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Definition
| "counting numbers {1, 2, 3…}" |
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Definition
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Definition
| "{0, 1, 2, 3…} hint: 0 looks like a hole" |
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Definition
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Definition
| "fractions, terminating and repeating decimals" |
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Term
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Definition
"look wacky!
non-terminating, non-repeating decimals" |
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Definition
| all the numbers you know about |
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Definition
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Term
| What set is a subset of every other set. |
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Definition
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Definition
| a set wholly contained in another |
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Definition
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Definition
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Definition
| just cut the extra digits off |
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Definition
| digit one to the right – 5 & higher go up |
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Definition
| numbers revolve around + or x |
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Definition
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Term
| Which property is 5(x + 2) = 5x + 10 |
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Definition
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Term
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Definition
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Definition
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Definition
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| definition of absolute value |
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Definition
| distance from zero on the number line |
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Term
| multiplication property of zero |
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Definition
| anything times zero is zero |
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Term
| the 1st Commandment of Math |
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Definition
| thou shalt not divide by zero! |
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Term
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Definition
| please excuse my dear aunt sally |
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Term
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Definition
| make birds nests ( ) first then substitute |
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Term
| when you evaluate, your answer will be |
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Definition
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Term
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Definition
| same letters to the same powers |
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Term
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Definition
| values it is allowed to be in that expression |
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Definition
| variable disappears and you have a true statement like 0 = 0 |
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Term
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Definition
| variable disappears and you have a false statement like 2 = 0 |
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Term
| When you have both a fraction and an equal sign... |
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Definition
| Multiply every term by a common denominator |
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Term
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Definition
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Term
| Consecutive even integers |
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Definition
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Term
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Definition
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Term
| In a story problem, the word "than" |
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Definition
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Term
| Last step of every story problem |
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Definition
| make sure you answered the question! |
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Term
| Comparison problems, make x |
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Definition
| the second thing mentioned |
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Term
| When using boxes to solve story problems, multiply |
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Definition
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Term
| When using boxes to solve story problems, add |
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Definition
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Term
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Definition
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| Formula for the area of a rectangle |
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Definition
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Term
| Sum of the measures of the angles in a triangle |
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Definition
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Term
| The value of a pile of dimes is |
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Definition
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Term
| The value of a pile of nickels |
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Definition
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Term
| The value of a pile of quarters is |
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Definition
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Term
| If they give you the before and after prices, the % increase or decrease is |
|
Definition
| difference of the prices over the original |
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Term
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Definition
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Term
| If you multiply or divide an inequality by a negative |
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Definition
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Term
| 3 < x is the same thing as |
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Definition
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Term
| To graph x < 5, darken the arrow head on the number line that points |
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Definition
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Term
| To graph x > 3, darken the arrow head on the number line that points |
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Definition
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Term
| To graph x < 5, the endpoint of the ray will be |
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Definition
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Term
| To graph x > 3, the endpoint of the ray will be |
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Definition
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Term
| If you use extra ink to make an equal sign under the inequality, to make the endpoint of the ray use |
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Definition
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Term
| To solve compound inequalities involving OR, picture the figure |
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Definition
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Term
| To solve compound inequalities involving AND, picture the figure |
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Definition
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Term
| Union of two sets, is the word AND or OR? |
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Definition
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Term
| Intersection of 2 sets, is the word AND or OR |
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Definition
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Term
| Compound inequalities involving OR, the graph will be |
|
Definition
| either shooting arrow(s) or whole number line |
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Term
| Compound inequalities involving AND, the graph will be |
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Definition
| a barbell, a point, or the empty set (no solution) |
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Term
| Two types of problems that give answers that are shooting arrows |
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Definition
| EleanOR and absolute value > |
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Term
| Two types of problems that give answers that are barbells |
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Definition
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Term
| What number can never be on the bottom of a fraction? |
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Definition
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Term
| In absolute value problems, how many answers do you usually expect? |
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Definition
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Term
| Absolute value < negative What is the answer? |
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Definition
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Term
| Absolute < 0 What is the answer? |
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Definition
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Term
| Absolute > negative What is the answer? |
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Definition
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Term
| Absolute > 0 What is the answer? |
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Definition
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Term
| Absolute = 0, no exponents How many answers do you expect? |
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Definition
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Term
| What 2 things do you do to solve absolute value inequalities? |
|
Definition
| Stuffing-copy-copy and stuffing-flip-neg |
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Term
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Definition
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Term
| If a point is on the graph, when you plug in the values you get |
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Definition
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Term
| If a point is NOT on the graph, when you plug in the values you get |
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Definition
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Term
| The 3 ways to graph a line |
|
Definition
| intercept method, slope-intercept, table of values |
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Term
| Table of values, pick numbers for the |
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Definition
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Definition
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|
Definition
| the slope-intercept equation of a line |
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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
| y = mx + b, the first point you plot is |
|
Definition
| b which is the y-intercept |
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Term
| If you have a negative fraction, I aways use the rule that negative signs |
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Definition
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Term
| Line goes down from left to right. The sign of the slope will be |
|
Definition
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Term
| Line goes up from left to right. The sign of the slope will be |
|
Definition
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Term
| The slope of a horizontal line is |
|
Definition
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Term
| The slope of a vertical line is |
|
Definition
|
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Term
| x-intercept is where the graph |
|
Definition
|
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Term
| y-intercept is where the graph |
|
Definition
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Term
| To get from one point on the line to another point on the line, use the |
|
Definition
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Term
| If the slope is positive, to get to another point go |
|
Definition
| up and then over to the right |
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Term
| If the slope is negative, to get to another point go |
|
Definition
| down and then over to the right |
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Term
|
Definition
| the set of allowable values for the x-coordinate |
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Term
|
Definition
| the set of allowable values for the y-coordinate |
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Term
| In a relation, same first elements map to different second element |
|
Definition
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Term
| A graph is NOT a function if it fails the |
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Definition
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Term
| A graph fails the vertical line test if a vertical line can |
|
Definition
| cross it a 2 or more different points |
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Term
| Most of the time, f(x) can be thought of as |
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Definition
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Term
| If you are asked to evaluate f(5) the your bird is |
|
Definition
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Term
Which equation of a line is this?
y – y1 = m( x – x1 ) |
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Definition
| point-slope equation of a line |
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Term
| What is the standard equation of a line? |
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Definition
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Term
| What are you probably going to have to do if they give you the coordinates of 2 points? |
|
Definition
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Term
| If the give you a point and the slope, which equation of a line should you use? |
|
Definition
| point-slope equation of a line |
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Term
| What are lines that go up and down called? |
|
Definition
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Term
| If a line is slanted, it's equation must have both |
|
Definition
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Term
| If an equation has both x and y, it's graph will be |
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Definition
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Term
| The graph of x = 5 is what kind of line? |
|
Definition
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|
Term
| The graph of y = 5 is what kind of line? |
|
Definition
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Term
| What is the graph of y = 0? |
|
Definition
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|
Term
| What is the graph of x = 0? |
|
Definition
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Term
|
Definition
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Term
|
Definition
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Term
|
Definition
|
|
Term
| Highway engineers call slope |
|
Definition
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Term
| By its nature, slope is a |
|
Definition
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Term
| If a slope is 2, think of it as |
|
Definition
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Term
| To find the equation of a line from 2 points |
|
Definition
First calculate the slope,
then use one of the points and the slope in the point-slope equation. |
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Term
| What is the point-slope equation of a line? |
|
Definition
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Term
| Which equation of a line is Ax + By = C? |
|
Definition
| Standard equation of a line |
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Term
| What is the slope-intercept equation of a line? |
|
Definition
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Term
| If the slope is zero, the line is |
|
Definition
|
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Term
| If the slope is undefined, the line is |
|
Definition
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Term
| All liner equations except for x = a are |
|
Definition
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Term
| The independent variable is always plotted on the |
|
Definition
|
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Term
| The dependent variable is always plotted on the |
|
Definition
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Term
| A linear equation is the equation of |
|
Definition
|
|
Term
| In absolute value problems, the first thing to do is |
|
Definition
| isolate the absolute value |
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|
Term
| To graph an inequality on the number line, you need to write the inequality with the variable |
|
Definition
|
|
Term
| If you have a fraction and an equal sign |
|
Definition
| multiply everything by a common denominator |
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|
Term
| When solving an equation, the last thing you do is almost always |
|
Definition
| divide by the coefficient of the variable |
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Term
| Formula for the perimeter of a rectangle |
|
Definition
|
|
Term
| two or more equations that are graphed on the same graph are called |
|
Definition
| a system of linear equations |
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|
Term
| Another phrase meaning a system of linear equations |
|
Definition
| simultaneous linear equations |
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Term
| A solution to a system of equations |
|
Definition
| the point(s) on both lines |
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Term
| To determine if an ordered pair is a solution to an equation |
|
Definition
| Plug in the values and see if you get an identity |
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Term
| To determine if a point is the intersetion of two lines |
|
Definition
| Plug the values into both equations and see if you get identities |
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Term
| When two straight lines are graphed on the same graph, what three things can happen? |
|
Definition
| The lines can intersect, be parallel or be coincident. |
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Term
| If lines are intersecting, how many points do they have in common? |
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Definition
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Term
| If lines are parallel, how many points do they have in common? |
|
Definition
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Term
| If lines are coincident, how many points do they have in common? |
|
Definition
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Term
| If lines have one or more points in common, the system is |
|
Definition
|
|
Term
| If lines have no points in common, the system is |
|
Definition
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Term
| If the system is consistent and the lines intersect in one point then the equations are |
|
Definition
|
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Term
| If the system is consistent and the lines intersect in infinitely many points then the equations are |
|
Definition
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|
Term
| If lines cross, the lines. |
|
Definition
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Term
| If lines in a plane never touch each other, the lines are |
|
Definition
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|
Term
| If one line is graphed directly on top of another, the lines are |
|
Definition
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Term
| If you solve a system of equations and your answer is an ordered pair, the lines |
|
Definition
|
|
Term
| If you solve a system of equations and your answer is an indentity, the lines |
|
Definition
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|
Term
| If you solve a system of equations and your answer is a contradiction, the lines |
|
Definition
|
|
Term
| What are the three ways to solve a system of linear equations? |
|
Definition
graphing
substitution
addition (elimination) |
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|
Term
Which method should you probably use to solve the system
x + y = 10
x - y = 8 |
|
Definition
Addition (elimination)
(because they're lined up in columns) |
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|
Term
What method should you probably use to solve the system
x = y + 2
5x + 3y = 18 |
|
Definition
substitution
(because one equation is already solved for x) |
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|
Term
| To graph a linear inequality in two variables (paint can), which equation of a line should you use? |
|
Definition
| slope-intercept y = mx + b |
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|
Term
| To graph a linear inequality in two variables (paint can), if no extra ink has been used to make an equal sign under the arrow, then |
|
Definition
|
|
Term
| To graph a linear inequality in two variables (paint can), if extra ink has been used to make an equal sign under the arrow, then |
|
Definition
|
|
Term
| To graph a linear inequality in two variables (paint can), if the inequality is y < you shade |
|
Definition
|
|
Term
| To graph a linear inequality in two variables (paint can), if the inequality is y > you shade |
|
Definition
|
|
Term
| The y-intercepts of paralle lines are |
|
Definition
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|
Term
| The slopes of parallel lines are |
|
Definition
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|
Term
| The slope of perpendicular lines are |
|
Definition
|
|
Term
| What is the slope of a line parallel to a line that has a slope of 5? |
|
Definition
|
|
Term
| What is the slope of a line pperpendicular to a line that has a slope of -2? |
|
Definition
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|
Term
| a horizontal and a vertical line are |
|
Definition
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Term
|
Definition
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|
Term
| If you are given a point and the slope, which form of the equation of a line should you use |
|
Definition
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Term
| Perpendicular lines intersect at |
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Definition
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Term
| Family A buys 5 hot dogs and 4 drinks for 14.00. Family B buys 4 hot dogs and 6 drinks for 14.00. Set up the system of equations. |
|
Definition
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Term
| Susie is 3 years younger than Bill. If Bill's age is x, what is Susie's age? |
|
Definition
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|
Term
| If you hop the equal sign you must |
|
Definition
swap your sign for the opposite
(change your sign) |
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|
Term
| In boat problems, downstream means |
|
Definition
|
|
Term
| In boat problems, upstream means |
|
Definition
|
|
Term
| In plane problems, tailwind means |
|
Definition
|
|
Term
| In plane problems, headwind means |
|
Definition
|
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Term
| If a boat is going with the current, the rate is |
|
Definition
|
|
Term
| If a boat is going against the current, the rate is |
|
Definition
|
|
Term
| In current problems, the first variable in the rate must always be |
|
Definition
the man-made object
(plane or boat) |
|
|
Term
| If I have 2 liters of a 50% acid solution, how much acid do I actually have? |
|
Definition
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|
Term
| Sue got a 5% raise. If her original salary was x, what is the amount of her raise? |
|
Definition
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|
Term
| What is the formula for the area of a rectangle? |
|
Definition
|
|
Term
| break-even point in cost and revenue problems |
|
Definition
| where the cost curve intersects the revenue curve |
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Term
|
Definition
|
|
Term
| Use x and y to write an equation for "The sum of two numbers is 10" |
|
Definition
|
|
Term
| Use x and y to write an equation for "The difference of two numbers is 8" |
|
Definition
|
|
Term
| The solution to a dependent system of equations is written as the set of a ordered pairs (x, y) such that |
|
Definition
| one of the equations in the system is true |
|
|
Term
| If a system of equations has infinitely many solutions, then the equations are |
|
Definition
|
|
Term
| If a system of equations has infinitely many solutions, then the system is |
|
Definition
|
|
Term
| Solving a system of equations by the addition (elimination) method works best if both equations are in which form? |
|
Definition
| standard form: Ax + By =C |
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|
Term
| In general, you've got a chance of finding a solution to a system of equations if the number of equations is equal to |
|
Definition
|
|
Term
| When using substitution to solve a system of equations, solve for the variable whose |
|
Definition
|
|
Term
| A solution to a system of equations must satisfy |
|
Definition
|
|
Term
| What signs do the points in quadrant I have? |
|
Definition
|
|
Term
| What signs do the points in quadrant II have? |
|
Definition
|
|
Term
| What signs do the points in quadrant III have? |
|
Definition
|
|
Term
| What signs do the points in quadrant IV have? |
|
Definition
|
|
Term
| Where is the point (0, 3) located? |
|
Definition
|
|
Term
| The point where the 2 axes meet is called the |
|
Definition
|
|
Term
| Where is the point (3, 0) located? |
|
Definition
| on the x-axis, 3 units to the right |
|
|
Term
| The graph of an equation is a geometric way of representing |
|
Definition
| all of the points that are solutions of the equation |
|
|
Term
| How many points are on a line? |
|
Definition
| infinitely many points are on a line |
|
|
Term
| The graph of a linear equation is the set of all ordered pairs (x, y) that |
|
Definition
|
|
Term
| When you find the union of two inequalitites, think of your little friend |
|
Definition
|
|
Term
| m = 5 and (2, 4) what equation do you use to get the equation of the line? |
|
Definition
y - y1 = m(x - x1)
point-slope equation of a line |
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|
Term
| m = 5 and (2, 4) what is x1? |
|
Definition
|
|
Term
| m = 5 and (2, 4) what is y1? |
|
Definition
|
|
Term
| m = 5 and (2, 4) what is the slope? |
|
Definition
|
|
Term
| y = 6x - 3 What is the slope? |
|
Definition
|
|
Term
| y = 6x - 3 What is the y-intercept? |
|
Definition
|
|
Term
| y = 6x - 3 What is the y value when the line crosses the y-axis? |
|
Definition
|
|
Term
| 3x + 4y = 12 What's the fastest way to graph this line? |
|
Definition
|
|
Term
| 3x + 4y = 12 If x = 0 what is y? |
|
Definition
|
|
Term
| 3x + 4y = 12 If y = 0 what is x? |
|
Definition
|
|
Term
| Is every integer a rational number? |
|
Definition
Yes
(because you can slap it over one and have a feraction) |
|
|
Term
| Is every irrational number a real number? |
|
Definition
Yes
(so far, every everything is a real number) |
|
|
Term
| What is the intersection of the rationals and the irrationals? |
|
Definition
|
|
Term
| What is the union of the rationals and the irrationals? |
|
Definition
|
|
Term
| What is the intersection of the rationals and the integers? |
|
Definition
|
|
Term
| What is the union of the rationals and the integers? |
|
Definition
|
|
Term
| Are the natural numbers a proper subset of the whole numbers? |
|
Definition
Yes
(every counting number is a whole number but the whole numbers are a bigger set - by one) |
|
|
Term
| 2x + 3y = 14 To solve for y, what would you do first? |
|
Definition
Hop and swap the 2x
3y = -2x + 14 |
|
|
Term
| If you are adding pure anti-freeze to your mixture, what is the % of anti-freeze that it has? |
|
Definition
100%
(that's why it's called "pure") |
|
|
Term
| If you are diluting an alcohol solution by adding pure water, what % alcohol does the water have? |
|
Definition
|
|
Term
| If you are supposed to drain part of a mixture and replace it with pure anti-freeze, what is the easy way to think of it? |
|
Definition
| Drain it ALL of it into a bucket and make your new solution from the bucket and the pure anti-freeze. |
|
|
Term
| Anything raised to the zero power equals |
|
Definition
|
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Term
|
Definition
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Term
|
Definition
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Term
|
Definition
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|
Definition
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|
