Algebra and Trigonometry (6th Edition)

Chapter 2

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To plot point A, move 2 units to the left of the ... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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This means the visible range of the -axis is from... more

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-axis ; The numbers on the -axis increases from ... more

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-axis ; The -axis is a number line perpendicular ... more

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origin ; The origin is located at and divides the... more

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quadrants; four ; Quadrants are labeled ... more

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-coordinate ; The -coordinate, also called as ... more

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solution ; A solution of an equation consists of... more

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-intercept ; A line which intersects the -axis at... more

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-intercept ; A line which intersects the -axis at... more

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Move 1 unit to the right of the origin along the -... more

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Move units to the right of the origin along the -... more

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Move units to the left of the origin along the -... more

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Move unit to the left of the origin along the -... more

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Move units to the left of the origin along the -... more

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Move units to the left of the origin along the -... more

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Move units to the right of the origin along the -... more

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Move units to the right of the origin along the -... more

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Move units to the left of the origin along the -... more

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Since the -coordinate is 0, the point is located ... more

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Move units to the right of the origin along the -... more

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Move units to the left of the origin along the -... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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by means the visible range of the -axis is from ... more

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The equation is not true for all values of . At ... more

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The equation is not true for all values of . At ... more

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no ; The origin has the coordinates . The points ... more

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yes ; The origin has the coordinates . The fourth ... more

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; A graph crosses the -axis at the point where ... more

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; A graph crosses the -axis at the point where ... more

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and ; Two graphs intersect at a common point. ... more

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and ; Using the table of values, look at the rows ... more

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Translate the mathematical sentence to ... more

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Translate the mathematical sentence to ... more

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Translate the mathematical sentence to ... more

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Translate the mathematical sentence to ... more

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Solve for by substituting the integral values of... more

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Solve for by substituting the integral values of... more

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Solve for by substituting , , , , , , , and to ... more

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Solve for by substituting , , , , , , , and to ... more

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; ; Using the red line graph, locate the lowest ... more

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; ; Using the blue line graph, locate the highest ... more

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; Locate from the -axis and imagine a vertical ... more

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; Locate from the -axis and imagine a vertical ... more

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A rectangular coordinate system is a two-... more

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To plot , move 2 units to the right of the origin ... more

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means move units to the right of the origin along... more

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To graph an equation, follow the following steps:... more

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by means the visible range of the -axis is from ... more

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Determine the sets of points which will be used to... more

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makes sense ; A rectangular coordinate system is ... more

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does not make sense ; A graphing calculator does ... more

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Connecting the ordered pairs does not create a ... more

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does not make sense ; The calories in the second ... more

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False; If the product of a point’s coordinates is ... more

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False; If a point is on the -axis, it is neither ... more

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True ; The -coordinate of the points which are on ... more

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False; The ordered pair satisfies . ; A point may... more

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Quadrant I and III ; Since the product of and is... more

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Quadrant II and IV ; Since the quotient of and ... more

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Quadrant IV ; Since the cube of positive number is... more

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Quadrant II ; Since the cube of positive number is... more

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Since the amount of snowfall increases ... more

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The graph shows the continuous increase of the ... more

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The volume gradually increases in inhaling, ... more

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The graph shows that the height of a person ... more

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The graph indicates that the speed of the bike ... more

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Substitute to the equation and simplify the left ... more

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; Distribute to each of the terms. ; Factor . ; ... more

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; Distribute to each term. ; Cancel common ... more

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; ; Subtract from both sides of the equation. ... more

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; ; Simplify both sides of the equation. ; ... more

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; ; Multiply both sides of the equation by the ... more

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; ; Multiply both sides of the equation by the ... more

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; Multiply both sides of the equation by the ... more

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; ; Equate and . ; Multiply both sides of the ... more

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; inconsistent equation ; Simplify the right side ... more

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; identity ; Simplify the right side of the ... more

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; located at ; Using the LH group equation, ... more

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linear ; A linear equation, such that , is a ... more

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equivalent ; Equivalent equations have identical ... more

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simplify the left side of the equation by using ... more

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least common denominator; ; To eliminate fractions... more

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; An equation will be undefined if any ... more

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; To eliminate fractions in an equation, multiply... more

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; To eliminate fractions in an equation, multiply... more

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; ; Since any denominator cannot be equal to , ... more

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; Distribute to both sides of the equation and ... more

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identity ; An equation is an identity if the ... more

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inconsistent ; An equation is inconsistent if the ... more

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; ; Add to both sides of the equation. Then, ... more

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; ; Add to both sides of the equation. Then, ... more

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; ; Change subtraction to addition and obtain the ... more

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; ; Change subtraction to addition and get the ... more

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; ; Subtract from both sides of the equation. ... more

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; ; Subtract from both sides of the equation. ... more

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; ; Subtract from both sides of the equation. ; ... more

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; ; Subtract and from both sides of the equation... more

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; ; Simplify both sides of the equation. ; ... more

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; ; Simplify both sides of the equation. ; Add to... more

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; ; Simplify both sides of the equation. ; Divide ... more

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; ; Simplify both sides of the equation. ; Add ... more

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; ; Simplify the right side of the equation. ; ... more

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; ; Simplify both sides of the equation. ; ... more

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; ; Simplify both sides of the equation using the ... more

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; ; Simplify both sides of the equation using the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; Substitute the values of and to the equation... more

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; Substitute the values of and to the equation... more

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; Substitute the values of and to the equation... more

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; Substitute the values of and to the equation... more

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; Substitute the values of , , and to the ... more

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; Substitute the values of , , and to the ... more

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; Substitute to the value of in the equation... more

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; Substitute to the value of in the equation... more

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; Substitute to the value of in the equation... more

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; conditional ; Substitute to the value of in ... more

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; identity ; Simplify the right side of the ... more

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; identity ; Simplify the right side of the ... more

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; inconsistent equation ; Simplify the left side ... more

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; inconsistent equation ; Simplify the left side ... more

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; conditional equation ; Subtract and from both ... more

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; conditional equation ; Subtract and from both ... more

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; inconsistent equation ; Determine the value of ... more

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; inconsistent equation ; Determine the value of ... more

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; conditional equation ; To eliminate the ... more

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; conditional equation ; To eliminate the ... more

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; inconsistent equation ; Determine the value of ... more

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; inconsistent equation ; Determine the value of ... more

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; conditional equation ; Simplify the left side of... more

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; identity ; Simplify the left and right side of ... more

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; conditional equation ; Determine the value of ... more

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; conditional equation ; Determine the value of ... more

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; conditional equation ; Determine the value of ... more

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; conditional equation ; Determine the value of ... more

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; inconsistent equation ; Determine the value of ... more

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; conditional equation ; Determine the value of ... more

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; ; To find the solution of two lines, a pair of ... more

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; ; To find the solution of two lines, a pair of ... more

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; ; To find the solution of two lines, a pair of ... more

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; ; To find the solution of two lines, a pair of ... more

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; Simplify the left and right side of the ... more

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; Simplify the left and right side of the ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the denominator, multiply the ... more

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; Simplify the left side of the equation. ; ... more

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; Simplify the left side of the equation. ; ... more

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; Simplify the right side of the equation. ; Add... more

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; Simplify both sides of the equation. ; Subtract... more

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; Simplify both sides of the equation. ; Subtract... more

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; Simplify both sides of the equation. ; Subtract... more

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; Simplify both sides of the equation. ; Subtract... more

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; Simplify both sides of the equation. ; Add and... more

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; Substitute to the value of in the first ... more

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; Substitute to the value of in the first ... more

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; ; Substitute to value of . ; To eliminate the ... more

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; ; Substitute to value of . ; To eliminate the ... more

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liters ; Substitute to the value of . Note that... more

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A linear equation in one variable, such that , is... more

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The obtained solution will still be the same. Both... more

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The second line of equation is incorrect. It ... more

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To find restrictions on the variables, factor out ... more

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Multiplying both sides of the equation by the ... more

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An identity is an equation which has infinitely ... more

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A conditional equation is an equation which has ... more

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An inconsistent equation is an equation which has ... more

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The trend of the graph is increasing from left to ... more

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Using a graphing utility, graph . ; Using a ... more

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Using a graphing utility, graph . ; Using a ... more

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Using a graphing utility, graph . ; Using a ... more

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Using a graphing utility, graph . ; Using a ... more

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makes sense ; To determine the number of items, ... more

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This makes sense. To eliminate the denominator, ... more

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This makes sense. To eliminate the decimals, ... more

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This makes sense. An inconsistent equation does ... more

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false; The equation has a solution. ; Adding to ... more

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false; The equations and are not equivalent. ; ... more

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true ; Adding to both sides of the first equation... more

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false; If and are any real numbers, then may ... more

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A number is five more than itself. ; Rewriting ... more

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; Substitute to the values of in the equation... more

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; To eliminate the denominator, multiply the ... more

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; Represent the man’s earnings by a variable. ; ... more

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; Represent the monthly charges numerically. ; ... more

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; Determine the formula for the perimeter of the ... more

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AD: $33,000; BD: $47,000; MD: $59,000 ; Represent ... more

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; Represent the percentage of FM who are into ... more

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; Represent the number of BC per month.  ; ... more

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$1,200 ; Represent the cost of the system before ... more

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$3,150 (at ); $1,850 (at ) ; Represent the amount ... more

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feet by feet ; Represent the width with a ... more

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; Subtract to both sides of the equation. ; ... more

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; Factor out .  ; Divide both sides of the ... more

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; The budget for defense for 2011 exceeded the ... more

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; In the year 2000, the initial percentage was ... more

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; The plan has a monthly cost of dollars, with ... more

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; The computer started at a price of .  Because ... more

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; The interest earned for a interest rate on ... more

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isolated on one side of the equation ; A formula ... more

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factoring out ; To only have a single in the ... more

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years will be spent sleeping, and years will be ... more

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years will be spent sleeping, and years will be ... more

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The median salary with Degree B is $81,000.   The ... more

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The median salary with Degree B is $81,000.   The ... more

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years; ; Represent the number of years after . ; ... more

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years; ; Represent the average age. ; Represent ... more

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; $165 ; Represent the number of months. ; ... more

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; $40 ; Represent the number of hours. ; Represent... more

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; Represent the number of times of use a month... more

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; Represent the number of crosses in a month. ; ... more

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; ; Represent the number of years using a variable... more

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$420 ; Using a variable, represent the original ... more

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$44 ; Using a variable, represent the original ... more

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$150 ; Using a variable, represent the original ... more

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$240 ; Using a variable, represent the original ... more

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$467.20 ; Using a variable, represent the original... more

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$12 ; Using a variable, represent the original ... more

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$2000 (at ) and $5000 (at ) ; Using a variable, ... more

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$5000 (at ) and $6000 (at ) ; Using a variable, ... more

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$6000 (at ) and $2000 loss (at ) ; Using a ... more

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$7000 (at ) and $5000 loss (at ) ; Using a ... more

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yards by yards ; Using a variable, represent the ... more

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feet by feet ; Using a variable, represent the ... more

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feet by feet ; Using a variable, represent the ... more

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meters by meters ; Using a variable, represent ... more

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inches ; Represent the width of the frame. ; Using... more

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feet ; Represent the path’s width. ; Using the ... more

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hours ; Represent the number of hours of work. ; ... more

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hours ; Represent the number of hours of work. ; ... more

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; Represent the number of inches for every inch ... more

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$1350 ; Represent the amount of the paycheck. ; ... more

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oz ; Represent the weight of an unpeeled food. ; ... more

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minutes ; Represent the number of additional ... more

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; width of a rectangle in terms of its area and ... more

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; rate in terms of the distance and time  ; Divide... more

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; length of the base of a triangle in terms of its... more

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; area of the base of a prism in terms of its ... more

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; principal of a simple interest in terms of the ... more

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; radius of a circle in terms of its circumference... more

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; mass in terms of its energy and light speed ; ... more

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; height of a cylinder in terms of its volume and ... more

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 The price to pay per month in terms of the total ... more

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 Markup price in terms of the selling and cost ... more

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 Length of the first base in terms of its area, ... more

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 Length of the second base in terms of its area, ... more

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 Rate of interest in terms of the principal amount... more

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 Time of investment in terms of the maturity value... more

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 Sales revenue per unit in terms of the total ... more

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 Markup rate in terms of the cost price and the ... more

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 Current in terms of the electromotive force, load... more

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 Height of the rectangular prism in terms of its ... more

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Focal length in terms of the object and image ... more

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 First resistor in terms of the total resistance ... more

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To solve an algebraic word problem, the following ... more

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The side of a rectangular lot is six times longer ... more

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To solve a variable in a given formula means ... more

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One of the problems which is challenging is ES29. ... more

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Using Exercise 9, let . Graph . ; Let . Graph . ; ... more

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does not make sense ; There is no given ... more

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does make sense ; Determining the equation for a ... more

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does not make sense ; Solving for a variable does ... more

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does not make sense ; The original price can be ... more

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N: students; S: students ; Represent the number ... more

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$200 ; Using a variable, represent the original ... more

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Age of the woman: years old; Age of the man: ... more

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; Use a variable to represent the number of ... more

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Mother’s portion: Boy’s portion: Girl’s portion... more

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; Use a variable to represent the number of the ... more

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; To eliminate the denominator, multiply both ... more

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Word Problem 1: Lois has more stickers than ... more

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; Use the FOIL Method to find the product of each... more

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; Factor out the radicands such that one of the ... more

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; To rationalize the denominator, multiply the ... more

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; Multiply the numerator and denominator by the ... more

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; Multiply the numerator and denominator by the ... more

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; ; represents the imaginary part of a number. The... more

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complex; imaginary; real ; A complex number is an ... more

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; Factor the imaginary unit, . Simplify the ... more

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; Changing the subtraction to addition and ... more

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; ; ; ; ; Using the FOIL method, the following are... more

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; To determine the conjugate of a complex number... more

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; To divide complex numbers, multiply the ... more

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; ; ; Since , then using the product rule for ... more

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; Use the commutative and associative property of... more

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; Use the commutative and associative property of... more

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; Change subtraction to addition, then get the ... more

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; Change subtraction to addition, then get the ... more

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; Change subtraction to addition, then get the ... more

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; Change subtraction to addition, then get the ... more

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; Change subtraction to addition, then get the ... more

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; Change subtraction to addition, then get the ... more

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; Distribute to each term inside the parentheses... more

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; Distribute to each term inside the parentheses... more

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; Use the FOIL method to determine the product of... more

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; Use the FOIL method to determine the product of... more

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; Use the FOIL method to determine the product of... more

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; Use the FOIL method to determine the product of... more

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; Using , determine the product of the sum and ... more

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; Using , determine the product of the sum and ... more

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; Using , determine the product of the sum and ... more

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; Using , determine the product of the sum and ... more

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; Using , determine the square of the sum of and... more

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; Using , determine the square of the difference ... more

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; Multiply the numerator and denominator by the ... more

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; Multiply the numerator and denominator by the ... more

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; Multiply the numerator and denominator by the ... more

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; Multiply the numerator and denominator by the ... more

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; Multiply the numerator and denominator by the ... more

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; Multiply the numerator and denominator by the ... more

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; Multiply the numerator and denominator by the ... more

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; Multiply the numerator and denominator by the ... more

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; Express each square root of a negative integer ... more

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; Express each square root of a negative integer ... more

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; Express each square root of a negative integer ... more

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; Express each square root of a negative integer ... more

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; Express the square root of a negative integer ... more

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; Express the square root of a negative integer ... more

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; Express the square root of a negative integer ... more

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; Express the square root of a negative integer ... more

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; Express the square root of a negative integer ... more

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; Express the square root of a negative integer ... more

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; Express the square root of a negative integer ... more

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; Express the square root of a negative integer ... more

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; Express each square root of a negative integer ... more

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; Express each square root of a negative integer ... more

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; Express each square root of a negative integer ... more

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; Express each square root of a negative integer ... more

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; Use the FOIL method to multiply the expressions... more

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; Use the  FOIL method to multiply the ... more

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; Using , determine the square of the sum of and... more

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; Using , determine the square of the difference ... more

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; Express the square root of a negative integer ... more

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; Express the square root of a negative integer ... more

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; Substitute for the value of in the expression... more

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; Substitute for the value of in the expression... more

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; Substitute to the value of in the expression... more

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; Substitute to the value of in the expression... more

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; Substitute for the value of and for the value... more

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; Substitute for the value of and for the value... more

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Find the sum and show it is equal to 10.  Find the... more

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represents the imaginary part of a complex number... more

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Adding complex numbers is just like adding ... more

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To multiply complex numbers like and , use the ... more

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; The product will be a real number. ; The complex... more

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To divide complex numbers, such as , multiply the ... more

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divided by is undefined. It is because any number... more

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Multiplying an imaginary number by another ... more

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. Radicals with different radicands cannot be ... more

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. Each should be written as before proceeding to... more

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makes sense; If it a number is real, it may be ... more

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does not make sense; Imaginary numbers are defined... more

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does not makes sense; 5 and are both constants. ... more

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makes sense; In adding or subtracting imaginary ... more

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false; All irrational numbers are complex numbers... more

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false; It is a real number. ; The expression may ... more

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false; The left side of the equation is equal to... more

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true ; can be written as .  Since , then .  ... more

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; Simplify the denominator by FOILing. ; Since , ... more

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; To eliminate the denominator, multiply the ... more

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; To eliminate the complex fraction, multiply the... more

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; Determine the numerical coefficient of the ... more

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; Determine the first two terms by factoring the ... more

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; Substitute the values of , , and , into the ... more

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; To isolate the terms with variable , add to ... more

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; The leading coefficient should be . Thus, ... more

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; Using , determine the values of , , and... more

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; Using , determine the values of , , and... more

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; Using , determine the values of , , and... more

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Approximately years old ; Using the given formula... more

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