years and many countries later, Pythagoras found himself in Egypt. It was here that he studied at the temple of Diospolis and was also imprisoned during the Persian invasion. During the time he was imprisoned, Pythagoras began to study the religion called Zoroastrianism (Lauer/Schlager, 2001). It was because of these teachings and ideals that Pythagoras eventually moved to Italy. At age 52, while living in Croton, Italy, Pythagoras established the Pythagorean society. It was through this society and his positions in local government that Pythagoras recruited men and women in order to lead them to the pure life with his spiritual and mathematical teachings. Pythagoras believed that number was limiting and gave shape to all matter and he impressed this upon his followers (Gale, 1998). During his time leading the Pythagoreans, Pythagoras not only proved the Pythagorean Theorem,......

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...Ben Lopez MATH112 Phase 4 Discussion Board September 10, 2014 I find the Quadratic Formula to be the easiest method to solve a quadratic equation. I like that this formula can be used to solve any quadratic equation, unlike factoring, for example, because there are some quadratic equations that cannot be factored. I also like that the formula is consistent and if I follow the formula’s steps every time, I will get the correct results. I find that solving quadratic equations by graphical properties of parabolas is tedious and inaccurate. I would rather use other methods like completing the square to find an accurate answer instead of approximating an answer based on an image of a graphed parabola. For my example, I will solve the equation x^2+5x+6=0 by factoring, then by the quadratic formula. Factoring x^2+5x+6=0 Factor: x^2+5x+6=0 = (x+2)(x+3) Set the factor equal to 0: (x+2)(x+3)=0 Solve each factor: x+2=0 or x+3=0 x=-2 or x=-3 Quadratic Formula x^2+5x+6=0 Values: a=1, b=5 and c=6 Plug values into this formula: x= | -b±√b^2-4ac | | 2a | x= | -5±√5^2-4(1)(6) | | 2(1) | Simplify: x= | -5±√25-24 | | 2 | Simplify: x= | -5±√1 | | 2 | x=-2 or x=-3 Let’s say that we are building a house and one of the rooms in the house needs walls. We know that we want the room to be 75 square feet and we want the width of the room to be 3 feet longer than the length of the room. We’ll let x represent the length of the room and x+3......

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...MAT 126 Week 4 Assignment Pythagorean Triple Get Tutorial by Clicking on the link below or Copy Paste Link in Your Browser http://hwguiders.com/downloads/mat-126-week-4-assignment-pythagorean-triple/ For More Courses and Exams use this form ( http://hwguiders.com/contact-us/ ) Feel Free to Search your Class through Our Product Categories or From Our Search Bar (http://hwguiders.com/ ) When we began to deal with Pythagorean Triples it can be very hard and difficult in doing any kind of mathematics problems. When we first starting this class and saw that it involve doing Pythagorean Triples knew it was going to be a challenge. When we deal with using formula you must know how to use them in the proper order and make sure you are using the correct one as well. If we can do that then we can be good at doing the problems as well as use the formulas later on. A Pythagorean triple is simply a right triangle whose sides are positive integers. After reviewing here’s the way to generate Pythagorean Triples is to multiply any known Pythagorean Triple by an integer (any integer). MAT 126 Week 4 Assignment Pythagorean Triple Get Tutorial by Clicking on the link below or Copy Paste Link in Your Browser http://hwguiders.com/downloads/mat-126-week-4-assignment-pythagorean-triple/ For More Courses and Exams use this form ( http://hwguiders.com/contact-us/ ) Feel Free to Search your Class through Our Product Categories or From Our Search......

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...Pythagorean Quadratic Melissa Hernandez MAT221: Introduction to Algebra Instructor Srabasti Dutta August 4, 2014 Pythagorean Quadratic Ever since I can remember when I was a little girl full of curiosity, I enjoyed the thought of finding a buried treasure and thus set out on treasure hunts with my sisters. Depending on how big your imagination is, you can take yourself to exotic locations, around town, or in your very own backyard. Finding buried treasures is a fun activity to do on your own or in a group. In this activity, we will be finding a buried treasure near Castle Rock with Ahmed and Vanessa. The assignment reads; 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? (Dugopolski, 2012, p. 371) In this problem, we will use the Pythagorean Theorem which says that when a triangle has a right angle of 90 degrees, and squares are made on each of the three sides, then the biggest square has the exact same area as the other two squares put together. The Pythagorean Theorem can be written as: a^2 + b^2 = c^2 with “c” being the longest side or otherwise called the hypotenuse of the triangle, and “a” and “b” are the...

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...sure to include all mathematical work and a discussion of how and why this is applicable to your everyday life. --------------------------------------------------------------------------------------------- ASHFORD MAT 221 Week 5 Assignment 5 Pythagorean Quadratic For more course tutorials visit www.tutorialrank.com To complete the following assignment, go to this week's Assignment link in the left navigation. Pythagorean Quadratic Read the following instructions in order to complete his assignment, and review the example of how to complete the math required for this assignment, and review theexample of how to complete the math required for this assignment: • Read problem 98 on page 371 of Elementary and Intermediate Algebra. Along with factoring, this problem also requires the use of the Pythagorean Theorem to solve it. o On your scratch paper draw a diagram which includes the location of Castle Rock and the dimensions of a triangle with the given number of paces. Seeing the relationship of the sides and where the right angle is will help you know how to apply the Theorem. You may include the diagram in your paper but are not required to do so. o Write the equation first by inserting the given binomials into the Pythagorean Theorem. Once you have your equation written, go ahead and solve it using the methods from section 5.6 of Elementary and Intermediate Algebra....

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