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

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,...
icon
Related questions
Question
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%) +
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education