Term
| additive property of inequality |
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Definition
| For any real number a, b, and c, if a>b, then a+c>b+c and c+a>c+b |
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| angles on opposite sides of a transversal |
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| a property of real numbers that notes that, for any real numbers a, b, and c (a+b)+c=a+(b+c) and (ab)c=a(bc) |
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Definition
| a property of real numbers that notes that, for any real number a and b,a+b=b+a and ab=ba |
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Definition
| a number of the form a+bi, where a and b are real numbers and i is the imaginary numbers satisfying the equation i^2=-1. The letter a represents the real part of the complex number, and the letter b represents the imaginary part of the complex number. |
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Term
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Definition
irrational number of the form a+/-bsquare root of c
or complex numbers in form a+/-bi whose product is always a rational number |
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Definition
| angles located in matching positions when two lines are cut by a transversal. also located in matching positions of similar triangles |
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| process of reasoning logically from clearly stated premises to a conclusion |
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Term
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Definition
| in reference to a function, the variable whose value depends on the value assigned to another variable, called the independent variable. For example in the function y=2x+3, y is this |
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Term
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Definition
| in reference to a function the variable whose value can be chosen. For example, in the function y+2x+3, x is this |
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Definition
| a relationship between two variable such that their ratio is constant. For example, the equation y=kx defines this between x and y where k is the constant of proportionality. |
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Term
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Definition
| for a quadratic equation of the form ax^2+bx+c, the expression b^2-4ac, whose value determines the nature of the equation's solutions. |
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Definition
| a property of real numbers that notes that, for any real numbers a, b, and c, a(b+c)=ab+ac and (b+c)a= ba+ca |
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Definition
| a mapping between two sets that associates w/ each element of the first set a unique (one and only one) element of the second set |
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Definition
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Definition
| in reference to a function, the variable whose value can be chosen. For ex. in the function y=2x+3, x is this |
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Definition
| a relationship in which a single quantity depends directly upon two or more other quantities and a constant of proportionality. |
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Definition
| line that intersects a curve at only one point |
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Term
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Definition
| a line that intersects a circle at two points |
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Term
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Definition
| a discription of the position of a point in the plane determined by the length segment from the origin to the point and the angle that the line segment makes w/ the positive x-axis |
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Definition
| a graphical designation of points in space using numbers to denote the distance from the axes. |
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| a statement that is accepted as true w/out proof, i.e., an assertion that is not proved. also called an axiom |
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Term
| Rationalizing the denominator |
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Definition
| Changing a nonrational denominator in a fraction into a rational number or expression by multiplying the fraction by an appropriate form of unity. |
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Term
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Definition
for any real numbers a, b, and c
if a is greater than b and b is greater than c then a is greater than c
if a is less than b and b is less than c then a is less than c
if a is equal to b and b is equal to c then a is equal to c |
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Term
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Definition
for any two real numbers a and b, exactly one of the following is true
a is less than b
a equals b
or
a is greater than b |
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Term
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Definition
| the set of numbers used to count objects or things; also called the positive integers, i.e., the members of the set 1,2,3... |
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Definition
| the set of numbers that includes all members of the set of rational numbers and all members of the set of irrational numbers |
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Definition
| any number that can be written a a quotient of integers (division by zero excluded) |
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Definition
| any number that cannot be written as a quotient of integers. For example, the number pi |
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Term
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Definition
| any member of the set ...-4,-3,-2,-1,0,1,2,3,4... |
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