Term
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Definition
A single number or variable, or numbers and variables multiplied together or divided by one another.
2x and 5z² are both terms.
8/(n+p) is also a term.
2x + 7p + x/2 contains three terms: 2x, 7p, and x/2. |
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| What Distinguishes Algebra from Arithmetic? |
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Definition
| The presence (or use) of variables. |
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Term
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Definition
A letter or symbol that represents a quantity whose value is unknown.
Usually expressed as a lowercase italic letter. |
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Term
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Definition
A term or group of terms which has one or more variables.
2x, 5z², 8/(n+p), and 2x + 7p + x/2 are all algebraic expressions. |
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Term
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Definition
| Two (or more) terms with the same variable. |
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Term
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Definition
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Term
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Definition
A number that is multiplied by variables in a term.
For 5x, 5 is the coefficient. |
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Term
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Definition
9x.
When adding algabraic expressions, like terms can combined by simply adding their coefficients. |
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Term
| What is the Rule For Adding Algabraic Expressions with Like Terms? |
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Definition
They can be combined by simply adding their coefficients.
3x+6x=9x |
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Definition
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Definition
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Term
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Definition
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| If xᵃ = xᵇ, a and b are Integers, and x is a Positive Number Other Than 1, What Do You Know? |
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Definition
a = b
For example, if you have 5ʸ = 125, you can determine that y=3, because 5³ = 125. |
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| How Do You Multiply Two Algebraic Expressions? |
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Definition
Multiply each term of the first expression by each term of the second expression.
(4x+9)(x-5) = 4x(x) + 4x(-5) + 9(x) + 9(-5) = 4x² - 20x + 9x - 45 = 4x² - 11x - 45 |
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Definition
| A statement of equality between two algebraic expressions which is true for all possible values of the variables. |
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Definition
| A statement of equality between two algebraic expressions that is true for only certain values of the variables. |
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Definition
| The values of the variables which make a particular algebraic equation true. |
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Definition
An algebraic equation in which each term is either a constant, or the product of a constant and a variable, and where the variable is not raised to any power greater than 1.
y = mx + b
4x + 7 = -10
2x + 3y = 0 |
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Definition
An algebraic equation which contains only one variable, where the variable is squared at least once.
Written in the form: ax²+bx+c = 0
Example: 4x²-20x-45 = 0 |
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| Base (in Relation to Powers) |
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Definition
When an integer has an exponent, the integer is the base.
In the expression 7², 7 is the base. |
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Definition
An integer which is used to indicate repeated multiplication of a number by itself.
In the expression 7², 2 is the exponent. |
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Term
| Convert x⁻ᵃ to a Fraction, Assuming x is a Nonzero Real Number, and a is an Integers. |
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Definition
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Term
| Convert 1/xᵃ to a Base and Exponent, Assuming x is a Nonzero Real Number, and a is an Integers. |
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Definition
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Term
| Convert (xᵃ)(xᵇ) to a Single Base with Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
| Convert xᵃ⁺ᵇ to an Algebraic Expression with Single-Variable Exponents, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
| Convert xᵃ/xᵇ to a Fraction Where the Numerator is 1, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
| Convert xᵃ/xᵇ to a Single Base with Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
| Convert 1/xᵇ⁻ᵃ to a Fraction with No Negative Numbers, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
| Convert 1/xᵇ⁻ᵃ to a Single Base with Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
| Convert xᵃ⁻ᵇ to a Fraction Where the Numerator is 1, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
| Convert xᵃ⁻ᵇ to a Fraction with No Negative Numbers, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
| What is the Value of x⁰, Assuming x is a Nonzero Real Number? |
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Definition
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Term
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Definition
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Term
| Convert (xᵃ)(yᵃ) to a Single Base with Exponent, Assuming x and y are Nonzero Real Numbers, and a is an Integer. |
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Definition
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Term
| Convert (xy)ᵃ to an Algebraic Expression Where x and y are Both Bases, Assuming x and y are Nonzero Real Numbers, and a is an Integer. |
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Definition
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Term
| Convert (x/y)ᵃ to a Simple Fraction, Assuming x and y are Nonzero Real Numbers, and a is an Integer. |
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Definition
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Term
| Convert (xᵃ)/(yᵃ) to an Algebraic Expression With a Single Exponent, Assuming x and y are Nonzero Real Numbers, and a is an Integer. |
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Definition
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Term
| Convert (xᵃ)ᵇ to an Algebraic Expression with a Single Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
| Convert xᵃᵇ to an Algebraic Expression Where b is an Individual Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
| Convert xᵃᵇ to an Algebraic Expression Where a is an Individual Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
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Term
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Definition
| No. The expansion of (x + y)ᵃ should contain terms of the form 4xy. |
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Term
| When Using a Negative Sign in Front of the Base, Does it Matter Whether or Not There are Parenthesis? |
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Definition
Yes!
-x² is the negative of x², while and (-x)² is -x to the second power. |
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Term
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Definition
| This cannot be done. While √(x²)=x and √(y²)=y, √(x²+y²) does NOT equal x+y. |
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Term
| Convert (a)/(x+y) to an Algebraic Expression Which Combines (Sums) Two Fractions, Assuming x is a Nonzero Real Number, and a and b are Integers. |
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Definition
| You can't do this. While (x+y)/a=(x/a)+(y/a), (a)/(x+y) does NOT equal (a/x)+(a/y) |
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| What Does it Mean to "Solve an Equation"? |
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Definition
| To find the values of the variables that make the equation true. |
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| What Does it Mean to "Satisfy an Equation"? |
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Definition
| To find the values of the variables that make the equation true. |
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| Fill in the Blank: To ______ an Equation, You Must Find the Values of the Variables that Make the Equation True. |
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Definition
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Term
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Definition
Two (or more) equations with the same solution.
x+2=4 and 2x+8=12 are equivalent equations, because they are both only true when x=2. |
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| What Happens When the Same Constant is Added or Subtracted from Both Sides of an Equation? |
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Definition
| The equality is preserved: the new equation is equivalent to the original equation. |
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Term
| If You Subtract 3 From One Side of an Equation, How Do You Ensure the New Equation is Equivalent to the Original? |
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Definition
| Subtract 3 from the other side. |
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Term
| If You Add 3 to One Side of an Equation, How Do You Ensure the New Equation is Equivalent to the Original? |
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Definition
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Term
| What Happens When Both Sides of an Equation are Multiplied or Divided by the Same Nonzero Constant? |
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Definition
| The equality is preserved: the new equation is equivalent to the original equation. |
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Term
| If You Multiply One Side of an Equation by 3, How Do You Ensure the New Equation is Equivalent to the Original? |
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Definition
| Multiply the other side by 3. |
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| If You Divide One Side of an Equation by 3, How Do You Ensure the New Equation is Equivalent to the Original? |
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Definition
| Divide the other side by 3. |
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| Solve: 5x-2-x = 3(x-2)-2x |
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Definition
5x-2-x = 3x-6-2x (factored)
4x-2 = x-6 (like terms combined)
4x-2+2 = x-6+2 (2 added to both sides)
4x-x = x-4-x (x subtracted from both sides)
3x = -4
3x/3 = -4/3 (both sides divided by 3)
x = -4/3 OR -1.33333... |
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Term
| How Do You Solve Linear Equations in One Variable? |
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Definition
| Simplify each side of the equation by combining like terms. Then use the rules for producing simpler equivalent equations. |
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Term
| What is One Way to Check Your Solution to a Linear Equation in One Variable? |
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Definition
| Substitute your solution into the original equation. |
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Term
| What is the Minimum Number of Solutions a Linear Equation Can Have? |
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Definition
| Zero. Some linear equations do not have solutions. |
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Term
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Definition
The solution to an equation with two variables.
Written like this: (x,y). |
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Term
| How Many Solutions Does a Linear Equation with Two Variables Have? |
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Definition
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Term
| How Do You Find the Solution to a Linear Equation with Two Variables? |
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Definition
You can do this if you have another linear equation with the same variables.
You would use either substitution or elimination. |
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Definition
| Two equations with the same variables. |
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Definition
| The equations in a sytem of variables. |
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Term
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Definition
| One equation is manipulated to express one variable in terms of the other. Then the expression is substituted into the other equation. |
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| Using Substitution, Solve This System: 2x-3y=-2 and 4x+y=24 |
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Definition
4x+y = 24
4x+y-4x = 24-4x (subtract 4x from each side)
y = -4x+24
2x-3(-4x+24) = -2 (substitute the solution for y into the other equation)
2x+12x-72 = -2 (factor)
2x+12x-72+72 = -2+72 (add 72 to both sides)
14x/14 = 70/14 (divide both sides by 14)
x=5
y = -4(5)+24 = -20+24 = 4 (substitute the value for x into the solution for y)
Solution: (5,4) |
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Term
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Definition
| Make the coefficients of one variable the same in both equations. Eliminate that variable using addition or subtraction. |
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Term
| Using Elimination, Solve This System: 4x-3y=25 and -3x+8y=10 |
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Definition
Multiply to get the same coefficient for one variable: 3(4x-3y=25) and 4(-3x+8y=10)
Factor both sides: 12x-9y=75 and -12x+32y=40
Add them together to get: 23y=115
Divide by 23: y=5
Substitute y into one of the equations: 4x-3(5)=25
Factor: 4x-15=25
Add 15 to both sides: 4x=40
Divide both sides by 4: x=10
Solution: (10,5) |
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Term
| How Many Solutions Does a Quadratic Equation Have? |
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Definition
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Term
| How Do You Solve a Quadratic Equation? |
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Definition
| Use the quadratic formula. You can also factor in some cases. |
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Term
| What is the Advantage of the Quadratic Formula Over Factoring? |
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Definition
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Term
| What is the Advantage of Factoring Over Using the Quadratic Formula? |
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Definition
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Term
| What is the Quadratic Formula? |
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Definition
x = [-b +/- √(b²-4ac)]/2a
The notation +/- means you have to solve it twice: once for - and once for +. |
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| Use the Quadratic Formula to Solve: x²-4x-8 = 0 |
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Definition
x = [-(-4) +/- √((-4)²-4(1)(-8))]/2(1)
x = [4 +/- √(16+32)]/2
x = (4 +/- √48)/2
x = [4 +/- √(3)(16)]/2
x = (4 +/- 4√3)/2
x = [2(2 +/- 2√3)]/2
x = 2 +/- 2√3
x = 2+2√3 AND 2-2√3
In decimal form: x = 5.464 AND -1.464 |
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Term
| Use Factoring to Solve: x²+5x+6 = 0 |
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Definition
Factor: (x+2)(x+3) = 0
Solve each Factor: x+2=0 and x+3=0
x=-2 and x=-3
Solution: -3,-2 |
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Term
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Definition
A mathematical statement that uses one of the inequality signs:
<
>
≤
≥
And where the variable is not raised by any power greater than 1. |
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Term
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Definition
| To find the set of all values of the variables that make the inequality true. |
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| Solution Set of an Inequality |
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Definition
| The set of all values of the variables that make the inequality true. |
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Term
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Definition
| Two qualities that have the same solution. |
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Term
| What Happens When the Same Constant is Added or Subtracted from Both Sides of an Inequality? |
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Definition
| The inequality is preserved: the new inequality is equivalent to the original inequality, and the direction of the inequality is preserved. |
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Term
| If You Subtract 3 From One Side of an Inequality, How Do You Ensure the New Inequality is Equivalent to the Original? |
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Definition
| Subtract 3 from the other side. |
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Term
| If You Add 3 to One Side of an Inequality, How Do You Ensure the New Inequality is Equivalent to the Original? |
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Definition
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Term
| What Happens When Both Sides of an Equation are Multiplied or Divided by the Same Nonzero Constant? |
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Definition
IF THE CONSTANT IS POSITIVE: The inequality is preserved: the new inequality is equivalent to the original inequality, and the direction of the inequality is preserved.
IF THE CONSTANT IS NEGATIVE: The direction of the inequality must be reversed to preserve the inequality. |
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Term
| If You Multiply One Side of an Inequality by 3, How Do You Ensure the New Inequality is Equivalent to the Original? |
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Definition
| Multiply the other side by 3. |
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Term
| If You Divide One Side of an Inequality by 3, How Do You Ensure the New Inequality is Equivalent to the Original? |
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Definition
| Divide the other side by 3. |
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Term
| If You Multiply One Side of an Inequality by -3, How Do You Ensure the New Inequality is Equivalent to the Original? |
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Definition
| Multiply the other side by -3 AND reverse the direction of the inequality. |
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Term
| If You Divide One Side of an Inequality by -3, How Do You Ensure the New Inequality is Equivalent to the Original? |
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Definition
| Divide the other side by -3 AND reverse the direction of the inequality. |
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Term
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Definition
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Term
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Definition
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Term
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Definition
-2x/-2 > 5/-2
x > -5/2
x > -2.5
NOTE THAT THE INEQUALITY IS REVERSED! |
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Term
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Definition
An algebraic expression which produces a single result for each value of the variable.
Any input for a function produces a single output.
They are usually denoted by the letters f, g, and h. For example: f(x) = 2x+6 |
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Term
| Fill in the Blank: g(x) = 2x+6 is an Example of a ______. |
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Definition
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Term
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Definition
The set of all permissible inputs of a function.
Sometimes, the domain of a function is given explicitly and is restricted to specific values of x. |
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Term
| If the Domain of a Function is Not Explicitly Defined, What is the Domain? |
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Definition
| All values of x for which f(x) is a real number. |
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Term
| What Does it Mean if a Particular Variable Causes a Function to be Undefined? |
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Definition
That variable is outside the range for the function.
For example, if we plug 9 into the equation: 3x/x-9, we get 27/0, which is undefined. Therefore, the domain of this function is all real numbers except for 9. |
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Term
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Definition
| An amount added to the original amount, usually over time. |
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Term
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Definition
| Interest which is based on the initial amount (called the principle) for the entire time period. |
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Term
| What is the Equation Used to Calculate Simple Interest? |
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Definition
V = P[1+(rt/100)]
Where V is the new value, P is the original value, r is the interest rate, and t is the time. |
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Term
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Definition
| Interest which is added to the principle at regular time intervals, where interest is earned on the new amount. |
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Term
| What is the Equation Used to Calculate Compound Interest Which is Compounded Yearly? |
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Definition
V = P(1+r/100)ᵗ
Where V is the new value, P is the original value, r is the interest rate, and t is the time. |
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Term
| What is the Equation Used to Calculate Compound Interest With and Annual Interest Rate Which is Compounded More Than Once Per Year? |
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Definition
V = P(1+r/100n)ⁿᵗ
Where V is the new value, P is the original value, r is the interest rate, t is the time, and n is the number of times per year it is compounded. |
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Term
| If $3000 is Invested At a Simple Interest Rate of 17%, What is the Value After 3 Years? |
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Definition
V = $3000[1+({17}{3}/100)]
V = $3000[1+(51/100)]
V = $3000(1+0.51)
V = $3000(1.51)
V = $4530 |
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Term
| If $3000 is Invested At a Compound Interest Annual Rate of 17% Which is Compounded Annually, What is the Value After 3 Years? |
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Definition
V = $3000(1+{17}/100)⁽³⁾
V = $3000[1+0.17]³
V = $3000(1.17)³
V = $3000(1.601613)
V = $4804.839
Which is simplified to: $4804.84 |
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Term
| If $3000 is Invested At a Compound Interest Annual Rate of 17% Which is Compounded Monthly, What is the Value After 3 Years? |
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Definition
V = P(1+r/100)ᵗ
V = $3000(1+{17}/100{12})⁽¹²⁾⁽³⁾
V = $3000(1+17/1200)³⁶
V = $3000[1+0.01416666666666666666666666666667]³⁶
V = $3000(1.01416666666666666666666666666667)³⁶
V = $3000(1.6593422013892234548898239271675)
V = $4978.0266041676703646694717815025
Which is simplified to: $4978.03 |
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Term
| If the Value is $4000 After 3 Years of Compound Interest with an Annual Rate of 17% Which is Compounded Monthly, What was the Original Investment? |
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Definition
V = P(1+r/100n)ⁿᵗ
$4000 = P(1+{17}/100{12})⁽¹²⁾⁽³⁾
$4000 = P(1+17/1200)³⁶
$4000 = P[1+0.01416666666666666666666666666667]³⁶
$4000 = P(1.01416666666666666666666666666667)³⁶
$4000 = P(1.6593422013892234548898239271675)
Now, we can solve it just like any other linear equation in a single variable:
$4000/(1.6593422013892234548898239271675) = P(1.6593422013892234548898239271675)/(1.6593422013892234548898239271675)
2410.5937862914271522006019561891
Which is simplified to: $2410.59 |
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Term
| If $3000 is Invested for Using a Compound Interest Which is Compounded Monthly, and the Value After 3 Years is $4000.26, What is the Annual Interest Rate? |
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Definition
V = P(1+r/100n)ⁿᵗ
$4000.26 = $3000(1+r/100{12})⁽¹²⁾⁽³⁾
$4000.26 = $3000(1+r/1200)³⁶
$4000.26/$3000 = (1200/1200+r/1200)³⁶
1.33342 = (1200+r)/1200)³⁶
1.33342 = (1200+r)³⁶/(1200)³⁶
(1.33342)(1200)³⁶ = (1200+r)³⁶
(1.33342)($7.08801)(10¹¹⁰) = (1200+r)³⁶
(9.45131)(10¹¹⁰) = (1200+r)³⁶
³⁶√[(9.45131)(10¹¹⁰)] = 1200+r
1209.63000-1200 = r
9.63000 = r
Which is simplified to: 9.63% |
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Term
| Rectangular Coordinate System |
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Definition
| Two real number lines that intersect at their respective zero points. |
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Term
|
Definition
| Two real number lines that intersect at their respective zero points. |
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Term
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Definition
| Two real number lines that intersect at their respective zero points. |
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Term
| What is it Called when Two Real Number Lines Intersect at Their Respective Zero Points. |
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Definition
| It can be called the rectangular coordinate system, the xy-coordinate system, or the xy-plane. |
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Term
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Definition
| The horizontal number line in a rectangular coordinate system. |
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Term
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Definition
| The verical number line in a rectangular coordinate system. |
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Term
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Definition
| The point where the x-axis and y-axis intersect in a rectangular coordinate system. |
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Term
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Definition
| Any one of the four regions created by the x-axis and y-axis in a rectangular coordinate system. |
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Term
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Definition
The top right of the rectangular coordinate system.
Note that both x and y are positive in this quadrant. |
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Term
|
Definition
The top left of the rectangular coordinate system.
Note that x is negative and y is positive in this quadrant. |
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Term
|
Definition
The bottom left of the rectangular coordinate system.
Note that both x and y are negative in this quadrant. |
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Term
|
Definition
The bottom right of the rectangular coordinate system.
Note that x is positive and y is negative in this quadrant. |
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Term
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Definition
| A point on the xy-plane, written as: (x,y) |
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Term
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Definition
| The first number in an ordered pair, indicating where along the x-axis the point is located. |
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Term
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Definition
| The second number in an ordered pair, indicating where along the y-axis the point is located. |
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Term
| What Are the Coordinates for the Origin? |
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Definition
|
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Term
| If a Point, P, Has the Coordinates (4,2) and Another Point, Q, Has the Coordinates (4,-2), What is Their Geometric Relation? |
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Definition
Q is a reflection of P about the x-axis.
OR: P and Q are symmetric about the x-axis. |
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Term
| If a Point, P, Has the Coordinates (4,2) and Another Point, Q, Has the Coordinates (-4,2), What is Their Geometric Relation? |
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Definition
Q is a reflection of P about the y-axis.
OR: P and Q are symmetric about the y-axis. |
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Term
| If a Point, P, Has the Coordinates (4,2) and Another Point, Q, Has the Coordinates (-4,-2), What is Their Geometric Relation? |
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Definition
Q is a reflection of P about the origin.
OR: P and Q are symmetric about the origin. |
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Term
| How Do You Find the Distance Between Two Points on the xy-Plane? |
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Definition
Use the Pythagoream theorem.
a²+b² = c² |
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Term
| What is the Pythagorean theorem? |
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Definition
The equation used to obtain a diagonal when the distance along the x-plane and the distance along the y-plane are both known.
a²+b² = c² |
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Term
| If P is at (4,3) and Q is at (-4,-3), What is the Distance Between Them? |
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Definition
Distance on the x-plane: (4)-(-4) = 4+4 = 8
Distance on the y-plane: (3)-(-3) = 3+3 = 6
Diagonal: (8)²+(6)² = c²
c² = 64+36
c² = 100
c = √100
c = 10
The distance between them is 10. |
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Term
| How Do You Represent an Equation in Two Variables on the xy-Plane? |
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Definition
| Graph the equation by finding the set of all points whose ordered pairs satisfy the equation. |
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Term
|
Definition
| The set of all points whose ordered pairs satisfy an equation in two variables. |
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Term
|
Definition
The ratio of two points along the graph of an equation, of the form (y₂-y₁)/(x₂-x₁).
This is often referred to as the rise over the run.
Note that it does not matter which point is defined as (x₁,y₁) and which is defined as (x₂,y₂). |
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Term
| What is the Slope of a Linear Equation with the Form y=mx+b? |
|
Definition
|
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Term
|
Definition
The x-coordinates of the point(s) where the graph intersects with the x-axis.
y=0 at this point. |
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Term
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Definition
The y-coordinates of the point(s) where the graph intersects with the y-axis.
x=0 at this point. |
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| If the x-Intercept is 6, What is the Value of y at This Location? |
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Definition
The value of y is 0.
The value of y is always 0 at the x-intercept. |
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| If the y-Intercept is -3, What is the Value of x at This Location? |
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Definition
The value of x is 0.
The value of x is always 0 at the y-intercept. |
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Term
| What is the y-Intercept of a Linear Equation with the Form y=mx+b? |
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Definition
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Term
| When Describing the Slope, Which Value is the Rise? |
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Definition
The change in y when moving from the first point to the second; (y₂-y₁).
This is the numerator of the slope ratio. |
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Term
| When Describing the Slope, Which Value is the Run? |
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Definition
The change in x when moving from the first point to the second; (x₂-x₁).
This is the denominator of the slope ratio. |
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Term
| What is the Slope of a Vertical Line? |
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Definition
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Term
| What is the Slope of a Horizontal Line? |
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Definition
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| What is the Form of the Equation for a Vertical Line? |
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Definition
| x = a, where a is the x-intercept. |
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Term
| What is the Form of the Equation for a Horizontal Line? |
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Definition
| y = b, where b is the y-intercept. |
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Definition
When two lines have the same slope, they are considered parallel.
This means they can continue forever without touching. |
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Definition
The inverse of a fraction, so that the numerator becomes the denominator, and the denominator becomes the numerator
The reciprocal of 3/5 is 5/3. |
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Definition
The inverse of a fraction with the opposite sign, so that the numerator becomes the denominator, and the negative of the denominator becomes the numerator
The negative reciprocal of 3/5 is -5/3. |
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Definition
When the slopes of two lines are negative reciprocals of one another.
They will intersect one another at a 90-degree angle. |
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Term
| What is the Slope of a Line Passing Through Points P(3,-5) and Q(-2,-1)? |
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Definition
[(-1)-(-5)]/[(-2)-(3)]
(-1+5)/(-2-3)
4/-5
-4/5 |
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Term
| If the Slope of a Line is 3 and One of the Points is (6,2), What is the y-Intercept? |
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Definition
y = 3x+b
2 = 3(6)+b
2 = 18+b
-16 = b
The y-intercept will be -16. |
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Term
| How Do You Use the Graph of a System of Linear Equations in Two Variables to Illustrate Its Solution? |
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Definition
Solve each equation for y in terms of x, then graph both equations.
The intersection will be the solution. |
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Term
| How Do You Use the Graph of a System of Linear Inequalities in Two Variables to Illustrate Its Solution? |
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Definition
Solve each equation for y in terms of x, graph both equations, then shade the appropriate side of the line.
If y is less than the x solution, the graph of the equation consists of the region below that line.
If y is more than the x solution, the graph of the equation consists of the region above that line.
If y is less than or equal to the x solution, the graph of the equation consists of the line AND the region below that line.
If y is more than or equal to the x solution, the graph of the equation consists of the line AND the region above that line.
The intersection of the two regions (all points where both graphs meet) is shaded. |
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Term
| What is Special About a Line with Equation y=x? |
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Definition
1) It will pass through the origin.
2) It will have a slope of 1.
3) It will make a 45-degree angle with each axis.
4) For any point with coordinates (a,b), the point with interchanged coordinates (b,a) will be a reflection of (a,b) about the line y=x.
To put it another way, (a,b) and (b,a) are symmetric about the line y=x. |
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Term
| What Happens if You Interchange x and y in the Equation of Any Graph? |
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Definition
| It yields another graph that is the reflection of the original graph about the line y=x. |
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Term
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Definition
| The line around which the two lines are reflected. |
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Term
| What is the Line of Symmetry for the Graphs of an Equation and the Interchange of that Equation? |
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Definition
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Term
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Definition
| The graph of a quadratic equation of the form y = ax²+bx+c, where a, b, and c are constants, and a is a nonzero real number. |
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Term
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Definition
| The point of the graph of a quadratic equation that lies on the line of symmetry. |
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Term
| If the Vertex of a Quadratic Equation of the Form y = ax²+bx+c is its Lowest Point, What Do You Know About a? |
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Definition
| You know that a is positive. |
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Term
| If the Vertex of a Quadratic Equation of the Form y = ax²+bx+c is its Highest Point, What Do You Know About a? |
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Definition
| You know that a is negative. |
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Term
| What Are the x-Intercepts of a Parabola? |
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Definition
| The solutions of the equation ax²+bx+c = 0. |
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Term
| What Are the x-Intercepts of an Equation of the Form y = ax²+bx+c? |
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Definition
| The solutions of the equation ax²+bx+c = 0. |
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Term
| When Graphing a Function, Which Axis Do You Use for the Input? |
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Definition
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Term
| When Graphing a Function, Which Axis Do You Use for the Output? |
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Definition
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Term
| Fill in the Blank: Every Parabola is ______ with Itself About the Vertical Line that Passes Through its Vertex. |
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Definition
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| Fill in the Blank: Every Parabola is symmetric with Itself About the Vertical Line that Passes Through its ______. |
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Definition
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Term
| Fill in the Blank: The Two x-Intercepts of a Parabola are ______ from the Line of Symmetry. |
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Definition
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Term
| Fill in the Blank: The Two x-Intercepts of a Parabola are Equidistant from the ______. |
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Definition
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Term
| What is the Graph of an Equation of the Form r² = (x-a)²+(y-b)²? |
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Definition
| A circle with its center at the point (a,b) and a radius of r. |
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Term
| Describe the Graph of this Equation: 100 = x²+y² |
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Definition
| A circle with its center at the origin and a radius of 10. |
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Term
| Describe the Graph of this Equation: (x-6)²+(y+5)² = 9 |
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Definition
| A circle with its center at (6,5) and a radius of 3. |
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Term
| How Do You Graph a Function? |
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Definition
| Represent each input, x, and its corresponding output, f(x), as a point (x,y) where y = f(x). |
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Term
| Piecewise-Defined Function |
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Definition
A function which is defined by multiple subfunctions, each of which applies to a certain interval of the function's domain.
Absolute value functions are examples of piecewise-defined functions. |
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Term
| What is the Shape of the Graph of an Absolute Value Function? |
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Definition
| It is v-shaped, with two linear pieces. |
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Term
| If f(x) = |x|+c, What is the y-Intercept? |
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Definition
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Term
| When Comparing the Graphs of f(x)=|x| and g(x)=|x|+c, What is Their Relationship? |
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Definition
| The graph of g(x) is shifted upwards from f(x) by c units. |
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Term
| When Comparing the Graphs of f(x)=|x| and g(x)=|x|-c, What is Their Relationship? |
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Definition
| The graph of g(x) is shifted downwards from f(x) by c units. |
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Term
| When Comparing the Graphs of f(x)=|x| and g(x)=|(x+c)|, What is Their Relationship? |
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Definition
| The graph of g(x) is shifted to the left of f(x) by c units. |
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Term
| When Comparing the Graphs of f(x)=|x| and g(x)=|(x-c)|, What is Their Relationship? |
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Definition
| The graph of g(x) is shifted to the right of f(x) by c units. |
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Term
| When Comparing the Graphs of f(x)=|x| and g(x)=c|(x)|, What is Their Relationship if c is More than One? |
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Definition
| The graph of g(x) is streched vertically versus f(x) by a factor of c. |
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Term
| When Comparing the Graphs of f(x)=|x| and g(x)=|(x-c)|, What is Their Relationship if c is More than Zero But Less than One? |
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Definition
| The graph of g(x) is shrunk vertically versus f(x) by a factor of c. |
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