Algebra full 1-7
Which of the following numbers is irrational? A. 0.78 B. 0.303030... C. square root 9 D. 0.3841697...
D. 0.38416971
In the expression 4/5 + _____, what number would result in a rational sum? A. square root 5 B. - square root 3 C. 2.5 D. 3/2
D. 3/2 c. 2.5
equivalent equation:
Equations that have the same solution or solutions.
perpendicular
Crossing at a right angle. The symbol means "is _____________ to." If you multiply the slopes of two __________ lines, the result is -1.
law of principle square root
(b½)²=b
The slope of a horizontal line is?
0
1 kilometer ≈ ????? miles
0.62
How many inches are in a foot?
12
How many ounces are there in a pound?
16
1 kilogram ≈ ????? pounds
2.2
1 inch = ????? centimeters
2.54
How many feet are there in 1 yard?
3
How many feet are in 1 mile?
5280
Rational + irrational Irrational + irrational
= irrational.
Term
A ______ may be a single number, a single variable, or a combination of numbers and variables multiplied together.
power
A small raised number that tells you how many times to multiply the base number by itself. It is also called an exponent.
boundary line
A solid or dashed line on a graph that provides a border for the solution set.
variable
A symbol that represents an unknown value or changeable quantity.
input-output table
A two-column table whose first column contains input values of a function and whose second column contains output values. The values in the first column are elements of the function's domain, and the values in the second column are elements of the function's range.
function notation
A type of writing that uses a letter to name a function and places parentheses around the independent variable. The notation f(x) is pronounced "f of x."
constant
A value in a formula that does not change (unlike a variable).
conversion ratio
A way to compare two equivalent measurements. It is equal to 1.
integer
A whole number or its opposite.
Explicit Formula for a Compound Interest Sequence
A(n) = P (1 + i)^n - 1
Explicit Formula simple interest
A(n) = P + (n - 1)(i*P)
Which of the following numbers is rational? A. 0.78 B. 0.303003000... C.square root 6 D. 0.3841697...
A. 0.78
Elimination method
Add or subtract the equations from each other. Multiply one by a number that will help cancel out a variable. Multiply what ever you choose by the equation. Add or Subtract each Equation together. Solve using algebra. Plug your answer back into a original equation and solve for the other variable.
Sum
Addition
literal equation
An equation with at least two variables, or with constants represented by letters
fractional exponent.
An exponent in fraction form.
exponential expression
An expression that involves an exponent. The expression may contain variables, which may be the base or the exponent.
exponential expression:
An expression that involves an exponent. The expression may contain variables, which may be the base or the exponent.
When a rational number and an irrational number are multiplied, the product is always_______________.
An irrational number.
inverse operation
An operation that reverses (undoes) the action of another operation.
Integers
Any positive or negative number that is not a fraction or a decimal.
relation
Any set of input and output values. In a _____________, a single input gives back one or more outputs.
relation
Any set of input and output values. In a relation, a single input gives back one or more outputs.
Describe the graph of a system of inequalities with no solution.
Parallel lines.
When two rational numbers are multiplied the product is always _______________.
Rational
The real numbers are made up of _____________ and _____________ numbers.
Rational and irrational numbers.
Every fraction can be written as a _____________ decimal or a _____________ decimal.
Repeating terminating
y2-y1/ x2 - x1
Slope formula
variables
Symbols that represent unknown or changeable values. A variable is usually represented by a lowercase, italicized letter, such as x or y.
like terms
Terms in an algebraic expression that have the same variables raised to the same powers.
elimination
The adding or subtracting of two equations to remove one of the variables. Elimination is a step in solving a system of equations.
accuracy
The closeness of an estimate or measurement to the actual value.
common ratio
The constant ratio between any two consecutive numbers in a geometric sequence.
common difference
The constant value, d, between any two consecutive numbers in an arithmetic sequence.
half plane
The graph of a linear inequality with two variables. If the inequality sign is < or >, the line is dashed to show that it is not included in the solution. If the inequality sign is or , the line is solid to show that it is included in the solution.
run
The horizontal distance between two points on a line. It equals the difference between the x-coordinates of the two points.
precision
The level of exactness of a measurement.
rate of change
The measure of how much a dependent variable y changes for a given change in the independent variable x. If the graph of the function is a straight line, the __________________ equals the slope of the line.
Ohm's Law
V = IR
constants
Values in a formula that do not change (unlike variables)..
How do you find the solution of a system from a table?
We look for the area where the Y values are the same, that is the Y coordinate. The X coordinate, was the value of X that was plugged in to get the same Y values.
Which of these numbers is a rational number? A. 3/4 B. pi C. -square root of 5 D. 6
a. 3/4 d. 6
Rational Numbers can be written in the form
a/b, where a and b are integers and b does not equal 0..
The domain of a function in the form f(x) = b^x is always _________________
all real numbers
Which of these expressions would result in an irrational number? A. 12/5 + 6/8 B. - 3/7 x square root 5 C. pi + 3 D. 1/2 x 7/11
b. -3/7 x square root 5 c. pi + 3
The graph of f(x) = bx will always contain the point (1, b), where b is the
base of the expression.
converting Fahrenheit to Celsius
c= 5/9 (f-32)
If 0 < b < 1, then the function
decreases.
quotient
divide
Irrational Numbers do not
end or repeat.
2x + 3 = 15 and 2x = 12 are?
equivalent equations
If b > 1, then the function
increases.
When a whole number is not a perfect square, its square root is ___________
irrational
what does the M in y = mx +B stand for?
it stands for Slope
Mixed numbers, Integers, Repeating decimals, Fractions with integer numerator and non-zero integer denominator, and Terminating decimals are______________ _____________________
rational numbers.
The Irrational numbers are all?
real numbers that cannot be written as rational numbers.
Difference
subtraction
the y-intercept of the function f(x) = a • bx is
the point (0, a),
What is the slope of a vertical line?
undefined
When do you use the point-slope equation
when you know one point and the slope.
another known point in the function f(x)=a• bx is
(1, a • b).
expression
A combination of numbers, variables, and operations that does not contain an equals sign or inequality sign. An expression that includes variables is often called an algebraic expression.
terminating decimal
A decimal number with a finite number of digits. The digits of a terminating decimal do not go on forever
mapping diagram
A diagram that shows how a specific relation maps input values to output values.
when two fractions are multiplied the product can always be written as ________.
A fraction
Exponential function
A function that has the form f(x)=A*b^x, where the coefficient is a constant, the base b is positive but not equal to 1, and the exponent x is any number
horizontal asymptote
A horizontal line that a curve approaches more and more closely.
equation
A mathematical statement that says two expressions are equal.
slope
A measure of the steepness of a line. The __________ equals rise divided by run for any two points on the line. A line that rises from left to right has a positive __________. A line that falls from left to right has a negative _________.
slope
A measure of the steepness of a line. The slope equals rise divided by run for any two points on the line. A line that rises from left to right has a positive slope. A line that falls from left to right has a negative slope.
vertical line test
A method for testing whether a given graph is that of a function. If a vertical line can be drawn that intersects the graph at two or more points, then the graph is not a function. If no such line can be drawn, the graph is a function.
base
A number in exponential form. It appears beneath the exponent.
input
A number that is entered into a function. The ___________ variable in a function is the independent variable.
input
A number that is entered into a function. The input variable in a function is the independent variable.
coefficient
A number that multiplies a variable
fraction
A number that names a part of a whole or group, written in the form .
decimal
A number whose value is based on powers of 10.
repeating decimal
A number with a decimal pattern that endlessly repeats itself. A _______________ is a rational number. A bar over one or more digits means that those digits repeat.
xy-plane
A plane formed by a horizontal number line (the x-axis) and a vertical number line (the y-axis) that intersect at the zero point of each. The _________ is also called the Cartesian coordinate system or coordinate plane.
derived rate
A rate that has been converted from a different unit of measurement..
function
A rule that tells how one number depends on another. For each input number, there is exactly one output number.
arithmetic sequence
A sequence of numbers in which the difference between any two consecutive terms is the same. The first term of the sequence is often denoted by a1 and the common difference by d.
geometric sequence:
A sequence of numbers in which the ratio of any two successive terms is equal. Each term can be multiplied by the common ratio to produce the next term in the sequence
geometric sequence
A sequence of numbers in which the ratio of any two successive terms is equal. Each term can be multiplied by the common ratio to produce the next term in the sequence.
pyramidal numbers
A sequence of numbers that are the sum of perfect squares.
Fibonacci sequence
A sequence of numbers that starts with the numbers 1, 1 and for which each subsequent number is the sum of the two previous ones.
real numbers
A set made up of all the numbers on the number line. Any ______________ is either a rational or irrational number.
Exponential decay
A situation in which a Quantity decreases by a common ratio at regular intervals.
exponential decay
A situation in which a quantity decreases by a common ratio at regular intervals.
Exponential growth.
A situation in which a quantity increases by a common ratio at regular intervals
exponential growth
A situation in which a quantity increases by a common ratio at regular intervals..
exponent
A small raised number that tells you how many times to multiply the base number by itself.
parallel
Extending in the same direction and never crossing. ____________ lines have the same slope. Two or more lines are ____________if they do not cross..
Recursive formula fibonacci
F(1) = F(2) =1 F(n) = F(n-1) + F(n-2)
What is each part of the formula for exponential function? f(x) = a bx,
F(X) is exponential function A is coefficient B is base x is exponent
systems of inequalities
Groups of inequalities that have the same variables and are used together to solve a problem.
systems of two linear equations
Groups of two linear equations that have the same variables and are used together to solve a problem.
radical
Indicates a square root. then if it's n√ its a number to the Nth power
compound interest
Interest calculated on both the principal and any previously earned interest.
Compound interest
Interest calculated on both the principal and any previously earned interests.
simple interest
Interest paid only on the principal balance. Simple interest is not added back to the principal.
what does the B in y = mx +B stand for?
It stands for the Y intercept
Area of rectangle
Length x width
algebraic expressions
Math expressions that contain one or more variables. An expression that does not contain any variables is called a numerical expression.
Product
Multiply
irrational numbers:
Numbers that cannot be written in the form , where a and b are integers. _______________ cannot be written as terminating decimals or repeating decimals.
coefficients
Numbers that multiply variables
To change a fraction into a decimal, divide the ____________ by the ____________.
Numerator by the denominator.
point-slope equation
One way to write the equation of a line. It is shown as , where m is the slope of the line and is any point on the line.
slope-intercept equation
One way to write the equation of a line. It is shown as y = mx + b, where m is the slope and b is the y-coordinate of the line's y-intercept.
perimeter of a rectangle
P = 2l + 2w
PEMDAS
P = Parentheses E = Exponents M = Multiplication D = Division A = Addition S = Subtraction
PEMDAS stands for?
P = Parentheses E = Exponents M = Multiplication D = Division A = Addition S = Subtraction
Explicit formula pyramidal
P(n) = n(n+1)(2n+1)/6
Recursive formula pyramidal
P(n-1) + n^2
ordered pairs
Pairs of numbers in parentheses that name the location of points on a coordinate plane. The first number is the x-value, and the second number is the y-value.
principle square root
The positive square root of a number. The principal square root of n is written as the √n or 1/n2 . If x is the principal square root of n, then x2 = n.
substitution
The process of replacing a variable with a number or expression..
output
The result of a function. The ___________variable in a function is the dependent variable.
output
The result of a function. The output variable in a function is the dependent variable.
distributive property
The rule that if a, b, and c are numbers or expressions, then a (b + c) = a b + a c.
range
The set of a function's output values (or y-values).
domain
The set of all allowable input values. If the function is graphed, the __________ is the set of all x-values on the graph.
domain
The set of all allowable input values. If the function is graphed, the domain is the set of all x-values on the graph.
rational numbers
The set of all numbers that can be written as a ratio of two integers, where the denominator is not zero. The ______________ are a subset of the real numbers.
conversion
The translation of a measurement to an equivalent measurement in different units.
Describe what you notice about the variable in the four examples of exponential functions.
The variable is in the exponent.
rise
The vertical distance between two points on a line. It equals the difference between the y-coordinates of the two points.
isolate the variable
To get the variable alone on one side of an equation or inequality.
Factor
___________ are multiplied together.
Explicit Formula if there is no percent use this formula.
a(n) = a(1) r^n - 1
The range of a function in the form f(x) = b^x is always_____________________
y is greater than 0.
The graph of f(x) = bx will always have the ____________________________________
y-intercept of (0, 1).
Slope equation using two points
y2-y1/x2-x1