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What are intersecting lines?

A line is defined as a geometrical object that is straight as well as infinitely thin and infinitely long. A line segment is defined as a straight line demarcated by two specific points. Although a line is defined as infinite, when a line segment is the subject, nothing extends beyond either of the identified points at the ends of that segment. A line segment has a midpoint that divides it into two equal parts.

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What are some good examples of math word problems about fractions?

Other than the obvious advice given to keep any educational problems at the appropriate level, problems that tie closely to the concepts the students are studying are preferable. Word problems with fractions about things not easily divided are obviously less preferable. For example, five friends splitting two pizzas makes far more sense than five siblings splitting two ponies. Even the wording chosen for particular objects in the stories can either engage or alienate students.

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How many ways can you make 25 cents in change?

By combining pennies and nickels, 25 cents can be made out of 20 pennies and one nickel, 15 pennies and two nickels, 10 pennies and three nickels, or five pennies and four nickels. Using dimes and pennies, 25 cents in change can be made from 15 pennies and one dime or five pennies and two dimes. Using a combination of nickels and dimes, 25 cents in change can be made from two dimes and one nickel or one dime and three nickels.\nCombining nickels, pennies and dimes, 25 cents worth of change can be made from five pennies, two nickels and one dime or 10 pennies, one nickel and one dime. Using onl..

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What is a math genius?

An individual rising to the level of genius is rare. In the 1950s, intelligence quotient testing was used to determine if someone qualified as a genius. However, as of 2014, a scientific consensus exists that while IQ tests may differentiate average people from gifted people, they are unable to differentiate levels of giftedness. Therefore, they are not an accurate measure of genius.\nThe recognition of genius typically occurs over time and after years of study in a specific field. The development of a gifted child into a genius in a specific field requires adequate education. It also requires..

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How many vertices does a rectangle have?

The geometric definition of a vertex is a point in a geometric solid where three or more sides intersect or where two sides intersect in a plane figure. Therefore, a vertex is a corner in a rectangle. There is another definition of a vertex, which is defined as a point farthest from the base. However, a rectangle may have many bases as opposed to a triangle, which has a side that is primarily used for the base.

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How do you find percent increase?

For example, consider Katie, who last year invested $100 in stock shares that are now valued at $145.\nTo calculate the percent increase of her investment, she would simply subtract her initial investment, $100, from the current value, $145, to determine an increase of $45.\nThis increase is then divided by the amount of the original investment, resulting in a quotient of .45, which equals 45 when multiplied by 100.\nTherefore, Katie's investment saw an increase of exactly 45 percent.\nIn the same way, a number value less than the previous one indicates a decrease, and may be expressed as..

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What are some methods for solving natural log equations?

To begin solving the natural log equation, look for terms that include the natural log of one or the natural log of e (the base of the natural log, which is approximately equal to 2.718). The natural log of 1 is zero, and the natural log of e is one; these terms can be canceled out of the equation. Next, look for sums and differences of logarithms. The sum of two logarithms simplifies to the logarithm of the product of the two arguments. The difference of two logarithms simplifies to the logarithm of the quotient of the two arguments. Logarithms with an exponent in the argument are simplified..

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How do you simplify algebraic expressions?

Remove any common factors to bring the expression to lowest termsFor example, start with the equation 4x ^2 + 100 = (x + 3)/(x - 5); 4 is a common factor in both 4 and 100, so remove it by using the distributive property. The result ends up as 4(x^2 + 25). Note that not all expressions will have factors to remove.Simplify polynomialsPolynomials are expressions with one or more degrees of variable. In the example expression, (x^2 + 25) can be further simplified into (x - 5)(x + 5). When you multiply it by the FOIL method, the middle terms cancel out. This expression is now in simplest form, so ..

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What formula do you use for the integral of inverse tangent?

Using integration by parts for the integral of inverse tangent, the variable u is set to arctan(x), which means that the derivative of u, expressed as du, is set to 1/((x^2)+1). The derivative dv is set to dx, which when integrated, sets v equal to x. The integral of arctan(x) is rewritten as x * arctan(x) minus the integral of x/((x^2) + 1) dx. Integrating v du gives u = (x^2) + 1. The derivative of u, du, is 2xdx, from which the formula x dx = du/2 can be derived.\nFrom those values, the integral of (x/(x^2) + 1) dx is evaluated as 1/2u du = (1/2) ln |u| = (1/2) ln |(x^2) + 1|. In these form..

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What is the domain of a function?

In a linear function, the range is all values of x. However, certain functions are undefined for some values of X. In those functions, the range is all values of x except those that make the function undefined. For example, where y equals a radical function of x, the range is all values of x that make the equation under the radical positive. Another example is where y equals a fraction where x is in the denominator. In that case, the range is all values of x that yield a nonzero denominator.

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