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What is the definition of "formal groups"?

Group properties include the algebraic properties of the associative property, the identity property and the reciprocal property in addition to closure. Closure simply means that there is no operation a person can perform using the elements of the group that would produce a sum, product, dividend or other result that is outside the group. Formal groups satisfy all the constraints put on Lie groups, but they are expressed algebraically, in terms of numbers and equations, rather than geometrically, as points on a figure.

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What is expanded notation?

There are two ways to display numbers in expanded form. The first method involves replacing all the numbers that come after a digit with 0 then adding them all together. For example, 5,872 will be written as 5,000 + 800 + 70 + 2. Five is in the thousands position because it is written as 5,000 while 8 is in the hundreds position because it is written as 800. Tens and 1s follow.In the second method each place value is written as a power of 10. In this case, 5,872 will be written as (5 x 1,000) + (8 x 100) + (7 x 10) + (2 x 1). Exponents can also be used to represent the powers; for example, (5 ..

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What is the square root of 51?

The negative version of this number is also the square root of 51, since multiplying a negative number by itself produces a positive product. Like the positive answer, the negative root is also an irrational number. Irrational numbers, so called because they cannot be expressed as a ratio of two integers, may seem rare or exotic. In fact, all integers that are not perfect squares have irrational square roots.

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How many right angles does a square have?

A square is a special kind of rectangle. A rectangle is a quadrilateral that has four right angles and two pairs of equal opposite sides. Since the four sides of a rectangle are not required to be equal, all squares are rectangles, but not all rectangles are squares.\nA square can also be classified as a rhombus. A rhombus is a quadrilateral with four equal sides and two pairs of equal opposite angles. However, since these angles are not required to be right angles, then all squares are rhombuses, but not all rhombuses are squares.

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What is a numerical expression?

In math, there are two types of equations: those with variables and those without variables. An equation with variables is an algebraic expression, such as x - 5 = 2. When an equation does not have variables, it is a numerical expression, such as 7 - 5 = 2. These are both essentially the same equation, but one is a numerical expression, and the other is an algebraic expression.

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What is the definition of "eutectoid"?

About.com describes "eutectoid" as a mixture of two or more constituents which forms on cooling from a solid solution and transforms on heating at a constant minimum temperature. For example, eutectoid steel contains approximately 0.83 percent carbon. The term "eutectoid" derives from the Greek word "eút?kt" in the late 1800s, which means easily melted or dissolved.

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What is the square root of 72?

To figure this problem without a calculator, first identify the two nearest perfect squares that surround the number 72. A perfect square is a number that can be divided by a whole number and yield the same whole number. For instance, 25 divided by 5 equals 5. So the square root of 25 is 5. Other perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 36 (6 x 6) and 49 (7 x 7).\nIn the case of 72, the numbers are 8 and 9. Multiplying 8 by 8 gives you 64, and multiplying 9 by 9 results in 81. 72 falls in between. Next, divide 72 by either 8 or 9. For instance, 72÷8=9. Now, determine the aver..

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What are some tips for solving math word problems?

First readings help students translate text into the relevant numeric equations. Students must represent unknowns using different letters to avoid confusion. Students should then list the variables identified and attach them with any units of measure mentioned. They should think of any shortcuts applicable in solving the problems, taking precaution to illustrate all required procedures through writing. It helps to look for key words such as "sum," "less than," "difference" and "take away" to identify the required operations.\nStudents should draw math word problems to enable proper flows of id..

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What are some math addition facts?

The commutative property states that the order in which two values are summed does not affect the resulting sum. For example, 2 + 3 = 5 and 3 + 2 = 5.\nThe associative property states that when three or more numbers are being grouped before addition, the grouping order does not effect the sum. For example, (2 + 3) + 4 = 9 and 2 + (3 + 4) = 9.\nThe distributive property states that the sum of two numbers multiplied by another number is equal to each addend multiplied by that third number and then summed. For example, 6 x (2 + 1) = 18 and 6 x 2 + 6 x 1 = 18.\nThe identity property states that th..

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What is the function of the numerator in mathematics?

The denominator is the number below the fraction line. It tells into how many equal parts the whole has been divided.\nFor example, when dividing an object into thirds, the fraction representing that object has a denominator of three. Its numerator depends on how many of the divided pieces the fraction represents. If it represents all three of them, the numerator is three and the fraction is three-thirds. If it expresses only one of the pieces, the numerator is one and the fraction is one-third.

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