Chapter 1

second

A quadratic equation is sometimes called a __________-degree equation.

closed interval

A(n) __________ is denoted [a,b].

solution

An admissible value for the variable that makes the equation a true statement is called a(n) __________ of the equation.

extraneous

An apparent solution that does not satisfy the original equation is called a(n) __________ solution.

linear; first

An equation of the form ax+b=0 is called a(n) __________ equation or a(n) __________-degree equation.

identity

An equation that is satisfied for every value of the variable for which both sides are defined is called a(n) __________.

x-coordinate; y-coordinate

If (x,y) are the coordinates of a point P in the xy-plane, then x is called the __________ of P and y is the __________ of P.

{a,b,c,d,e,i,o,u}

If A={a,e,i,o,u} and B={a,b,c,d,e}, what is AUB?

negative

If each side of an inequality is multiplied by a(n) __________ number, then the inequality symbol is reversed.

negative

If the discriminant of a quadratic equation is __________, the equation has no real solutions.

midpoint

If three distinct points P, Q, and R all lie on a line and if d(P,Q) = d(Q,R), then Q is called the __________ of the line segment from P to R.

real; imaginary

In the complex number 5+2i, the number 5 is called the __________ part and the number 2 is called the __________ part.

0

Multiplying both sides of an equation by any number except __________ results in an equivalent equation.

uniform motion

Objects that move at a constant speed are said to be in _________.

0

On a real number line the origin is assigned the number __________.

fourth

Powers of i repeat every __________ power.

interest

The money paid for the use of money is __________.

imaginary unit

The number i is called the __________.

mathematical modeling

The process of using variables to represent unknown quantities and then finding relationships that involve these variables is referred to as __________.

True

True or False. All real numbers are complex numbers.

False

True or False. Factoring can be used to solve only quadratic equations or equations that are quadratic in form.

True

True or False. If an object moves at an average speed r, the distance d covered in time t is given by the formula d=rt.

False

True or False. Quadratic equations always have two real solutions.

True

True or False. Radical equations sometimes have no real solutions.

True

True or False. Rational numbers and irrational numbers are in the set of real numbers.

True

True or False. Some equations have no solution.

True

True or False. The absolute value of a negative number is positive.

False

True or False. The amount charged for the use of principal for a given period of time is called the rate of interest.

False

True or False. The conjugate of 2+5i is -2-5i.

False

True or False. The distance between two points is sometimes a negative number.

True

True or False. The midpoint of a line segment is found by averaging the x-coordinates and averaging the y-coordinates of the endpoints.

False

True or False. The point (-1,4) lies in quadrant IV of the Cartesian plane.

True

True or False. The principal square root of any nonnegative real number is always nonnegative.

True

True or False. Two triangles are congruent if two angles and the included side of the one equals two angles and the included side of the other.

False

True or False. When solving equations using a graphing utility, the solutions are always exact.

2i

What number is the principal square root of -4?

division

Which operation involving complex numbers requires the us of a conjugate?

quadrants

the coordinate axes divide the xy-plane into four sections called __________.