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First, factor the second term:

x² - 9 is a difference in squares so it equals (x + 3)(x - 3)

This means the terms are now:

(x - 3)² , (x + 3)(x - 3) , (x + 3)² , and (x - 1)²

Now the factors of these terms are: (x - 3) , (x + 3) , and (x - 1)

The least common multiple (LCM) is just the term with the largest power that holds these factors. 
This means the LCM is (x - 3)²(x + 3)²(x - 1)², which is also your answer :)

I believe it's 1 OR -1.

Since 2=sqrt1+1, it could be 1/(-1) or 1/1 

We can use the binomial theorem, which is explained here --> https://www.mathsisfun.com/algebra/binomial-theorem.html
 

Since we're only finding the coefficient of y⁴, the exponent of the y is, well 4, while the exponent of the 7 is 1 (5-4). 

This means the y⁴ term is 5C1 * (2y)⁴-7¹

= 5(2y)⁴-7

= -35(2y)⁴

= -560y⁴

Which means the coefficient of y⁴ is -560, which is also your answer :)

(9 x 10⁹ Nm²/C²) (3C) (6C)/10 N     note that the C's   and the 'N' will cnacel and the final result will be m^2

9 x 10⁹   *  18/10 = 9 x 10⁹  * 1.8 = 16.2 x 10⁹ =    1.62 x 10¹⁰  m²

The remainder is 7x + 3.

p= total number of pens originally

sell 1/2    then 1/2 remain

p - 1/2 p  -30    = pens after Tuesday

(p- 1/2 p - 30) 2/3   = pens after Wednesday    and this = 40 that were sold on Thursday

(p-1/2p-30)2/3 = 40

(1/2 p-30)(2/3) = 40

1/3 p - 20 = 40

1/3 p = 60

p = 180 pens  

acid in ingredients    =   acid in final sol'n

x = 25% gallon amount

.25 x   +  .12 (10)   =     .20 (10+x)

.05x = .8

x = 16 gal of 25% 

Just add and subtract them as indicated

2x^2   + 3x    -9      - 5x    - 11       + 3x^2    +1       gather 'like' terms

5x^2    -2x     -19  

The arc covers 45 degrees of the 360 degree circle or   45/36o fraction of the entire circle

45/360 * x = 22            where x is the total circumference

x = 22 * 360/45 = 176 cm

Position 1     L T L T L T

Position 2     T L T L T L       EACH OF THOSE POSITIONS OF THE LIONS CAN ARRANGE THE THREE LIONS SIX WAYS

                                                    IN EACH OF THOSE ARRANGEMENTS THE TIGERS CAN BE ARRANGED IN 6 WAYS

2 *  6 * 6   =  72 WAYS

1 and -1 are real numbers and i and -i are nonreal numbers.

Just directly plug it in according to the piecewise function:

\(i^2+1+2-1+2+(-i)^2 =-1+4-1=\boxed{2}\)

Thank you!! That's what I was missing! That makes sense!!!

The Question says 140% more. That means that we would do 100% + 140%  which is 240%.

What you did is of. Which means we would multiply directly.

Hope that helps!!!!

🙃🙃👌

Unless you are familiar with the standard formula for the solution of a cubic equation, you will need to use a numerical method here, such as the following:

Corrections:     If [BDF] = [EFC] then  ΔABE ~  ΔADC 

 If [BDF] = [ACE] then  ΔABE ~  ΔADC

AB / AE = AD / AC

AC = 4.5

EC = 1.5

thank you haha, I sure could DO it this way, however the class I'm in, I know that would actually be incorrect lol. The answers right but the method isn't what would be wanted.

Just  to add to CitrusCornflakes  response

arcsin (1/5)  ≈   11.54°    = angle of elevation

Total Muffins ÷ 6 = Muffin's per tray

New Amount of Muffins per tray is: Muffin's per tray + 5 which is 20.

20-5 = 15 muffin's in the original tray

15 x 6 = 90

Therefore, she had 90 muffin's in her original batch

If  we  draw  perpendicular  GM    to  BE        then  we  form two triangles

Triangle  GMD is similar to triangle ABD   ....and  triangle  FEC  is similar to triangle GMC

So                                                        And

AB/ BD  = GM / x                                FE  / CE    =  GM/ 3 -x                      

12/6  =   GM  /x                                    8 / 6  =  GM  / 3 - x

2  = GM  / x                                          4 / 3  = 2x  /  3 - x                cross- multiply

GM =  2x                                              4(3  -x)  = 3 * 2x

                                                            12 - 4x =  6x

                                                            12 = 10x 

                                                              x  =12/10  = 6/5

So  GM = 2 (6/5)  =   12/5

So   [ GCD  ]    =   1/2  ( CD) ( GM)  = 1/2  ( 3) (12/5)  =  36/10  = 3.6

Read a question again. 

At  the  end  of 90 days,   90 /200   = 9/20  of  the job was finished

Then 10 workers were fired  so,  20 remain

Notice  that   if  30  workers  can finish the job  in  200 days, then each day  1  worker  can complete  1 / (30 * 200)  =    1/6000  of the job

So  20 workers in one day  can complete  20/6000 = 1/300 of  the job....so in  30 days,  they  can complete  another

30 / 300   =  1/10   of the  job  = 2/20  of the job

So before  the last  30  workers  were  hired     9/20  + 2/20  = 11/20  of the job is  complete   and 9/20  is left

So....20 + 30   =  50 workers  complete  the job 

Every  day     50 /6000  =   1/120  more of  the job is now finished

So   the  number  of  days  it  takes to  complete  this is

Part  that remains  / Part  completed each day  = 

(9/20 ) / ( 1/120)  =  120 ( 9)  /20   =  54 days

So....the total number  of  days    = 90  + 30   + 54  =  174  days.....so....ahead of schedule

Using Heron's formula: √s(s-a)(s-b)(s-c), we can calculate this easily :)

s = semiperimeter = (3 + 4 + 5) / 2 = 6

√s(s-a)(s-b)(s-c) 

= √6(6-3)(6-4)(6-5)

= 6 units², which is your answer :)