Properties of Real Numbers
Interval Notation
Exponents and Radicals
Simplifying Expressions
Lines
Analytic Geometry
100
Property of Real numbers being demonstrated with 7+3=3+7
What is the Commutative Property of Real Numbers?
100
The interval notation equivalent to
What is [a,b]?
100
An exponential way to write 3\cdot3\cdot3\cdot x.
What is 3^3x?
100
4x^2 and -2x^2 are called this when we can combine the coefficients.
What are like terms?
100
Given two points (x_1, y_1) and (x_2,y_2) this is the slope.
What is (y_2-y_1)/(x_2-x_1)?
OR
What is (y_1-y_2)/(x_1-x_2)?
100
The quadrant where the x-coordinate is positive and the y-coordinate is negative.
What is Quadrant IV?
200
Property of real numbers being displayed with (2\times 4)\times 5 = 2\times (4\times 5).
What is the associative property of real numbers?
200
The interval notation equivalent to
What is (-\infty, 0) ?
200
A positive number x is said to written this form if it is expressed as x=a \times 10^n where 1 \leq a < 10 and n is an integer.
What is scientific notation?
200
The acronym FOIL is used to multiply these two types of expressions together.
What are binomials?
200
Two nonvertical lines are parallel if these two conditions are satisfied.
What are
1) the lines have the same slope, and
2) the lines have different y-intercepts?
200
The exact distance between (1,2) and (-3,-4) , simplified of course.
What is 2sqrt(13)?
300
This property is crucial to real numbers since it describes the way addition and multiplication interact with each other.
What is the distributive property?
300
The interval notation equivalent to a<x\leq c.
What is (a,c]?
300
The exponent used to represent
What is 3^(1/3)?
300
The domain of the algebraic expression
sqrt(x)/(x-5)
What is [0,5)\cup(5,\infty)?
300
Two lines are perpendicular if they have this condition.
What is the product of the slopes is negative one?
300
The midpoint of the line segment with endpoints (1,2) and (-5,-7).
What is (2,-2.5)?
400
If a and b are real numbers, then d(a,b)=|b-a| represents this.
What is the distance between the points a and b ?
400
Interval notation for x \ne a
What is (-\infty, a)\cup(a,\infty)?
400
sqrt(x^2) simplifies to this.
What is |x|?
400
The least common denominator for 3/(x-1) +x/(x+2) in factored form.
What is (x-1)(x+2)?
400
Given the line Ax+By=C the perpendicular line would be this written in standard form.
What is Bx-Ay=C?
400
Given (x-1)^2 +(y+2)^2 = 16 these are the center and radius of this circle.
What are the radius is 4 and the center is located at (1,-2)?
500
The property of real numbers being displayed here:
|x+y| \leq |x| + |y|.
What is the Triangle Inequality?
500
Translation of the statement: "all values less than 3 and all values between 3 and 5 inclusive", most efficiently.
What is (-infty, 5] ?
500
Process demonstrated here:
2/sqrt(3)\cdot\sqrt(3)/sqrt(3)
What is rationalizing the denominator?
500
Simplify this expression:
(1+x/y)/(1-y/x)
What is (x(x+y))/(y(x-y))?
500
A hose is being used to fill a swimming pool. The water depth y (in feet) in the pool t hours after the hose it turned on is given by y=1.5t+2 . What do the slope any y-intercept represent?
What is "the slope represents an increase of 1.5 feet per hour. And the y-intercept represents the water's initial depth was 2 feet"?
500
This is the type of symmetry y=x^3-9x^2 displays.
What is symmetry to the origin?