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What did Pythagoras discover?

Pythagoras was an Ionian Greek philosopher, mathematician and religious scholar. His greatest contribution to mathematics is the Pythagorean theorem. The theorem states that in a right triangle, the area of the square of the hypotenuse, which is the side across from the right angle, is equal to the sum of the square of the areas of the other two sides. Despite the theorem bearing his name, Pythagoras was not the first person to use this calculation. This computation was in use in Mesopotamia and India long before Pythagoras lived. There is some speculation that Pythagoras and his students are ..

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Why are high school math word problems important?

The more problematic the tasks presented by such word problems are, the more students can build on concepts and rules that they already know. Some researchers have also developed a set of criteria that problems should meet in order to effectively teach the application of concepts already known. Problems should contain useful mathematics and require high-level thinking to solve. They should allow for multiple solution strategies that can be applied and defended both verbally and mathematically. Problems also should promote student discussion about other mathematical concepts.\nAdding to the imp..

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What is the square root of 135?

Each positive number has a positive and negative square root. These two square roots have the same absolute value. When the negative root is multiplied by itself, the product becomes positive. In the case of the square roots of 135, both (3 * sqrt(15))^2 and (-3 * sqrt(15))^2 equal 135. Note that the term "sqrt" represents taking the square root of the number.\nThe reason that the positive square root of 135 simplifies to 3 * sqrt(15) is because sqrt(135) = sqrt(9 * 15) = sqrt(9) * sqrt(15) = 3 * sqrt(15). The square root of 15 has no factor greater than 1 that is a square of another integer,..

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How do you solve polynomial word problems?

Determine what is unknown and knownFor example, if asked to find the perimeter of a rectangle whose area is equal to 55 square meters and whose length is 1 meter less than twice the width, the unknown is the width. The width can be assigned the variable x. The known variables in this problem are the area and length. The reason the length is considered a known is because it is directly related to the width. The length can be expressed as 2x - 1.Determine any equations to be usedAlthough the problem is asking for the perimeter, the equation for perimeter cannot be used to determine the value of ..

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What does "average" mean in math?

The mean is obtained by dividing the sum of scores by the number of scores. If the sum of the weights of 10 students of a class is 520 kilograms, then the average, or mean, weight of these students is 520 divided by 10, which equals 52 kilograms. The median is also an average, and it is the middlemost score in a given set of scores. The mode is the score that has the highest frequency or the score that occurs the most in a set of scores.

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How many numbers between one and 100 are divisible by three or seven?

To work out how many numbers between one and 100 are divisible by three, divide 100 by three and round the result down to the nearest whole number. This is 33. Work out how many numbers between one and 100 are divisible by seven in the same way. This result is 14. Subtract the number of numbers that are divisible by both three and seven, of which there are four: 21, 42, 63 and 84.

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How do you make Bisquick scones?

Preheat the oven to 450 degrees Fahrenheit, and mix 2 1/2 cups Bisquick with 1/4 cup sugar. Cut 1/4 cup unsalted butter into the mixture until the butter forms pea-size pieces. In a separate bowl, beat 2 eggs and 1/4 cup milk together, and combine the eggs and milk with the dry ingredients. Mix to form a dough. Fold 1/2 cup blueberries into the dough if desired, and place the dough on a floured surface.\nRoll the dough to 3/4-inch thickness, cut the dough into four squares, and cut each square into two triangles. Place the triangles on a baking sheet, and bake the scones for 15 minutes at 450 ..

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How do you write the Roman numeral for 16?

The basic Roman numeral units for numbers through 50 are as follows: I is equal to 1, V is equal to 5, X is equal to 10 and L is equal to 50. The number 16 is equal to 10 + 5 + 1, or XVI. A letter may not appear more than three times in succession. When a letter of lesser value directly precedes a letter of greater value, the one of lesser value is subtracted from the larger number. For example, the number 19 is XIX, where the first X is equal to 10 and the IX represents 10 - 1, for a total of 19.

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How do you explain a gradient vector field in calculus?

A gradient vector is the gradient of a function, which represents the directional change in a scalar function. It is crucial to determine if a vector field is conservative, as this makes it easier to find out whether the field is a gradient vector field. The easiest way to determine whether a vector field is conservative is by finding its potential function, which demonstrates that a vector field is conservative. Another method used to determine if a vector field is conservative is by demonstrating that all the infinite closed curves in a vector filed have no circulation, which means the resul..

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How do you calculate weighted grades?

Start with a standardEvery weighted grade system needs a point of reference. Other grades can be compared to that standard. For example, an essay in an English class might be worth 100 points and not weighted, or it could be described as weighted at a value of 1.0. A 91 percent grade on the assignment appears as 91 points when the weighted grade is calculated.Assign weight to assignmentsTeachers may want to grade a project out of 100 so they can easily input a percentage, but they might want that project to be valued higher than an essay. In that case, the project might be weighted at 3.0, whi..

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