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What is dilation in geometry?

In dilations, lines that are parallel in the original figure remain parallel in the resized object. Each point that was on the original line moves to the dilated line, including the midpoint. The dilated figure retains the same order for labels as the original figure. Artists use dilations when painting landscapes in perspective. They reduce the size of each object by the same amount while keeping the angles the same. Maps are dilations that use a scale factor to condense information onto easy-to-handle sheets of paper.

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What is 45 degrees in radians?

A circle has 360 degrees and 2(pi) radians, and therefore, 180 degrees is equal to pi radians. Using these ratios, the easiest way to convert degrees to radians is to multiply the number of degrees by (pi/180). In the above example, 45 times (pi/180) is equal to (pi/4). The same formula can be used for other common degree calculations. For example, 30 degrees is (pi/6), 60 degrees is (pi/3) and 270 degrees is (3pi/2). To convert the answer to decimal, just replace pi with 3.14. However, in degree/radian calculations, it is customary to just leave pi as is without converting to decimal.

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How do you divide decimals?

Move the decimal in the divisor as many places to the right as necessaryThe objective is to make the number in question a whole number. After doing this, move the decimal in the dividend the same number of places. The ratio is the same. For example, if you are dividing 72.9 by 8.1, the decimal point needs to move a place to the right and yield 729/81.Proceed with long divisionWrite the number of times the divisor goes into the dividend, then multiply this quotient by the divisor, and subtract the result from the dividend. Repeat until all digits have been accounted for. In the example, this yi..

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Who invented geometry?

Euclid is the author of "The Elements." This series of 13 books covers number theory, irrational numbers, plane geometry and solid geometry. The series once sold more copies than any other book, other than the Bible. Euclid proved that a person can draw a straight line between any two points and that all right angles are equal, among other theories. He also organized geometric ideas. Euclid wrote other works as well, including "Phaenomena" and "Data."

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What is the unit used to express volume?

In the U.S., two measurement systems, the U.S. System and the metric system, are used. The SI system, which was introduced for worldwide standardized measurements, is based on the metric system. Gallon, quart, pint, fluid ounce and cup are part of the U.S. System. One gallon is equivalent to 4 quarts, while 1 quart is equivalent to 2 pints. One pint is equivalent to 16 fluid ounces. Liter is part of the metric system. One liter is equivalent to 1 cubic deciliter.

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What figure has five faces, eight edges and five vertices?

The sides of a three-dimensional solid are called its faces. Since a square pyramid has four triangular sides connected to the perimeter of the fifth square side, this solid is said to have five faces. Edges are places where two sides of a three-dimensional solid meet. Vertices are where three sides of a dimensional solid meet and are often called corners.

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How is slope used in real life?

Slope is very important in the construction field because it often dictates the best way to complete a project. Special building materials are used for low-slope roofs, so a construction worker must know the slope of the roof before beginning a shingling project. The slope of a road affects water runoff, so civil engineers and construction workers must plan accordingly. Most municipalities have rules regarding the minimum slope of their roads.\nSkiing enthusiasts pay special attention to the slopes of their favorite trails. The greater the slope of a trail, the more challenging it is. Knowing ..

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Where did Roman numerals come from?

The seven basic letters or symbols used in Roman numerals include I, V, X, L, C, D and M. Historians believe that the ancient Romans started using Roman numerals because they needed a common method for counting. The counting system was devised based on the human hand's 10 fingers.Each letter or symbol has a specific meaning in the Roman numeral system. A single line, represented by what we know as an "I" was used to reference one finger or one unit. A "V" symbol represented five fingers, while an "X" was representative of two hands or 10 fingers. The Roman numeral M, which represents 1,00..

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What are triangular numbers?

The first element in the first row represents the first triangular number. The three elements in the first two rows constitute the second triangular number. They are added to the three elements in the third row to obtain the next triangular number, which is six. Those six are added to the four points in the fourth row, resulting in a total of ten, which is the next triangular number. This same pattern continues to repeat itself so that the first twelve triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 and 78.

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What is the square root of 40?

Numbers such as 4, 9, 16 and 25 are perfect squares. Their square roots are 2, 3, 4 and 5, respectively. However, the prime factors of 40 are 2 x 2 x 2 x 5. This indicates that 40 is not a perfect square, as each prime factor must be present in multiples of 2 for a number to be a square. The prime factors of 36 are 2 x 2 x 3 x 3, and this shows that the square root of 36 is 2 x 3, which equals 6.

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