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Vesnalui [34]
3 years ago
9

How many permutations five-letters long can be formed from the letters HISTOGRAM?

Mathematics
1 answer:
xeze [42]3 years ago
7 0

Answer:

104 different words

Step-by-step explanation

1) imago 2). simar 3). hoars 4). hairs 5). stair 6). sigma 7). stoai 8). staig 9). harms 10). harts 11). horas 12). tarsi 13). smart 14). hosta 15). sight 16). smith 17). ihram 18). hoist 19). sitar 20). horst 21). iotas 22). short 23). moats 24). moira 25). moist 26). ratio 27). moras 28). morts 29). ragis 30). moths 31). ostia 32). omits 33). oaths 34). ohias 35). ogams 36). ogham 37). ratos 38). right 39). mirth 40). shoat 41). shirt 42). magot 43). mairs 44). maist 45). saith 46). marsh 47). marts 48). rotis 49). maths 50). roast 51). roams 52). riots 53). might 54). rotas 55). grots 56). toras 57). trams 58). trash 59). trigo 60). ghost 61). giros 62). girsh 63). tharm 64). girth 65). girts 66). gismo 67). airts 68). taros 69). ghast 70). gator 71). amigo 72). torah 73). astir 74). torsi 75). argot 76). atoms 77). togas 78). gaits 79). amort 80). tiros 81). tragi 82). garth 83). amirs 84). airth 85). ghats 86). stoma 87). stria 88). trigs 89). trios 90). agios 91). trois 92). grist 93). agist 94). grith 95). grits 96). agism 97). groat 98). storm 99). griot 100). grams 101). goats 102). tahrs 103). tamis 104). trims

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D = {x:x is a factor of 12<br>​
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(6y + 3) minus (3y + 6) when y=7
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Answer:

y

Step-by-step explanation:

((((2•3y3) -  22y2) -  3y) -  —) -  2

                               y    

STEP

4

:

Rewriting the whole as an Equivalent Fraction

4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  y  as the denominator :

                      6y3 - 4y2 - 3y     (6y3 - 4y2 - 3y) • y

    6y3 - 4y2 - 3y =  ——————————————  =  ————————————————————

                            1                     y          

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

5

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Pulling out like terms

5.1     Pull out like factors :

  6y3 - 4y2 - 3y  =   y • (6y2 - 4y - 3)

Trying to factor by splitting the middle term

5.2     Factoring  6y2 - 4y - 3

The first term is,  6y2  its coefficient is  6 .

The middle term is,  -4y  its coefficient is  -4 .

The last term, "the constant", is  -3

Step-1 : Multiply the coefficient of the first term by the constant   6 • -3 = -18

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -4 .

     -18    +    1    =    -17

     -9    +    2    =    -7

     -6    +    3    =    -3

     -3    +    6    =    3

     -2    +    9    =    7

     -1    +    18    =    17

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

5.3       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

y • (6y2-4y-3) • y - (6)     6y4 - 4y3 - 3y2 - 6

————————————————————————  =  ———————————————————

           y                          y        

Equation at the end of step

5

:

 (6y4 - 4y3 - 3y2 - 6)    

 ————————————————————— -  2

           y              

STEP

6

:

Rewriting the whole as an Equivalent Fraction :

6.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  y  as the denominator :

        2     2 • y

   2 =  —  =  —————

        1       y  

Checking for a perfect cube :

6.2    6y4 - 4y3 - 3y2 - 6  is not a perfect cube

Trying to factor by pulling out :

6.3      Factoring:  6y4 - 4y3 - 3y2 - 6

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -3y2 - 6

Group 2:  6y4 - 4y3

Pull out from each group separately :

Group 1:   (y2 + 2) • (-3)

Group 2:   (3y - 2) • (2y3)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

6.4    Find roots (zeroes) of :       F(y) = 6y4 - 4y3 - 3y2 - 6

Polynomial Roots Calculator is a set of methods aimed at finding values of  y  for which   F(y)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  y  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  6  and the Trailing Constant is  -6.

The factor(s) are:

of the Leading Coefficient :  1,2 ,3 ,6

of the Trailing Constant :  1 ,2 ,3 ,6

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        1.00    

     -1       2        -0.50        -5.88    

     -1       3        -0.33        -6.11    

     -1       6        -0.17        -6.06    

     -2       1        -2.00        110.00    

Note - For tidiness, printing of 13 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

6.5       Adding up the two equivalent fractions

(6y4-4y3-3y2-6) - (2 • y)      6y4 - 4y3 - 3y2 - 2y - 6

—————————————————————————  =  ————————————————————————

            y                            y            

Polynomial Roots Calculator :

6.6    Find roots (zeroes) of :       F(y) = 6y4 - 4y3 - 3y2 - 2y - 6

    See theory in step 6.4

In this case, the Leading Coefficient is  6  and the Trailing Constant is  -6.

The factor(s) are:

of the Leading Coefficient :  1,2 ,3 ,6

of the Trailing Constant :  1 ,2 ,3 ,6

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        3.00    

     -1       2        -0.50        -4.88    

     -1       3        -0.33        -5.44    

     -1       6        -0.17        -5.73    

     -2       1        -2.00        114.00    

Note - For tidiness, printing of 13 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

 6y4 - 4y3 - 3y2 - 2y - 6

 ————————————————————————

            y            

4 0
2 years ago
Read 2 more answers
10.(06.01 LC)
storchak [24]
Need more explanation
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