Key Words From Algebra 1 Lesson 2

Front 1

If two lines make square corners at the point of intersection, what do we say the angles are? (not train tracks)

Back 1

Perpendicular

Front 2

What are the angles made by perpendicular lines?

Back 2

Right Angles are the angles made by perpendicular lines.

Front 3

What do two right angles form?

Back 3

Two right angles form a Straight Angle.

Front 4

And angle smaller than a right angle is called an ___

Back 4

acute angle

Front 5

What is an angle greater than a right angle but less than a straight angle?

Back 5

obtuse angle

Front 6

What is a special kind of geometric figure?

Back 6

A polygon is a special kind of geometric figure.

Front 7

What is a Simple closed, flat geometric figure, whose sides are line segments

Back 7

Polygon

Front 8

What is each segment of a polygon called?

Back 8

side

Front 9

Each endpoint of a side is called a

Back 9

Vertex of the polygon

Front 10

the plural of vertex is

Back 10

vertices

Front 11

For each polygon, the number of sides is always equal to the number of

Back 11

vertices

Front 12

What is a Convex polygon?

Back 12

If a polygon has an indentation (a cave), the polygon is called a Convex Polygon.

Front 13

If all the sides of polygon have the same length, the polygon is called an

Back 13

equilateral polygon

Front 14

If all the angles of a polygon have the same measure, what is the polygon called?

Back 14

equiangular polygon

Front 15

polygons in which all sides have he same length and all angles have the same measure are called

Back 15

regular polygons

Front 16

A regular triangle is called an

Back 16

equilateral triangle.

Front 17

all the angles in an equilateral trangle are __ Angles

Back 17

60 degree

Front 18

What is a polygon with four sides?

Back 18

quadrilateral

Front 19

What is another name for a square?

Back 19

regular quadrilateral

Front 20

The sum of the measures of the three angles in any triangle is

Back 20

180 degrees

Front 21

if a triangle has a right angle, the triangle is a

Back 21

right triangle

Front 22

if all angles have a measure less than 90 degrees, the triangle is an

Back 22

acute triangle

Front 23

if one angle has a measure greater than 90 degrees, what is the triangle?

Back 23

obtuse triangle

Front 24

equiangular means

Back 24

equal angles

Front 25

What is a triangle in which the measures of all angles are equal?

Back 25

an Equiangular Triangle is a triangle in which the measures of all the angles are equal.

Front 26

Each angle in an ___ ___ must have a measure of 6- degrees because 3 x 60 degrees equals 180 degrees.

Back 26

Equiangular triangle

Front 27

What is a triangle that has at least two sides of equal length?

Back 27

isosceles triangle

Front 28

What is a triangle with equally long sides called?

Back 28

eqilateral triangle

Front 29

What do we call a triangle that's sides are all different lengths?

Back 29

sclene triangle

Front 30

What is a quadrilateral that has two pairs of parallel sides.

Back 30

A quadrilateral that has two pairs of parallel sides is a parallelogram.

Hint 30

http://illuminations.nctm.org/Lessons/AreaForms/Parallelogram1.jpg

Front 31

What do we call a parallelogram with four right angles?

Back 31

A parallelogram with four right angles is called a rectangle.

Front 32

What is a quadrilateral that has exactly two parallel sides.

Back 32

trapaziod

Front 33

What is an equilateral parallelogram?

Back 33

A rhombus is an equilateral parallelogram.

Front 34

what is a rhombus with four right angles?

Back 34

square.

Front 35

Has 3 Sides

Back 35

Triangle

Front 36

Has 4 sides

Back 36

Quadrilateral [square]

Front 37

How many sides does a Pentagon have?

Back 37

A pentagon has 5 sides.

Front 38

How many sides does a Hexagon have?

Back 38

A Hexagon has 6 sides.

Front 39

Has 7 Sides

Back 39

Heptagon

Front 40

Has 8 sides

Back 40

Octagon

Front 41

has 9 Sides

Back 41

Nonagon

Front 42

Has 10 Sides

Back 42

Decagon

Front 43

Has 11 Sides

Back 43

Undecagon

Front 44

Sides How Many sides does a Dodecagon have?

Back 44

A Dodecagon has 12 sides.

Front 45

Has N sides

Back 45

n-gon

Front 46

what is a 'Number.'

Back 46

A number is an idea.

Front 47

A single symbol or a collection of symbols that we use to express the idea of a particular number

Back 47

Numeral (The value of a numeral is the number represented by the numeral, and we see that the words value and number have the same meaning)

Front 48

The system of numeration that we use to designate numbers is called

Back 48

the Decimal System

Hint 48

(invented by the Hindus of India, passed to their arab neighbors, and finally transmitted to Europe circa A.D. 1200)

Front 49

We call the numbers that we use to count objects or things

Back 49

natural numbers or the Counting Numbers

Front 50

any number that can be used to describe a physical distance greater than zero

Back 50

A positive real number

Front 51

What is a Real Number?

Back 51

Zero, negative numbers, and positive numbers

Front 52

We say that every positive real number has a negative counterpart, and we call these number the

Back 52

negative real numbers

Front 53

When we are referring to negative numbers as well as positive numbers, what kind of numbers do we say that we are talking about?

Back 53

Signed numbers

Front 54

What is the base point on a number line, (we associate the number zero with this point)

Back 54

Origin

Front 55

When we place a dot on the number line to indicate the location of number, we say that we have ____ the number and that the dot is the ___ of the number

Back 55

Graphed, Graph

Front 56

Converselty, the number is said to be the _____ of the point that we have graphed

Back 56

Coordinate

Front 57

What is the opposite of -2?

Back 57

2

Front 58

Addend + Addend = ___

Back 58

Sum

Front 59

What is the sum of zero and any particular real number?

Back 59

the particular real number itself [i.e. 4+0=4....4 being the real number itself... value does not change]

Front 60

Minuend - Subtrahend =

Back 60

difference

Front 61

factor x Factor =

Back 61

product

Front 62

Dividend / divisor =

Back 62

quotient

Front 63

when the indicated division is expressedin the form of a fraction such as 10/5,
What do we say the 10 is?
What do we say the 5 is?

Back 63

10 is the numerator of the fraction
5 is the denominator of the fraction

Front 64

3 ft/ 1 yd : the fractions have units and are equal to 1 because 3 ft is another name for 1 yd. we cal these fractions

Back 64

unit multipliers. ( we can use unit multipliers to change units of a number)

Front 65

1 ft = __ inches

Back 65

12 inches

Front 66

How many Cm in a M?

Back 66

there are 100 cm in a meter

Front 67

How many Feet are in a Yard?

Back 67

There are 3ft in a yard.

Front 68

how many mm in a cm?

Back 68

10 mm

Front 69

How many cm in an inch?

Back 69

2.54 cm

Front 70

how many feet in a mile?

Back 70

5280 ft

Front 71

how many m in 1 km

Back 71

1000 m

Front 72

What word do we use to designate a well-defined collection of numbers, objects, or things.

Back 72

Set

Front 73

What are the individual objects or things that make up the set?

Back 73

Elements, or Members

Front 74

What are Natural Numbers?

Back 74

1,2,3,4,5,...

Front 75

What are Whole Numbers?

Back 75

0,1,2,3,4,5,...

Front 76

...,-3,-2,-1,0,1,2,3,...

Back 76

Integers

Front 77

The absolute value of zero =

Back 77

zero

Front 78

the absolute value of any nonzero real number is a

Back 78

positive number

Front 79

Commutative Property for Addition

Back 79

The order in which two real numbers are added does not affect the sum. (i.e. 4+3=7 and 3+4=7)

Front 80

To add algebraically two signed numbers that have the SAME SIGN, we add the absolute values of the numbers and give the result the same sign as the sign of the numbers.

Back 80

i.e. --->
(+1) + (+3) = (+4)
(-1) + (-3) = - 4

Front 81

To add algebraically two signed numbers (Signed numbers = positive&negative numbers) that have OPPOSITE SIGNS, we take the difference in the absolute values of the numbers and give to this result the sign of the original number
whose absolute value is the greatest.

Back 81

i.e. --->
(-2) + (+5) = +3
(+2) + (-5) = - 3

Front 82

Every real number except zero has an opposite, and the sum of any real number and its opposite is zero. another name for the opposite of a number is the additive inverse of the number, so we can also say that the sum of any real number and its additive inverse is zero.

Back 82

i.e.
-7 and +7 = Additive inverse numbers. or just opposite numbers

Front 83

We let the sign preceding the number designate whether the number is a positive number or a negative number, and we will mentally insert a plus sign in front of each number to indicate algebraic addition.

Back 83

if we use this process:
4 - 3 + 2 can be read as
(+4) + (-3) + (-2)

Front 84

Algebraic Subtraction:

Back 84

if a and b are real numbers, then
a - b = a + ( -b)
where -b is the opposite of b

Front 85

Point of distance from the centre of a circle

Back 85

Radius

Front 86

Twice the length of the radius

Back 86

diameter

Front 87

What is another name for the perimeter of something? (esp. a circle)

Back 87

circumference

Front 88

The circumference of a circle =

Back 88

pi x Diameter = pi(2r) = 2pi.r

Front 89

The ___ of a closed figure is the number of square units contained in the figure

Back 89

area

Front 90

What is square that has sides that measure one unit in length?

Back 90

Square Unit

Hint 90

[any shape that fills a closed figure without overlapping can be used to measure area, but the square is used because of its simplicity]

Front 91

area of a rectangle =

Back 91

length x width

Front 92

area of a square

Back 92

= (length of side) 2 <-- {squared}

Front 93

Units are used for

Back 93

length

Front 94

used for area

Back 94

square units

Front 95

The perpendicular [straight up&down] distance from either the base of the triangle or an extension of the base to the opposite vertex. {any one of the three sides can be designated as the base}

Back 95

Altitude or Height

Front 96

the altitude can

Back 96

[a] be one of the sides of the triangle
[b] fall inside the triangle
[c] fall outside the triangle

Front 97

Area of a triangle =

Back 97

= base x height / 2

Front 98

Area of a Circle

Back 98

πR2 [2 is an exponent]

Front 99

What are the first three decimals of π (pi)?

Back 99

3.14 (pi) are the first three decimals of pi.

Hint 99

mmmm, pi

Front 100

Area of a parallelogram

Back 100

= the sum of the areas of two triangles {divide the parallelogram in half}

Front 101

The area of a trapezoid =

Back 101

the sum of the areas of the two triangles. (A diagonal of a trapezoid divides the figure into two triangles.)

Front 102

Rules for multiplication of signed numbers #1 (of three)

Back 102

1. The product of two positive real numbers is a positive real number whose absolute value is the product of the absolute values of the two numbers.
[ (a) (+3)(+4)=-8 (b) 2(9)=18 (c) 4x5=20 ]

Front 103

Rules for multiplication of signed numbers #2 (of three)

Back 103

2. The product of two signed real numbers that have opposite signs is a negative real number whose absolute value is the product of the absolute values of the two numbers.
[ (a) (-2)(4)=-8 (b) 6(-2) = 12 (c) (-3)(5)=-15

Front 104

Rules for multiplication of signed numbers #3 (of three)

Back 104

3. The product of two negative real numbers is a positive real number whose absolute values the product of the absolute values of the two numbers.
[ (a) -2(-3)=6 (b) (-5)(-3) = 15 (c) -4(-5)=20

Front 105

What kind of 'operations' are addition and subtraction?

Back 105

Addition and Subtraction are inverse operations.

Hint 105

More inverse operations:
Addition & Subtraction
Multiplication & Division

Front 106

Multiplication and Division are both ____ operations

Back 106

inverse operations

Front 107

If one operation will undo another operation, what are the two operations called?

Back 107

Inverse Operations

Hint 107

If we multiply 7 by 2 and then divide by 2, the result is seven.
7x2/2 = 7
there has been no change since dividing by 2 undoes the effect of multiplying by 2/

Front 108

Like signs. The product or the quotient of two signed (positive and negative) numbers that have the same sign is a positive number whose absolute value is the absolute value of the product or the quotient of the absolute values of the original numbers.

Back 108

.

Front 109

Unlike signs. The product or the quotient of two signed numbers that have opposite signs is a negative number whose absolute value is the absolute value of the product or the quotient of the absolute values of the original numbers

Back 109

.

Front 110

In both Multiplication and Division:
1. Like signs YIELD (produce) a positive number.
2. Unlike signs YIELD (produce) a negative number.

Back 110

.

Hint 110

Yield definition:
to produce or provide, to deliver

Front 111

If the bottom of a fraction is not zero and the top is zero, what does the fraction equal?

Back 111

zero

Front 112

What is an undefined Expression?

Back 112

When an expression (i.e. 13/0) has no meaning, and thus has no value. It doesn't have a value of infinity, but it does not equal zero. Thus, it is undefined.

Front 113

What is the commutative property for multiplication?

Back 113

The order in which signed numbers are multiplied does not affect the value of the product. (i.e. 4x3=12....3x4=12)

Front 114

Are Inverse Numbers and Additive Inverse Numbers the same?

Back 114

Yes.

Front 115

If one fraction is the inverted form of another fraction, What is each of the fractions said to be? (of the other fraction)

Back 115

Reciprocal

Hint 115

2/3 is the reciprocal of 3/2
3/2 is the reciprocal of 2/3
-4/11 is the reciprocal of -11/4...and so on
Since numbers such as 4 can also be written in a form such as 4/1, these numbers also have reciprocals.
1/4 is the reciprocal of 4
and so on...
The number zero does not have a reciprocal.

Front 116

What is the only number to not have a reciprocal?

Back 116

Zero

Hint 116

The number zero does not have a reciprocal because if we try to write the reciprocal of zero we get 1/0 (meaningless) Which we say is a meaningless notation because division by zero is undefined.

Front 117

What is the reciprocal of a number often called?

Back 117

The Multiplicative Inverse of the the number.

Front 118

Definition of Reciprocal or Multiplicative Inverse

Back 118

For any nonzero real number a, the reciprocal or multiplicative inverse, of the number is 1/a.

Front 119

What is the product of a number that is multiplied by its reciprocal? (or its multiplicative inverse?

Back 119

The product is 1

Hint 119

4x1/4=1 ~ -5x1/-5=1
and so on.

Front 120

Order of Operations

Back 120

1. exponents and roots
2. multiplication and division
3. addition and subtraction

Hint 120

If there is not + or - sign between symbols, multiplication is indicated.

Front 121

Is the product of two negative numbers always a positive number?

Back 121

Yes

Front 122

What is an obtuse angle?

Back 122

an obtuse angle is an angle that is larger than a right angle and smaller than a straight angle.

Front 123

What is an Acute angle?

Back 123

An acute angle is an angle that is smaller than a right angle.

Front 124

What are the symbols of inclusion?

Back 124

Parentheses, brackets, braces, and bars.

Hint 124

Can be used to help us emphasize the meaning of our notation.
Braces are normally reserved to indicate a set, and bars are most often used in fraction lines.

Front 125

What is the product of an even number of negative numbers?

Back 125

Positive

Front 126

What is the product of an odd number of negative numbers?

Back 126

Negative

Front 127

What is a numerical expression?

Back 127

"A meaningful arrangement of numerals and symbols that designate specific operations"

i.e. 7 14/2 4+3...ect. we call each of these notations a numerical expression. or just a numeral.

Hint 127

Every numerical expression represents only one number and we call this number the value of the expression.

Front 128

What is an Algebraic expression or Mathematical expression?

Back 128

When letters as well as numbers are used in an expression.

Hint 128

Used to describe numerical expressions, and also to describe expressions that contain variables.

Front 129

What are variables? [also known as 'Unknowns']

Back 129

Letters used in an expression.

Hint 129

While the values assigned to variables may change or be changed, under any set of conditions the value assigned to a particular variable in an algebraic expression is the same value throughout the algebraic expression. Also, when we begin solving equations and working problems, we much remember that the value assigned to any particular variable under any set of conditions must be the same value regardless of where the particular variable appears in the equation or the problem.

Front 130

What is a constant?

Back 130

The symbol that we denote a number is called a constant.

Front 131

What is the number of cubic units contained in a geometric solid?

Back 131

The volume of the geometric solid

Front 132

What is a Geometric solid whose sides are at right angles to the bases?

Back 132

Right Geometric Solids

Hint 132

Or just right solids

Front 133

What are the "top" and "bottom" of a right solid called?

Back 133

bases.

Hint 133

The bases of the right solid are identical geomtric figures.

Front 134

What do we call a right solid whose bases are polygons?

Back 134

right prism

Front 135

What is the surface area of a geometric solid? (definition, not formula)

Back 135

the total area of all the exposed surfaces of the geometric solid.

Front 136

What is the definition for the lateral surface area of a right circular cylinder? (can)

Back 136

The area of the curved surface between the bases. (the label around the can)

Hint 136

The lateral surface area of a right circular cylinder is equal to the perimeter of a base times the height.

Front 137

Surface area of a right circular cylinder =
(formula)

Back 137

base area + base area + lateral surface area

Front 138

What is the definition of the lateral surface area of a right solid?

Back 138

The area of the surface between the bases.

Hint 138

THe lateral surface area of a right solid is equal to the perimeter of a base times the height.

Front 139

What is the lateral surface area of a right solid?

Back 139

The surface area of a right solid is equal to the areas of the two equal bases added to the lateral surface area.
Surface area = Base area + Base area + lateral surface area

Hint 139

Lateral surface area = (perimeter of a base)(height)

Front 140

What is the surface area of a geometric solid?

Back 140

the total area of all the exposed surfaces of the geometric solid.

Hint 140

Area of top + Area of Bottom + Area of Front + Area of back + Area of Side + area of Side = surface area

Front 141

What is the surface area of a right triangular prism?

Back 141

The sum of the areas of the five faces. [Two faces are right triangles and three faces are rectangles]

Hint 141

Area of one end + area of one end + Area of bottom + Area of Back + Area of Front = Surface Area

Front 142

What is the formula for finding the perimeter of a circle when given the radius?

Back 142

2πR

Hint 142

R = Radius

Front 143

If you are subtracting, and one number is positive, while the other is negative, how do you determine if the answer is negative or positive?

Back 143

Painless Solution: Pretend both numbers are positive. Subtract the smaller number from the larger number. Give the answer the sign of the number that would be larger if both numbers were positive.

Front 144

What is an indicated product?

Back 144

If the form in which variables and constants are written in an expression indicates that the variables and constants are to be multiplied, we say that the expression is an indicated product.

Hint 144

If we write
4xy
we indicate that 4 is to be multiplied by the product of x and y.
(each of the symbols is said to be a factor of the expression)

Front 145

What is a Coefficient?

Back 145

Any one factor (factor x factor = product) of an expression or any product of factors of an expression can also be called the coefficient of the rest of the expression.

Hint 145

4xy

4 is the coefficient of xy 4(xy)
x is the coefficient of 4y x(4y)
y is the coefficient of 4x y(4x)
xy is the coefficient of 4 xy(4)
4y is the coefficient of x 4y(x)
4x is the coefficient of y 4x(y)

Front 146

What is a Numerical coefficient?

Back 146

When the coefficient is a number.

Hint 146

We need to speak of numerical coefficients so often that we usually drop the adjective numerical and use the single word coefficient.

Front 147

What is a literal coefficient?

Back 147

When the coefficient consists entirely of either variables or letters.

Front 148

What is a term?

Back 148

A term is thought of as a single entity that represents or has the value of one particular number.

A term is an algebraic expression that
1. Consists of a single variable or constant.
2. Is the indicated product or quotient of variables (letters) and/or constants. (numbers)
3. is the indicated product or quotient of expressions that contain variables and/or constants.

Hint 148

Terms can consist of single symbols.

Front 149

What is the commutative property for addition?

Back 149

It states that it doesn't matter which order you add numbers, you still get the same answer.

Front 150

What is the commutative property for multiplication?

Back 150

States that it doesn't matter what order you multiply numbers by, you still get the same answer.

Front 151

What is the distributive property of real numbers?

Back 151

States that we get the same result if we distribute the multiplication over the algebraic addition.

Hint 151

(a) 4 (5 - 3)
4(2)
8

(b) 4(5-3)

4 x 5 + 4(-3)

20 - 12

8

Front 152

What are like terms?

Back 152

Like terms are terms that have the same variables (letters) in the same form or in equivalent forms so that the terms (excluding numerical coefficients) represent the same number regardless of the nonero values assigned to the variables.

Hint 152

4xmp - 2pmx + 6mxp
Whether terms are like terms or not does not depend on the signs of the terms or on the values of the numerical coefficients. so we will not consider the + and - signs or the numbers 4, 2, and 6. we just need to know if
xmp, pmx, and mxp
are in the same form or equivalent forms and if each expression represents the same number regardless of the nonzero values that are assigned to the variables.

Front 153

Like terms rules

Back 153

1. They are in equivalent forms, for they have the same variables in the form of an indicated product, and the order of multiplication of the factors does not affect the value of the product.

Hint 153

2. they represent the same number regardless of the nonzero values assigned to the variables.

Front 154

How do we algebraically add like terms?

Back 154

To add like terms, we algebraically add the numerical coefficients. (coefficient is a factor or product in an equation)

Front 155

What is a term of an algebraic expression?

Back 155

A term is though of as a single entity that represents or has the value of one particular number.

Front 156

What is exponential notation?

Back 156

A formula that allows us to write expressions more concisely.

(That little number that is written smaller in the upper right hand corner above another number.)

Hint 156

...x to the power of x...

Front 157

When a number is raised to an even power, is the result negative or positive?

Back 157

positive

Front 158

When a negative number is raised to an odd power, what is the result?

Back 158

Negative

Front 159

What is the number under the radical sign called?

Back 159

Radicand

Front 160

What is the little number that designates the root called?

Back 160

index

Front 161

What kind of terms may be added in algebraic expression?

Back 161

Like Terms

Front 162

Is the product of 7 positive numbers and 6 negative numbes a positive number or a negative number?

Back 162

Positive Number

Front 163

What is a right triangle?

Back 163

A right triangle is a triangle that contains one right angle

Front 164

What is an acute triangle?

Back 164

An acute triangle is a triangle that contains three acute angles.

Front 165

What is an obtuse triangle?

Back 165

an obtuse triangle is a triangle that contains one obtuse angle

Front 166

What is an equiangular triangle?

Back 166

an equiangular triangle is a triangle in which all angles have equal measure.

Front 167

What is a geometric solid?

Back 167

A geometric figure that has three dimensions.

Front 168

What is a cubic unit?

Back 168

A cubic unit is a cube having edges that measure one unit in length.

Front 169

What is a cube?

Back 169

A cube is a geometric solid that has six identical square faces.

Front 170

What are Volumes measured in?

Back 170

Volumes are always measured in cubic units.

(some common units of volume are the cubic centimeter (cm3) and the cubic meter (m3) ) {the number are sup post to be the little ones in the right hand corner}

Front 171

What is length always measured in?

Back 171

Lengths are always measured in units.

Front 172

What is area always measured in?

Back 172

Area is always measured in Square Units.

Front 173

How do you calculate the volume of stacked "sugar cubes."
(or any right solid)

Back 173

The Volume of stacked "sugar cubes" equals the number of cubes on the bottom layer times the number of layers.
(this works for any right solid)

Front 174

What is a right Solid?

Back 174

A right solid is a geometric solid whose sides are at right angles to the bases.

Front 175

What is a right solids called when the bases are polygons?

Back 175

When a right solid's bases are polygons we call it a right prism.

Front 176

What is the volume of a right solid?

Back 176

the volume of a right solid is equal to the area of a base times the height.

Front 177

What is an Exponent?

Back 177

a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression (e.g., 3 in 2 3 = 2 × 2 × 2).

Front 178

True or False?
We see that when we multiply exponentials (little right hand corner numbers) whose bases are the same, the exponent of the product (5x5= product) is obtained by adding the exponents of the factors.

Back 178

True. :-P

Front 179

What is the Product (5X5=product) rule for exponents? (little right hand numbers)

Back 179

If M and N are real numbers and p=0, then pm (m=exponent) x pn (n=exponent) = p m+n (m+n=exponents)

Hint 179

Cont. We can use this rule to help simplify expressions that contain exponents.

Front 180

What is an Isosceles triangle?

Back 180

An isosceles triangle is a triangle that has at least two sides of equal length.

Front 181

what is an equilateral triangle?

Back 181

An equilateral triangle is a triangle that contains three sides of equal length.

Front 182

What is a scalene triangle?

Back 182

A scalene triangle is a triangle that contains three sides of unequal length.

Front 183

What does " = " mean?

Back 183

equal

Front 184

What does " ≠ " mean?

Back 184

Not Equal

Front 185

What does " > " mean?

Back 185

Greater than

Hint 185

Read left to right

Front 186

What does " < " mean?

Back 186

Less Than

Hint 186

Read left to right

Front 187

8 x 8 = 64
This is an...
(a) Equation or (b) inequality?

Back 187

8 x 8 = 64 is an equation because it uses the equals sign.

Front 188

When a statement/expression does not use an equals sign, what is it?

Back 188

Inequality

Front 189

What is an Equation?

Back 189

An equation is an algebraic statement consisting of two algebraic expressions connected by an equals sign.

Hint 189

Equations are not always true equations. (correct, or depending on the given value of a variable)

Front 190

What is a Conditional Equation?

Back 190

An equation where its truth or falsity is conditioned by the number used as a replacement for the variable.

Hint 190

think variable

Front 191

What is the solution of an equation?
(also called the roots of the equation)

Back 191

Replacement values of the variable that turn the equation into a true equation are called solutions of the equation or roots of the equation and are said to satisfy the equation.

Hint 191

It satisfies the equation.

Front 192

What is the additive property of equality?

Back 192

If a, b, and c are any real numbers and if a = b, then
a + b = b +c and also c + a = c + b

Front 193

What does "solve an equation" mean?

Back 193

To solve an equation means to find the value(s) of the unknown that makes the equation true.

Front 194

What are equivalent equations?

Back 194

Two equations are said to be equivalent if every solution of either one of the equations is also a solution of the other equation.

Hint 194

A. 6+x=9 B. 10+x=13
the two equations shown are equivalent equations, for the number 3 will satisfy both equations and 3 is the only number that will satisfy either equation.

Front 195

What is the multiplicative property of equality? (hint)

Back 195

If every term on both sides of an equation is multiplied or divided by the same nonzero quantity, the resulting equation will be an equivalent equation to the original equation, and thus every solution of one of these equations will be a solution of the other equation. (hint)

Hint 195

If a, b, and c are any real numbers and if a = b,
then
ca = cb and also ac = bc

Front 196

What are the measures of an equiangular triangle?

Back 196

60 degrees

Front 197

What are the measures of the angles of an equilateral triangle?

Back 197

60 degrees

Front 198

When can a number or a variable that is written as an exponential expression be written in reciprocal form?

Back 198

If the sign of the exponent is changed.

Hint 198

If the exponent is positive, the exponent is negative in the reciprocal form. (multiplicative inverse) If the exponent is negative, the exponent is positive in the reciprocal form.

Front 199

What is the product rule for exponents?

Back 199

If 'M' and 'N' are real numbers and 'X' is equal to 0, then

X to the power of M multiplied by X to the power of N is equal to X to the power of M + N.

Xm * Xn = Xn+m

Hint 199

When the bases are the same, we multiply exponential expressions by adding the exponents. This is true even if some of the exponents are negative numbers.

Front 200

What does zero raised to the power of zero equal?

Back 200

zero

Front 201

What is the value of any nonzero quantity raised to the power of zero?

Back 201

Any nonzero quantity raised to the zero power must have a value of 1.

Front 202

What does the word 'sum' mean?

Back 202

The word sum means that things are added.

Hint 202

Algebraic Phrases

Front 203

What does the word product mean?

Back 203

The word product means that things are multiplied.

Hint 203

Algebraic Phrases

Front 204

What does 'more than,' or 'increased by' mean?

Back 204

More than, or increased by means to add.

Hint 204

Algebraic Phrases

Front 205

What does 'less than,' or 'decreased by' mean?

Back 205

Less than or decreased y means to subtract.

Hint 205

Algebraic Phrases

Front 206

If we use N to represent an unknown number, then what will we use to represent the opposite of the unknown number.

Back 206

We will use -N to represent the opposite of the unknown number.

Hint 206

Algebraic Phrases

Front 207

What does 2N represent?

Back 207

Twice a number

Hint 207

Algebraic Phrases

Front 208

What does 5(-N) Represent?

Back 208

5 times the opposite of a number would be represented by 5(-N).

Hint 208

Algebraic Phrases

Front 209

What does 7(2N - 10) represent?

Back 209

Seven times the sum of twice a number and negative ten.

Hint 209

Algebraic Phrases.

Front 210

(D) x (Of) = Is

What Decimal part = (D)
Of 42 = (of)
Is 26.04 = (is)

Back 210

We replace D with WD, of with 42, and is with 26.04. Then we solve.
WD(42) = 26.04 ---> WD(42) / 42 = 26.04 / 42 ---> WD = 0.62

Front 211

There are five steps that 'we' will use to solve equations. sometimes one of the steps is not necessary.

Back 211

1. Eliminate parentheses
2. Add like terms on both sides.
3. Eliminate x on one side or the other.
4. Eliminate the constant term.
5. Eliminate the coefficient of x.

Front 212

what are the two rules for eliminating parentheses preceded by a plus sign or a minus sign?

Back 212

1. When parentheses are preceded by a plus sign, both the parentheses and the sign may be discarded, a demonstrated here
+(-4 + 3x) = -4 + 3x

Hint 212

2. When parentheses are preceded by a minus sign, both the minus sign and the parentheses may be discarded if the signs of all terms within the parentheses are changed. This rule is used because the minus sign indicates the negative of, or the opposite of, the quantity within the parentheses.
-(x - 3y + 6 - k) = -x + 3y - 6 + k

Front 213

Is every Square also a rectangle?

Back 213

Yes, every square is also a rectangle.

Front 214

What is a composite number?

Back 214

A Composite number is a number that can be composed by multiplying two counting numbersthat are both greater than 1.

Hint 214

i.e. 2 x 3 = 6
2 and 3 are greater than zero
6 is a composite number

Front 215

What is a prime number?

Back 215

A prime number is a counting number greater than 1 whose only counting number factors are 1 and the number itself.

Front 216

What is a prime factor?

Back 216

A prime factor is a factor that is a prime number.

Front 217

What do we call factors that are numbers?

Back 217

Numerical factors.

Hint 217

The umber 210 has four prime number factors, as shown here
2x3x5x7 = 210

Front 218

What are factors that are letters?

Back 218

Literal Factors.

Front 219

What is a factor that is either a letter or number, or both letters and numbers?

Back 219

Algebraic Factor.

Front 220

What is the greatest common factor of two or more terms? (GCF)

Back 220

The greatest common factor (GCF) of two or more terms is the product of all prime algebraic factors common o every term, each to the highest power that it occurs in all the terms.

Hint 220

4xpyz - 8yxz
the GCF is..
4xyz

Front 221

What is "factoring"?

Back 221

Factoring is the process of writing an indicated sum as a product of factors.

Front 222

What are Rational Expressions?

Back 222

Expressions that contain fractions are often called rational expressions.

Front 223

What does a mnus sign in front of an expression indicate??

Back 223

A minus sign in front of an expression indicates the opposite of the expression, whereas a negative exponent has a meaning that is entirely different

Front 224

What is a Solutions Set?

Back 224

We call the set of numbers that will satisfy a given equation or inequality the solution set of the equation or inequality.

Front 225

What is another name for a fraction?

Back 225

Another name for a fraction is ratio.

Hint 225

3/4
We can say that we have written the fraction thee fourths
we can also say that we have written the ratio of three to four

Front 226

What is another name for a ratio?

Back 226

Another name for a ratio is fraction.

Hint 226

3/4
We can say that we have written the fraction thee fourths
we can also say that we have written the ratio of three to four

Front 227

What are equal ratios?

Back 227

Ratios that designate the same number are equal ratios.
Called a PROPORTION.
proportion

Hint 227

All equal ratios:
3/4 300/400 6/8 15/20 27/36 111/148

Front 228

What is a proportion?

Back 228

An equation or statement in which two ratios are equal is called a proportion.

Front 229

How do we solve proportions that contain an unknown?

Back 229

We can solve proportions that contain an unknown by setting the corss products equal and then dividing to complete the solution.

Hint 229

to solve
7/5 = 91/g
we first set the cross products equal
7g=5x91
and then finish by dividing both sides by 7
7g/7 = 5x91/7 --> g = 455/7 --> g = 65
when we set the cross products equal, we say that we have cross multiplied.

Front 230

What does it mean to 'Cross Multiply'?

Back 230

When we set the cross products equal, we say that we have cross multiplied.

Front 231

What is the quotient rule for exponents?

Back 231

The quotient rule for exponents is really an extension of the next-to-last definition above that says if 'x' is any real number and 'n' is any real number that is not zero, then n -x (x is an exponent) = 1/nx (x is an exponent)

Front 232

What is the quotient rule for exponents?

Back 232

if 'm' and 'n' are real numbers and x is not equal to 0, then Xm/Xn (m&n are exponents) = Xm-n (m&n are still exponents) = 1/Xn-m (n and m are exponents, notice that N and M got switched around in the last step.)

Front 233

What is LCM? (least common multiple)

Back 233

We call the smallest number that can be divided evenly by each of a group of small group of specified numbers the least common multiple (LCM) of the specified numbers.

Front 234

How do we find the LCM? (least common multiple)

Back 234

1. rite each numer as a product of prime factors.
2. compute the LCM by using every factor of the given numbers as a factor of the LCM. use each factor the greatest number of times it i a factor in any of the numbers.

Hint 234

e.g. LCM 18, 81, and 500
1. 18 = 2*3*3
81=3*3*3*3
500=2*2*5*5*5

2. 2*2*3*3*3*3*5*5*5=40,500

3. 40,500 = LCM

Front 235

What is the rule for adding fractions wiht equal denominators?

Back 235

Fractions with equal denominators are added by adding the numerators algebraically and recording the um over a single deonminator.

Front 236

What are the three rules of algebra that some believe are more iportant than all the rest of the rules put together?

Back 236

1. the same quantity can be added to both sides of an equation.
2. every term on both sides of an equation can be multiplied (or divided) by the same quantity.
3. the denominator and numerator of a fraction can be multiplied by the same quantity

Front 237

What is the denominator-Numerator Same-Quality Rule?

Back 237

The denominator and the numerator of a fraction may be multilied by the same nonzero quantity without changing the vaue of the fraction.

Hint 237

also called the fundamental theorem of fractions of the fundamental theorem of raitonal expressions.

Front 238

What is a LCD? (least common denomentator) (not lcd screen..lol)

Back 238

the least common multiple of the deonminators of a number of fractions.

Front 239

What is a range?

Back 239

Describes the numerical difference between the least and greatest measurement.

Front 240

What is a Median?

Back 240

The middle measurement

Front 241

What is a Mode?

Back 241

the measurement that appears the most frequently, or most fashionable.

Front 242

What is the mean?

Back 242

the average of the measurements.

Front 243

What does 'bimodal' mean?

Back 243

when a set of numbers has two modes.

Front 244

What does the term statistic mean?

Back 244

the word statistic desribes the mathematics used in the collection, organization, and interpretation of numerical data.
can be a single measurement, but most often refers to a parameter such as range, median, mode or mean that is obtained from the numerical data.

Front 245

What are the measures of central tendency?

Back 245

Median, mode and mean. (they can sometimes help us to understand how a set of measurements is grouped about a central point)

Front 246

What does the word 'conjunction' mean?

Back 246

describes a statement of two conditions, both of which must be met.

Hint 246

x > 5 and x < 10
designates the numbers that are greater than 5 and are less than 10
this is a conjunction

Front 247

In a equation, what part is the Base?

Back 247

also the word of

Hint 247

p/100 x base = percentage
rate x base = percentage

Front 248

what is the percentage also called in an equation? _ x _ = _

Back 248

is

Hint 248

rate x base = percentage
p/100 x base = percentage

Front 249

What is a Polynomial?

Back 249

A polynomial in one variable (letter) is one term or a sum of individual terms each of which has the form
axn (n is a exponent)
where a is a real number and n is a whole number.

Hint 249

Also called 'simplenomial'

Front 250

what are the three requirements for something to be called a polynomial?

Back 250

1. Each algebraic expression is in the form of axn. (N is a exponent)
2. The numerical coefficient of each algebraic expression, a, is a real number.
3. the exponent of the variable, n, is a positive integer or it is the number zero.

Front 251

What is a monomial?

Back 251

A polynomial of one term.

Front 252

What is a binomial?

Back 252

a polynomial of two terms.

Front 253

What is a trinomial?

Back 253

A polynomial of three terms.

Front 254

What is the definition of a polynomial in one unknown?

Back 254

A polynomial in one unknown is an algebraic expression where the coefficients are real numbers, x is a variable, and the exponents are whole numbers.

Front 255

What is the definition of a polynomial in one or more unknowns?

Back 255

A polynomial in one ore more unknowns is an algebraic expression having only terms where the coefficient is a real number and the exponents are whole numbers.

Front 256

What is the degree of a term? (of a polynomial)

Back 256

The degree of a term of a polynomial is the sum of the exponent of the variables in the tirm.

Front 257

What is the degree of a polynomial?

Back 257

THe degree of a polynomial is the same as the degree of it's highest degree term.