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7x3 + 6x2 + 5x + 4
What is the 7 called? |
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7x3 + 6x2 + 5x + 4 What is the 7 called?
Coefficient |
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| 7x3 + 6x2 + 5x + 5 What is the x called? |
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7x3 + 6x2 + 5x + 5 What is the x called?
Base |
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7x3 + 6x2 + 5x + 5 What is the 3 called?
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7x3 + 6x2 + 5x + 5 What is the 3 called?
Exponent |
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| 7x3x2 + 5x + 7 What is the degree of this expression? |
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Definition
7x3x2 + 5x + 7 What is the degree of this expression?
The degree is 3+2= 5th degree |
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| 7x3 + 6x2 + 5x + 8 What is the name of this expression? |
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Definition
7x3 + 6x2 + 5x + 8 What is the name of this expression?
Cubic with 4 terms |
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| 7x3 + 5x + 9 What is the name of this expression? |
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Definition
7x3 + 5x + 9 What is the name of this expression?
Cubic trinomial |
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| 7x3 + 9 What is the name of this expression? |
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Definition
7x3 + 9 What is the name of this expression?
Cubic binomial |
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| 7x3 What is the name of this expression? |
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Definition
7x3 What is the name of this expression?
Cubic Monomial |
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| 6x2 + 5x + 12 What is the name of this expression? |
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Definition
6x2 + 5x + 12 What is the name of this expression?
Quadratic trinomial |
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| 6x2 + 12 What is the name of this expression? |
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Definition
6x2 + 12 What is the name of this expression?
Quadratic Binomial |
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| 6x2 What is the name of this expression? |
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Definition
6x2 What is the name of this expression?
Quadratic Monomial |
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| 5x + 15 What is the name of this expression? |
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Definition
5x + 15 What is the name of this expression?
Linear Binomial |
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| 5x What is the name of this expression? |
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| 5x What is the name of this expression? Linear Monomial |
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| 17 What is the name of this expression? |
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| 17 What is the name of this expression? A constant because it does not vary. It is always 17. |
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| 6x2 + 7x3 + 5x + 18 What is the name of this expression? |
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Definition
6x2 + 7x3 + 5x + 18 What is the name of this expression?
Cubic with 4 terms |
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| 5x + 6x2 + 19 What is the name of this expression? |
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Definition
5x + 6x2 + 19 What is the name of this expression?
Quadratic Trinomial |
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| 6x2 + 7x + 5x2 + 18 What is the name of this expression? |
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Definition
6x2 + 7x + 5x2 + 18 What is the name of this expression?
Quadratic Trinomial. You must combine like terms. So it becomes 11x2 + 7x + 18 |
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| Factors are numbers multiplied together. |
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| A power is the result of repeated multiplication, such as 3^4 = 3*3*3*3 |
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| A product is the result of multiplying two numbers, such as 3x4 |
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| Terms are numbers added together (or subtracted) |
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Absolute Value : The distance from a number to the origin.
|-5| = 5 because -5 is 5 spaces from the origin |
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Additive Inverses : Two numbers are _________________ of each other if their sum equals zero
5 + (-5) = 0 |
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| Adjacent Angles : If two angles have the same vertex and share a side between them |
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| An equation says that an expression equals some number |
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| An expression stands for a number |
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| the area is a measure of the "space" inside. |
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| Arithmetic Operation : Addition, subtraction, multiplication, & Division |
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| Complementary angles : If the sum of the measures of two angles is 90 degrees |
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| Components of a Power : Base and Exponent |
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| Define a conditional equation |
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| A conditional equation is one that is true for some value of the variable and not true for other values of the variable. |
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| an identity is an equation that is true for all values of the variable |
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| Define and give an example of a commutative axiom for addition |
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An axiom is something that is true it is not something that you do.
X + y = y + x |
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| Define and give an example of a commutative axiom for multiplication |
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Commutative axiom for multiplication
To commute is to move
An axiom is something that is true it is not something that you do.
Xy = yx |
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| Define and give an example of a distributive axiom for multiplication over addition |
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Distributive axiom for multiplication over addition.
To distribute is to spread around.
An axiom is something that is true it is not something that you do.
X ( Y + Z ) = XY + XZ |
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| Define and give an example of a multiplicative Inverse |
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| Define and give an example of a multiplicative Inverse : The reciprocal of a number. Any two numbers (excluding zero) whose product is 1. for example 2/3 + 3/2 = 1 |
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| Define and give an example of addition property of equality |
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Addition property of equality
if x = y then x + z = y + z |
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| Define and give an example of Additive Identity Axiom |
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Definition
Additive Identity Axiom.
An axiom is something that is true it is not something that you do.
Zero added to any number gives that number.
X + 0 = X |
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| Define and give an example of additive Inverses Axiom |
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Definition
Additive Inverses Axiom.
An axiom is something that is true it is not something that you do.
Any number x has an opposite, -x
for which x + (-x) = 0 |
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| Define and give an example of an associative axiom for addition |
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Associative axiom for addition
An axiom is something that is true it is not something that you do.
To associate is to group
( x + y ) + z = x + ( y + z ) |
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| Define and give an example of an associative axiom for multiplication |
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Definition
An axiom is something that is true it is not something that you do.
To associate is to group.
( xy )z = x(yz) |
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| Define and give an example of Associating |
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| Define and give an example of Associating : To group numbers in parenthesis to show which should be done first. 2+4+6 becomes 2+(4+6) |
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| Define and give an example of commuting |
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| Define and give an example of commuting : to interchange or reverse the positions of two numbers. 3+2 becomes 2+3 |
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| Define and give an example of Multiplication Property of 0 |
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Multiplication property of 0
zero times a number equals zero
0 (x) = 0 |
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| Define and give an example of Multiplication Property of -1 |
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Definition
Multiplication property of -1
-1 times a number equals the opposite of that number
-1 (x ) = -x |
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| Define and give an example of multiplication property of equality |
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Definition
Multiplication property of equality
if x = y then xz = yz |
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| Define and give an example of Multiplicative Identity Axiom |
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Definition
Multiplicative Identity axiom.
An axiom is something that is true it is not something that you do.
One times any number gives that number.
X ( 1 ) = X |
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| Define and give an example of multiplicative Inverses Axiom |
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Definition
Multiplicative Inverses
An axiom is something that is true it is not something that you do.
Any number x (except for 0) has a reciprocal, 1/x
x ( 1/x ) = 1 |
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| Define and give an example of reflexive axiom of equality |
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Definition
Reflexive Axiom of Equality
An axiom is something that is true it is not something that you do.
A number equals itself
x = x |
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| Define and give an example of symmetric axiom of equality |
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Definition
Symmetric axiom of equality
An axiom is something that is true it is not something that you do.
The two members of an equation can be reversed without affecting their equality
if x = y then y = x |
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| Define and give an example of Transitive axiom of equality |
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Definition
Transitive axiom of equality
An axiom is something that is true it is not something that you do.
If the first number equals a second number, and the second number equals a third number, then the first number equals the third number.
If x = y and y = x then x = z |
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| An axiom is a basic assumption about a mathematical system. It is a property that is assumed to be true without proof. |
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| In an expression, c is a common factor is c is a factor of each term in that expression |
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Two terms in an expression are called like terms (or similar terms) if they have the same variable raised to the same power.
5y and -13y
x and 8x
2ye5 and 5ye5 |
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| Define Numerical Coefficient |
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Definition
The numerical coefficient of a term is the constant that is multiplied by the variables.
For example, in 5xy, 5 is the numerical coefficient of xy) |
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| A property is a fact that is true about a mathematical system. |
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| Define the Distributive Axiom |
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Definition
Multiplication or division distribute over addition and subtraction of two or more terms from the left or from the right.
X ( y + z ) = xy + xz
x ( y - z ) = xy - xz |
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Equation : Number sentence that says one expression is equal to another expression
X+5=17 |
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| Evaluating an expression means to? |
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Definition
To evaluate an expression means to find the number for which the expression stands
Evaluating means finding the expression's value when you know the value of "x" |
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Name the axiom, property, or definition for this expression :
(3+k)+2n = 2n +(3+k) |
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Definition
| Commutative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
.3 + (-.3) = .3 - .3 |
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Definition
| Definition of subtraction |
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Term
Name the axiom, property, or definition for this expression :
.3 + (-.3) = 0 |
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Definition
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Term
Name the axiom, property, or definition for this expression :
[11x+(-11x)]+5 = 0+5 |
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Definition
| Combination of like terms |
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Term
Name the axiom, property, or definition for this expression :
0+3t = 3t |
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Definition
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Term
Name the axiom, property, or definition for this expression :
0+5 = 5 |
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Definition
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Term
Name the axiom, property, or definition for this expression :
1*(4p-2) = 4p-2 |
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Definition
Multiplicative Identity axiom.
An axiom is something that is true it is not something that you do.
One times any number gives that number.
X ( 1 ) = X |
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Term
Name the axiom, property, or definition for this expression :
-1*ahs = -ahs |
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Definition
Multiplication property of -1
-1 times a number equals the opposite of that number
-1 (x ) = -x |
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Term
Name the axiom, property, or definition for this expression :
11/b * 1 = 11/b |
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Definition
Multiplicative Identity axiom.
An axiom is something that is true it is not something that you do.
One times any number gives that number.
X ( 1 ) = X |
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Term
Name the axiom, property, or definition for this expression :
11/b * b/11 = 1 |
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Definition
Multiplicative Inverses
An axiom is something that is true it is not something that you do.
Any number x (except for 0) has a reciprocal, 1/x
x ( 1/x ) = 1 |
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Term
Name the axiom, property, or definition for this expression :
11/b = 11 * 1/b |
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Definition
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Term
Name the axiom, property, or definition for this expression :
11x+[(-11x)+5] =
[11x+(-11x)]+5 |
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Definition
| Associative axiom of Addition |
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Term
Name the axiom, property, or definition for this expression :
11x+5(-11x) =
11x+[(-11x)+5] |
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Definition
| Commutative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
11x+5+(-11x)=
11x + [5+(-11x)] |
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Definition
| Associative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
11x+5-11x =
11x+5+(-11x) |
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Definition
| Definition of subtraction |
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Term
Name the axiom, property, or definition for this expression :
2001x * 0 = 0 |
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Definition
Multiplication property of 0
zero times a number equals zero
0 (x) = 0 |
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Term
Name the axiom, property, or definition for this expression :
2n-5*3 = 2n+(-5*3) |
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Definition
| Definition of subtraction |
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Term
Name the axiom, property, or definition for this expression :
3+(k+2n) = (3+K)+2n |
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Definition
| Associative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
4(pt) = (pt)*4 |
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Definition
| Commutative axiom for multiplication |
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Term
Name the axiom, property, or definition for this expression :
4(pt) = 4(tp) |
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Definition
| Commutative axiom for multiplication |
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Term
Name the axiom, property, or definition for this expression :
5m+5n = 5(m+n) |
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Definition
| Distributive axiom for multiplication over addition |
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Term
Name the axiom, property, or definition for this expression :
6r+9r = (6+9)r |
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Definition
| Distributive axiom for multiplication over addition |
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Term
Name the axiom, property, or definition for this expression :
7k+7j = 7(k+j) |
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Definition
| Distributive axiom for multiplication over addition |
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Term
Name the axiom, property, or definition for this expression :
8f |
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Definition
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Term
Name the axiom, property, or definition for this expression :
a+(b+c) = a + (c+b) |
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Definition
| Commutative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
a+5 = 5+a |
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Definition
| Commutative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
c/d = c*1/d |
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Definition
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Term
Name the axiom, property, or definition for this expression :
k*5 = 5k |
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Definition
| Commutative axiom for multiplication |
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Term
Name the axiom, property, or definition for this expression :
p(mt) = p( t m ) |
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Definition
| commutative axiom for multiplication |
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Term
Name the axiom, property, or definition for this expression :
rs = sr |
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Definition
| Commutative axiom for multiplication |
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Term
Name the axiom, property, or definition for this expression :
x+y = y+x |
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Definition
| Commutative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
x-y = x + (-y) |
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Definition
| Definition of subtraction |
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Term
Name the axiom, property, or definition for this expression :
(2/3)x=12 -->
(2/3)x*(3/2)=12*(3/2) |
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Definition
Multiplication property of equality
if x = y then xz = yz |
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Term
Name the axiom, property, or definition for this expression :
0*x=x*0 |
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Definition
| commutative axiom for multiplication |
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Term
Name the axiom, property, or definition for this expression :
0x=0 |
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Definition
| Multiplication property of zero |
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Term
Name the axiom, property, or definition for this expression :
-1*3=-1*3 |
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Definition
Reflexive Axiom of Equality
An axiom is something that is true it is not something that you do.
A number equals itself
x = x |
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Term
Name the axiom, property, or definition for this expression :
-1*3t=-3t |
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Definition
Multiplication property of -1
-1 times a number equals the opposite of that number
-1 (x ) = -x |
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Term
Name the axiom, property, or definition for this expression :
1066x+2001x=(1066+2001)x |
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Definition
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Term
Name the axiom, property, or definition for this expression :
13*t=43 -->
t*13=43 |
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Definition
| Commutative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
13+t=43 --> t=30 |
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Definition
| Addition property of equality |
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Term
Name the axiom, property, or definition for this expression :
1492w+1492v=1492(w+v) |
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Definition
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Term
Name the axiom, property, or definition for this expression :
14x+28=n -->
28+14x=n |
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Definition
| Commutative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
14x=28 --> x=2 |
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Definition
Multiplication property of equality
if x = y then xz = yz |
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Term
Name the axiom, property, or definition for this expression :
15=8+2x --> 8+2x=15 |
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Definition
Symmetric axiom of equality
An axiom is something that is true it is not something that you do.
The two members of an equation can be reversed without affecting their equality
if x = y then y = x |
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Term
Name the axiom, property, or definition for this expression :
19=5X+3 -->
5X+3=19 |
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Definition
Symmetric axiom of equality
An axiom is something that is true it is not something that you do.
The two members of an equation can be reversed without affecting their equality
if x = y then y = x |
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Term
Name the axiom, property, or definition for this expression :
1p=p |
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Definition
Multiplicative Identity axiom.
An axiom is something that is true it is not something that you do.
One times any number gives that number.
X ( 1 ) = X |
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Term
Name the axiom, property, or definition for this expression :
1x=x |
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Definition
Multiplicative Identity axiom.
An axiom is something that is true it is not something that you do.
One times any number gives that number.
X ( 1 ) = X |
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Term
Name the axiom, property, or definition for this expression :
2x+[8+(-8)]=15+(-8)-->
2x+0=15+(-8) |
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Definition
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Term
Name the axiom, property, or definition for this expression :
2x+0=15+(-8) -->
2x=15+(-8) |
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Definition
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Term
Name the axiom, property, or definition for this expression :
2x+8(-8)=15+(-8)-->
2x+[8+(-8)]=15+(-8) |
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Definition
| associative property of equality |
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Term
Name the axiom, property, or definition for this expression :
2x=15+(-8) -->
2x=15-8 |
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Definition
| Definition of subtraction |
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Term
Name the axiom, property, or definition for this expression :
2x=15-8 -->
2x=7 |
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Definition
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Term
Name the axiom, property, or definition for this expression :
2x=7 --> x=3.5 |
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Definition
Multiplication property of equality
if x = y then xz = yz |
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Term
Name the axiom, property, or definition for this expression :
3(50*90)=(3*50)*90 |
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Definition
| associative axiom of multiplication |
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Term
Name the axiom, property, or definition for this expression :
3(50*90)=(50+90)*3 |
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Definition
| commutative axiom for multiplication |
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Term
Name the axiom, property, or definition for this expression :
3(50+90)=3(90+50) |
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Definition
| Commutative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
3(50+90)=3*50+3*90 |
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Definition
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Term
Name the axiom, property, or definition for this expression :
3+(50+90)=(3+50)+90 |
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Definition
| associative axiom for addition |
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Term
Name the axiom, property, or definition for this expression :
3-50=3+(-50) |
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Definition
| Definition of subtraction |
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Term
Name the axiom, property, or definition for this expression :
3-50=-47 and -40-7=-47
then 3-50=-40-7 |
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Definition
Transitive axiom of equality
An axiom is something that is true it is not something that you do.
If the first number equals a second number, and the second number equals a third number, then the first number equals the third number.
If x = y and y = x |
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Term
Name the axiom, property, or definition for this expression :
3c/3=3c(1/3) |
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Definition
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Term
Name the axiom, property, or definition for this expression :
3x+5x+7 -->
3x+(-5x)=5x+7+(-5x) |
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Definition
Addition property of equality
if x = y then x + z = y + z |
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Term
Name the axiom, property, or definition for this expression :
3x+5x=(3+5)x |
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Definition
|
|
Term
Name the axiom, property, or definition for this expression :
3x+5x=8x -->
8x=3x+5x |
|
Definition
Symmetric axiom of equality
An axiom is something that is true it is not something that you do.
The two members of an equation can be reversed without affecting their equality
if x = y then y = x |
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Term
Name the axiom, property, or definition for this expression :
5(X+3)=(X+3)(5) |
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Definition
| Commutative axiom for multiplication |
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Term
Name the axiom, property, or definition for this expression :
5(X+3)=5(3+X) |
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Definition
| Commutative axiom for addition |
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Name the axiom, property, or definition for this expression :
5(X+3)=5X+15 |
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| Distributive axiom for multiplication over addition |
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Name the axiom, property, or definition for this expression :
5+(X+3)=(5+X)+3 |
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| Associative axiom for addition |
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Name the axiom, property, or definition for this expression :
5X+3=5X+3 |
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Reflexive Axiom of Equality
An axiom is something that is true it is not something that you do.
A number equals itself
x = x |
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Name the axiom, property, or definition for this expression :
8+12=20 and 23-3=20
therefore 8+12=23-3 |
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Transitive axiom of equality
An axiom is something that is true it is not something that you do.
If the first number equals a second number, and the second number equals a third number, then the first number equals the third number.
If x = y and y = x |
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Name the axiom, property, or definition for this expression :
8+2x+(-8)=15+(-8)-->
2x+8+(-8)=15+(-8) |
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| Commutative Axiom of Addition |
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Name the axiom, property, or definition for this expression :
8+2x=15 -->
8+2x+(-8)=15+(-8) |
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| Commutative axiom for addition |
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Name the axiom, property, or definition for this expression :
d(1/d)=1 |
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Definition
Multiplicative Inverses Axiom
An axiom is something that is true it is not something that you do.
Any number x (except for 0) has a reciprocal, 1/x
x ( 1/x ) = 1 |
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Name the axiom, property, or definition for this expression :
-d+d=0 |
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Definition
Additive Inverses : Two numbers are _________________ of each other if their sum equals zero
5 + (-5) = 0 |
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Name the axiom, property, or definition for this expression :
d-d=d+(-d) |
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| Definition of subtraction |
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Name the axiom, property, or definition for this expression :
If p=a and a=f, then p=f |
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Transitive axiom of equality
An axiom is something that is true it is not something that you do.
If the first number equals a second number, and the second number equals a third number, then the first number equals the third number.
If x = y and y = x |
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Name the axiom, property, or definition for this expression :
w*0=0 |
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| Multiplication Property of zero |
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Name the axiom, property, or definition for this expression :
w*1/w=1 |
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Definition
Multiplicative Inverses Axiom
An axiom is something that is true it is not something that you do.
Any number x (except for 0) has a reciprocal, 1/x
x ( 1/x ) = 1 |
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Name the axiom, property, or definition for this expression :
w+(-w)=0 |
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Definition
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Name the axiom, property, or definition for this expression :
w+0=w |
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Name the axiom, property, or definition for this expression :
X+3=X+3 |
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Reflexive Axiom of Equality
An axiom is something that is true it is not something that you do.
A number equals itself
x = x |
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Name the axiom, property, or definition for this expression :
x=7 & 7=z -->
x=z |
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Definition
Transitive axiom of equality
An axiom is something that is true it is not something that you do.
If the first number equals a second number, and the second number equals a third number, then the first number equals the third number.
If x = y and y = x |
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Definition
Commutative
Associative
Distributive
Identity
Inverses
Transitive Axiom of Equality
Symmetric Axiom of Equality
Reflexive Axiom of Equality |
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Property of -1
Property of 0 |
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| Negative Numbers : Numbers to the left of the origin (0) on a number line |
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On a sheet of paper write the steps using axioms and definitions to prove that
Multiplication Distributes over Subtraction
x(y-z)=xy-xz |
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Definition
x(y-z) --> Start
x[y+(-z)] --> Definition of subtraction
xy+x(-z) --> Distributive axiom for multiplication over addition
xy+(-xz) --> Positive times negative is negative
xy-xy --> Definition of subtraction
therefore
x(y-z)=xy-xz --> transitive axiom of equality |
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Order of Operations :
Evaluate Powers
Multiply & Divide from left to right
Add & Subtract from left to right |
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| The perimeter is the distance around |
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| Solving an equation means to? |
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| Solving means finding x's value when you know what the expression equals |
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| State the definition of division. |
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| Dividing by a number means multiplying by its reciprocal. |
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| Supplementary Angles : If the sum of the measures of two angles is 180 degrees |
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| Symbols of Inclusion : Parentheses, brackets, & viniculum which are used in a problem to tell which operations to do first. |
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Tell what transformation is to be done first for each equation :
1/3x = 5 |
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| Multiply each member by 3 |
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Tell what transformation is to be done first for each equation :
1/5x + 3 = 7 |
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| Subtract 3 from each number |
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Tell what transformation is to be done first for each equation :
1/8x - 7 = 45 |
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Tell what transformation is to be done first for each equation :
2x - 5 = 9 |
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Tell what transformation is to be done first for each equation :
3x + 4/7 = 9 |
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| Subtract 4/7 from each member |
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Tell what transformation is to be done first for each equation :
4c - 2 = -1 |
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Tell what transformation is to be done first for each equation :
4x = 7 |
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Tell what transformation is to be done first for each equation :
5 + 2x = 3 |
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| Subtract 5 from each member |
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Tell what transformation is to be done first for each equation :
5p + 1 = -13 |
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| Subtract 1 from each member |
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Tell what transformation is to be done first for each equation :
5x - 2/9 = 1 |
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Tell what transformation is to be done first for each equation :
6x + 4 = 7 |
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| Subtract 4 from each member |
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| Terms : Numbers that are added or subtracted from each other |
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Transforming an equation:
To do the same operation to each member of an equation where your left member is to the left side of the equal sign and the right member is to the right side of the equal sign.
X-2=7
(2)+x-2=7+(2)
Add (+2) to both sides is to ___________ an equation. |
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| Variable : letter that represents a number |
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| What are additive inverses |
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| What are additive inverses : Two numbers that add up to zero such as -3+3=0 |
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| Factors are Numbers that are multiplied together |
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| What are integers? : A whole number or its opposite -2, -1, 0, 1, 2 |
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| Two terms in an expression are called like terms or similar terms if they have the same variable raised to the same power |
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| what are negative numbers |
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| what are negative numbers : A number less than zero |
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| What are positive numbers |
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| What are positive numbers : A number greater than zero |
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| What are real numbers? : All numbers on the numberline, including positive, negative, zero, fractions, and decimals |
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| What does (-x)^2 require you to do? |
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| (-x)^2 means (-x)(-x) and therefore answer is XX |
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| What does it mean to evaluate an expression? |
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To evaluate an expression means to find the number for which the expression stands
Evaluating means finding the expression's value when you know the value of "x" |
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| What does Substituting mean? |
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| Substituting involves replacing a variable with a constant; such as replacing variable "x" with constant 12. |
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| What does -x^2 require you to do? |
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| -x^2 means -(x)(x) and therefore answer is -XX |
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| In an expression, c is a common factor if C is a factor of each term in that expression for example 3c+4c^2-5c |
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| What is a negative number? |
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| A negative number is a number less than zero |
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| What is a numerical coefficient? |
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| The numerical coefficient of a term is the constant that is multiplied by the variables. For example the 5 in 5xy |
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| A real number is any number that has a place on the number line. |
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An expression is a collection of numbers, operations signs, and inclusion symbols that stands for a number
3x+5 |
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| An integer is a positive, negative, or zero "whole" number. |
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| What is division : Multiplying by a reciprocal |
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| What is subtracting? : subtracting a number means adding its opposite. X-y is x+(-Y) |
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| What is the difference between "power" and "exponent" |
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A power is the whole expression such as z^4
An exponent tells how many times the base is multiplied together. |
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| What is the origin : On a number line, the zero point; on a Carteian coordinate system the (0,0) point |
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| What is the sign of a negative power whose exponent Is an odd number (-4) with an exponent of -3 |
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Definition
| What is the sign of a negative power whose exponent Is an odd number (-4) with an exponent of -3 : The answer will be negative. If the exponent was even then it would have had a positive number |
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