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What is the difference between standard, expanded and word form in math?

Examples of numbers written in standard form are "543" and "1,351." Standard form is the numerical form most often used in equations and general mathematics. Examples of numbers written in word form are "twelve," "five hundred forty-three" and "one thousand five hundred fifty-one." All compound numbers between 21 and 99 are hyphenated when written in word form. The word "and" is not necessary when writing out whole numbers; it is necessary when writing out a number with digits to the right of a decimal point.\nExpanded form consists of breaking down a number by degrees of place value. For exam..

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What is a dependent variable?

Independent and dependent variables are used both in mathematics equations and in the application of mathematics for scientific experimentation. In a scientific experiment, the independent variable is manipulated to demonstrate its impact on the dependent variable.\nFor instance, the amount of rainfall provided to two identical plants could be manipulated so that one plant received a rainfall value of one inch per week and the other plant received a rainfall value of two inches per week. Then, the plants could be measured for growth. The rainfall would be the independent variable while the gro..

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How do you factor trinomials of the equation ax2+bx+c?

Factor out the greatest common factorIf the quadratic has a greatest common factor, then factor it out and write it to one side. This number does not disappear just because it is factored out. For example, if given the quadratic 3(x^2 - 15x + 18), the greatest common factor is 3. The quadratic now looks like x^2 - 5x + 6.Choose a pair of factorsFind a pair of numbers that, when added, equal "b" and when multiplied equal "c." In the case of the quadratic 3(x^2 - 5x + 6), "c" is equal to 6 and has factors of 1, 2, 3 and 6. The factors 2 and 3 add to 5. However, "b" is equal to negative 5. The so..

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Why do we use standard deviation?

Data is considered to have a normal distribution if it follows the standard bell curve when plotted. If data has a normal distribution, about 68 percent of all data falls within one standard deviation from the mean, or average. Additionally, 95 and 99.7 percent fall within two and three standard deviations, respectively.\nStandard deviation is also used to measure uncertainty. Polling companies express the standard deviation in terms of percentage points, and use it to determine how closely a sample population represents the whole of that population. This is how 51 percent to 49 percent on a p..

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How do you calculate the size of an angle with a calculator?

Finding the dimensions of an angle numerically requires that some basic information be known about the angle, or the two line segments or rays which compose it. The simplest method is to use lengths of two sides forming the angle, and then calculate the dimension using the inverse cosine function. The inverse cosine function takes as input the two side lengths for the line segments of which the angle is composed. Other, more difficult functions require the addition of another line segment to solve the problem with a calculator.\nObtaining the side lengths manually can present a problem, as emp..

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How does "X" vary from "Y"?

Essentially, "X" and "Y" are just arbitrary letters that mathematicians use as regular placeholders in equations to make things more consistent. This allows mathematicians to communicate with one another easily. The notational standard ensures that X = 3Y - 2 can't be confused with the functions Y = 3X - 2 and Y = (X + 2)/3.

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What is an undefined slope?

In a vertical line, the slope calculation results in a number divided by zero, because by definition, a vertical line has the same x values for every point on the line. Any number divided by zero is by necessity undefined, as there are an infinite number of solutions to the equation.\nThe slope of a line is also called its rise over its run. When graphed, the rise is the amount that the line goes up or down, and the run is how far right or left the line goes. The calculation for slope is the rise of the line divided by the run of the line. A line with a positive slope goes from lower left to u..

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What do you call a polygon with four sides, none of which are the same size?

A polygon that does not have equal sides has a special name, an irregular polygon. However, that name can be applied to a polygon that has any number of sides, as long as the sides don't match up. Therefore, a polygon with 12 sides could be an irregular polygon. Alternatively, an irregular polygon can be one that does not have matching angles, such as a concave polygon, whether or not pairs of the sides are equal in length.

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What are some tips for solving differential equations?

To classify an equation, a person must learn which symbols are constants and which symbols vary. Authors write equations in different ways that often mean the same thing, so one tip for solving differential equations is to study the various ways that authors write them. For example, some textbooks use a modified format for lengthy exponential numbers, and other textbooks only use the standard format.\nLike solving basic integrations, to solve a differential equation, a person first finds the general solution and then substitutes various numbers to find particular solutions. Finding the general..

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Why are triangles so strong?

Edges can be made much stronger than connections. Triangles hold large loads without collapsing or having their structure altered. Triangles are the only polygons that have this characteristic. For instance, triangles have three connections, while squares have four. When forces are applied to a square, a square is more prone to lose its shape. Engineers often add a diagonal through the middle of a square, effectively turning it into two triangles and making it stronger. Triangles are the fundamental building blocks of many contemporary structures. Their strong, inflexible structure makes them ..

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