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hen dealing with permu f one type, b identical ite n! ormula ab!c!...

hen dealing with permu f one type, b identical ite n! ormula ab!c!...

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Please give short tutorial similar to the one circled to teach how to solve permutations with identical terms questions and what they are.
could perin identi Barbara can arrange the display in 27 720 different ways. Key Concepts • When dealing with permutations of n items that include a identical items of one type, b identical items of another type, and so on, you can use the formula a!b!c! n! Communicate Your Understanding 1. Explain why there are fewer permutations of a given number of items if some of the items are identical. 2. a) Explain why the formula for the numbers of permutations when some items are identical has the denominator alb!c!... instead of a b ..... b) Will there ever be cases where this denominator is larger than the numerator? Explain. c) Will there ever be a case where the formula does not give a whole number answer? What can you conclude about the denominator and the numerator?
Transcribed Image Text:could perin identi Barbara can arrange the display in 27 720 different ways. Key Concepts • When dealing with permutations of n items that include a identical items of one type, b identical items of another type, and so on, you can use the formula a!b!c! n! Communicate Your Understanding 1. Explain why there are fewer permutations of a given number of items if some of the items are identical. 2. a) Explain why the formula for the numbers of permutations when some items are identical has the denominator alb!c!... instead of a b ..... b) Will there ever be cases where this denominator is larger than the numerator? Explain. c) Will there ever be a case where the formula does not give a whole number answer? What can you conclude about the denominator and the numerator?
HOW TO SOLVE RATIONAL RATIONAL EQUALITIES 1. Completely factor and state restrictions of the denominators. 2. Find lowest common denominator and multiply all rationals by it. ancel, expand, then simplify to solve for variable. e sure solutions aren't in the restrictions are, reject because they are us solutions). RATIONAL INEQUALITIES 1. Make one side equal to zero. simplified rational expression. 2.Factor numerator and denominator as much as you can. 7+68 748-520 3.Determine values of both numerator and denominator where they are zero (isolate for the variable). 2+8 4. Find the test intervals surrounding these values (such as by using a number line). 5.Choose a value for each interval to determine the sign of the function using a chart. 7+68-52-40 248 428 7+8 6. Compare the sign and the equation to find the solutions. >0 - 4(x-7) 7.Numerator values are inclusive (square brackets), but the denominator values are not since you can't divide by 0 (soft brackets) 20 a 218 Retake EQUATIONS 240 +³+ z+5+5) x(x+6) **(+6) (+)*+5) 1 - a(2+5) =(z+5)=(x+5) 2-1-4 Not in restrictions (-5) (+8) 20 >0 www X-7 x+5 Sign y in fata the reciprocal of the original function's y int Vortex Domain Range Intervals of increase Decrease Positive Negative Numerator: -720 #27 Denominator: +820 (.x. 8) . 12-8 z € (-8, 7) (-8. 71 . + Use Photo (11%) +
Transcribed Image Text:HOW TO SOLVE RATIONAL RATIONAL EQUALITIES 1. Completely factor and state restrictions of the denominators. 2. Find lowest common denominator and multiply all rationals by it. ancel, expand, then simplify to solve for variable. e sure solutions aren't in the restrictions are, reject because they are us solutions). RATIONAL INEQUALITIES 1. Make one side equal to zero. simplified rational expression. 2.Factor numerator and denominator as much as you can. 7+68 748-520 3.Determine values of both numerator and denominator where they are zero (isolate for the variable). 2+8 4. Find the test intervals surrounding these values (such as by using a number line). 5.Choose a value for each interval to determine the sign of the function using a chart. 7+68-52-40 248 428 7+8 6. Compare the sign and the equation to find the solutions. >0 - 4(x-7) 7.Numerator values are inclusive (square brackets), but the denominator values are not since you can't divide by 0 (soft brackets) 20 a 218 Retake EQUATIONS 240 +³+ z+5+5) x(x+6) **(+6) (+)*+5) 1 - a(2+5) =(z+5)=(x+5) 2-1-4 Not in restrictions (-5) (+8) 20 >0 www X-7 x+5 Sign y in fata the reciprocal of the original function's y int Vortex Domain Range Intervals of increase Decrease Positive Negative Numerator: -720 #27 Denominator: +820 (.x. 8) . 12-8 z € (-8, 7) (-8. 71 . + Use Photo (11%) +
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