#### Study sets matching "term:algebra = solutions"

#### Study sets matching "term:algebra = solutions"

If D ≠ 0

If D = 0, Dy ≠ 0

If D = 0, Dy = 0

discriminant is positive

graphs intersect; consistent independent

graphs are parallel; inconsistent

graphs coincide; consistent dependent; IMF

two different rational numbers

If D ≠ 0

graphs intersect; consistent independent

If D = 0, Dy ≠ 0

graphs are parallel; inconsistent

consistent equations

dependent equations

equivalent equations

inconsistent equations

a system of linear equations that contain at least one common…

a system of linear equations that rely on each other for the…

equations having all common solutions

a system of linear equations that do not contain any common p…

consistent equations

a system of linear equations that contain at least one common…

dependent equations

a system of linear equations that rely on each other for the…

absolute value

IxI symbol means:

Select the graph for the solution of t…

Select the graph for the solution of t…

the distance from zero on the number line

the absolute value of some number x

no solution

https://internationalvla.sooschools.com/media/g_alg01_ccss_20…

absolute value

the distance from zero on the number line

IxI symbol means:

the absolute value of some number x

consistent system

inconsistent system

independent system

dependent system

a system of equations or inequalities that has at least one s…

a system of equations or inequalities that has no solution (s…

a system of equations that has exactly one solution (differen…

a system of equations that has infinitely many solutions (sam…

consistent system

a system of equations or inequalities that has at least one s…

inconsistent system

a system of equations or inequalities that has no solution (s…

Consistent equations

Dependent equations

Equivalent Equation

inconsistent equations

A system of linear equations that contain at least one common…

A system of linear equations that rely on each other for the…

Equations have all common solutions

a system of linear equations that do not have any points

Consistent equations

A system of linear equations that contain at least one common…

Dependent equations

A system of linear equations that rely on each other for the…

When Ax=b has no solution,

Linear system is homogenous if

Is a homogenous solution consistent or…

Trivial solution

the solution set is empty

it is of the form Ax = 0 vector in matrix equation form.

ALWAYS consistent because you can always write down the solut…

x = 0; of Ax = 0

When Ax=b has no solution,

the solution set is empty

Linear system is homogenous if

it is of the form Ax = 0 vector in matrix equation form.

Homogeneous Solution:

Trivial Solution:

Nontrivial Solution:

[THEOREM] The homogeneous equation Ax…

Ax = 0; 0 is the zero vector.

the zero solution.

a nonzero vector x that satisfies Ax = 0.

the equation has at least one free variable.

Homogeneous Solution:

Ax = 0; 0 is the zero vector.

Trivial Solution:

the zero solution.

#3. y=(x-1)(x+3). ... Find the x-interce…

#8. y=(x-2)(x+2). ... Graph, find the ve…

#8. The Graph to the above equation.

#13. y= x^2 -9 (x squared minus 9)... Gr…

#3. y=(x-1)(x+3). ... Find the x-interce…

#8. y=(x-2)(x+2). ... Graph, find the ve…

consistent equations

dependent equations

equivalent equations

inconsistent equations

a system of linear equations that contain at least one common…

a system of linear equations that rely on each other for the…

equations having all common solutions

a system of linear equations that do not contain any common p…

consistent equations

a system of linear equations that contain at least one common…

dependent equations

a system of linear equations that rely on each other for the…

#57. Write the quadratic function repr…

#60. Write the quadratic function repr…

#62. Use zeros to graph the function.…

#68. Use zeros to graph the function.…

#57. Write the quadratic function repr…

#60. Write the quadratic function repr…

solution

a=b

x=a

a=a

a value that when in place of a variable holds the equation t…

no values of the variable for which the equation is true

the equation is true for exactly one value of the variables

the equation is true for all values of the variable

solution

a value that when in place of a variable holds the equation t…

a=b

no values of the variable for which the equation is true

variables

constant

coefficient

Distribution

x, y, or any letter that can represent a number that changes

a number that has a set value (it is not next to a variable)

a number that is directly next to a variable... A number multipl…

when a number outside parentheses multiples with all the term…

variables

x, y, or any letter that can represent a number that changes

constant

a number that has a set value (it is not next to a variable)

Constant of Variation

Non linear

Direct Variation

Midpoint

The slope of a Direct Variation, y=kx, the "K" value

Not a line, can be a curve or a set of line segments.

A line in the form of y=kx, goes through origin, is proportio…

The point separating a line segment into two equal halves.

Constant of Variation

The slope of a Direct Variation, y=kx, the "K" value

Non linear

Not a line, can be a curve or a set of line segments.

variable

Algebraic expression

Numerical expression

power

A symbol, usually a letter, that represents one or more value…

A mathematical phrase that includes one or more variables.

A mathematical phrase involving numbers and operations.

A number that can be expressed using a base and an exponent.

variable

A symbol, usually a letter, that represents one or more value…

Algebraic expression

A mathematical phrase that includes one or more variables.

addition property of equality

algebraic expressions

division property of equality

solutions of a equation inequality

the addition property of equality state that if the same valu…

a algebraic expressions is a mathmatical pharse that uses var…

the equality states that if both sides of an equation are div…

value or values that make an equation or inequality true

addition property of equality

the addition property of equality state that if the same valu…

algebraic expressions

a algebraic expressions is a mathmatical pharse that uses var…

algebraic term

constants

variables

coefficients

either a single number or a variable, or numbers and variable…

the terms in the algebraic expression that contain only numbers

unknown values, often represented by letters

the number part of the terms with variables

algebraic term

either a single number or a variable, or numbers and variable…

constants

the terms in the algebraic expression that contain only numbers

elimination method

linear inequality

solution of a system of linear inequal…

solution of a system of linear equations

solving systems by adding or subtracting equations to elimina…

an inequality in two variables whose graph is a region of the…

a set of values that make all inequalities in a system true.…

a set of values that make all equations in a system true. [p.…

elimination method

solving systems by adding or subtracting equations to elimina…

linear inequality

an inequality in two variables whose graph is a region of the…

inverse operation

equivalent equations

reciprocal

like terms

two operations that undo each other; ... addition and subtractio…

equations that have the same solution

two non-zero numbers who product is 1

terms that have the same variable parts

inverse operation

two operations that undo each other; ... addition and subtractio…

equivalent equations

equations that have the same solution

absolute value

counterexample

independent system

vertices

a number's distance from zero on the number line

a specific case that shows that a statement is false

a system of equations that has exactly one solution

the maximum or minimum values that a linear function has for…

absolute value

a number's distance from zero on the number line

counterexample

a specific case that shows that a statement is false

Absolute Value

Reciprocal

Term

Constant

The distance a number is from 0 on with number line.

A numbers multiplicative inverse (used for dividing fractions)

A number, a variable, or the product of a number and one or m…

A term that has no variable

Absolute Value

The distance a number is from 0 on with number line.

Reciprocal

A numbers multiplicative inverse (used for dividing fractions)

axis of symmetry

completing the square

complex conjugates

complex number

a line about which a figure is symmetrical

a process used to make a quadratic expression into a perfect…

two complex numbers of the form a-bi and a+bi

any number that can be written in the form a+bi where a and b…

axis of symmetry

a line about which a figure is symmetrical

completing the square

a process used to make a quadratic expression into a perfect…

axis of symmetry

maximum point

minimum point

parabola

a line that divides a plane figure or a graph into two congru…

the vertex of a parabola that opens downwards.

the vertex of a parabola that opens upwards.

the graph of a quadratic function that forms a U-shaped curve.

axis of symmetry

a line that divides a plane figure or a graph into two congru…

maximum point

the vertex of a parabola that opens downwards.

Binomial

Coefficient

complex conjugates

complex numbers

A polynomial equation with 2 terms

A number multiplied by a variable in an algebraic expression.

Opposites of your complex number Ex: (a+bi) and (a-bi)

They are often represented as A + Bi.

Binomial

A polynomial equation with 2 terms

Coefficient

A number multiplied by a variable in an algebraic expression.

SOLUTION

BOUNDRY CURVE

BOUNDRY LINE

BOUNDARY POINT

a number or expression that makes the equation or inequality…

The visual dividing marker of a non-linear graph representing…

The visual dividing symbol in a linear graph representing whe…

The endpoint of a ray or segment on a number line where an in…

SOLUTION

a number or expression that makes the equation or inequality…

BOUNDRY CURVE

The visual dividing marker of a non-linear graph representing…

inequality

set-builder notation

compound inequality

intersection

An open sentence that contains the symbol <, ≤, >, ≥.

A concise way of writing a solution set. For example, {t ｜t <…

A ______________ containing 'and' is true if both of the ineq…

The graph of a compound inequality containing 'and' is the __…

inequality

An open sentence that contains the symbol <, ≤, >, ≥.

set-builder notation

A concise way of writing a solution set. For example, {t ｜t <…

variables

constant

coefficient

Distribution

x, y, or any letter that can represent a number that changes

a number that has a set value (it is not next to a variable)

a number that is directly next to a variable... A number multipl…

when a number outside parentheses multiples with all the term…

variables

x, y, or any letter that can represent a number that changes

constant

a number that has a set value (it is not next to a variable)

reciprocal

power

exponent

base

multiplicative inverse

expression used to abbreviate repeated multiplication of the…

the number of times the base is multiplied by itself

factor to be multiplied by itself in a power

reciprocal

multiplicative inverse

power

expression used to abbreviate repeated multiplication of the…

variables

constant

coefficient

Distribution

x, y, or any letter that can represent a number that changes

a number that has a set value (it is not next to a variable)

a number that is directly next to a variable... A number multipl…

when a number outside parentheses multiples with all the term…

variables

x, y, or any letter that can represent a number that changes

constant

a number that has a set value (it is not next to a variable)

Absolute Value

Addition

Algebraic Expression

All Real Numbers

The distance a number is from zero on the number line. |-5| = 5

The inverse operation of subtraction

An expression that contains at least one variable... 3x-4 is an…

An equation with a solution x = x

Absolute Value

The distance a number is from zero on the number line. |-5| = 5

Addition

The inverse operation of subtraction

Absolute Value

Algebraic Expression

Compound Inequality

Constraint

distance from zero, the quantity of the number as a positive.

an expression built up from integer constants, variables, and…

contains at least two inequalities that are separated by eith…

The number of tickets sold was more than 200

Absolute Value

distance from zero, the quantity of the number as a positive.

Algebraic Expression

an expression built up from integer constants, variables, and…