The Tutoring Center, Rosenberg, TX

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05/23/2017
Vertical Angles

You must be familiar with a few lessons from geometry. Know that vertical angles are congruent. When two lines intersect to form an X, the angles formed opposite each other are called vertical angles. The two adjacent angles will always add up to 180 degrees, and the vertical angles are always equal to each other.

Perpendicular Lines

Two lines that intersect at a 90 degree angle are called perpendicular. The slopes of these lines are negative reciprocals of each other. If the slope of one is 3, the slope of the other is -1/3.

Negative Exponents

Some variables will have negative exponents. A negative exponent is the reciprocal of the number to the exponent. For example 2^(-2) is 1/(2^2) or 1/4.

Fractional Exponents

A fractional exponent is the same as the root of the fraction's denominator. 16^(1/2) is the square root of 16, or 4. 27^(1/3) is the cube root of 27, or 3. If the numerator is not 1, then you take the number to the numerator's power and then the root of the denominator. For example, 4^(3/2)=√(4³)=√64=8. In general, the equation looks like this: 

Factor Tree

You should know how to build a factor tree and perform a prime factorization of a number. A prime factorization means to reduce all the number's factors to prime numbers. The prime factors of 18, for example, are 3, 3, and 2.

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