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(f - g)x    means   f(x)  *  g(x)   =

(x^2  - 3x + 2)  ( x^3  - 8)   =

x^5  - 3x^4 + 2x^3

                               -8x^2   + 24x  - 16

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x^5  -3x^4  +2x^3  -8x^2  + 24x  - 16    ⇒   answer

Excellent answer, DragonLord   !!!!

No..... it means that as  t gets larger and larger,  the owl population will stabilize at 22.2  [  this must  be in some unit like thousands  ]

(f  - g) (x)    means   f(x)  - g(x)  =

[ x^4  - 4x^2 + 4   ] -   [ x^3   - 2x^2   + 4x   - 8  ]    =

x^4   - x^3  - 4x^2  + 2x^2 - 4x  + 4    + 8    =

x^4    - x^3  - 2x^2  - 4x   + 12

AD = 3.5

ND = 1.75

BD = 3.13

DG = 2.97

FG = 0.99

DE = 2.475

EG = 0.495

Area of  Δ DFG = 1.47 u²

Area of  Δ EFG = 0.245 u² 

Area of  Δ DEF = 1.225 u²     

We have  178  peanuts.....

We   could either  choose  one of  the  19 of one-shelled peanuts  that  were cracked  or  we could choose  one of the 25 two-shelled  peanuts  that were cracked

So....

P ( chhosing  one of the 19 cracked  one-shelled peanuts  or 25 of the 2 cracked two-shelled peanuts )  =

19/ 178   +  25  /178   =

44  / 178   =

22 / 89   ≈  24.7 % 

The  3  longest measurements  are

3 1/2      3  1/2       4

Adding these  gives

7  +  4     =

11

The period  is  12

The curve  starts  at   62  and decreases  untl  it bottoms out  at  38  at 3 hours....this is (1/4) of the period

Then ii rises  back to  62   agai at  6  hours.......this is 1/2   of the period

Then.....it  rises  to a max  of 86  at 9  hours.....this is  3/4 of  the period

Then  it will fall to 62   [not shown ]  at 12 hours

Where  the  numbers  in the   columns  under  f(x)  and g(x)  are the same   tells  us  what the solutions are

Note  that they are the  same at  x   =  1    and   x   = 2 

So....these are the solutions

We  can  use  the tangent  inverse  (arctan)  to solve this

We  have  a right triangle  with legs  of  (22 - 10)  = 12    and  30

tan  (angle)  =   12 / 30

So.....the  angle can be found  as

arctan  (12 /30)  ≈  21.8°  =   22°  (rounded) =  angle of elevation

Volume  of aquarium =  20 x 18  x 10  =  360 x 10   =   3600 in^3

Time to empty  =  

3600 in^3 /  360 in^3 / min  =   10  min

We can solve this as follows :

Since AC:CB  =  3:1......then  C  is 3/4  the distance from A  to B

The  x coordinate of B  is found as

[ (  + (3/4) (x - 2)  ]   =  4

2 + (3/4)x - 3/2 =   4    

1/2  + (3/4)x    =    8/2      subtract  1/2 from both sides

(3/4)x =  7/2          multiply both sides  by  4/3

x  = 28/6 =  14/3  =   x coordinate of   B

The y coordinate  of  B  is found as

[ -1 + (3/4) ( y - -1)  ]  =  2

-1 + (3/4)y + 3/4    = 2

-1/4  + (3/4)y   = 2

-1/4  + (3/4)y  = 8/4      add 1/4 to both sides

(3/4)y   =  9/4

3y   = 9

y  = 3

So....the  coordinates  of B  are   ( 14/3 , 3)

A square picture frame has a perimeter of (20x + 32) inches. What is the length of one side of the picture frame?   

All four sides of a square are equal, i.e., the same length 

The perimeter is around the outside of the square, all four sides 

If around all four sides is (20x + 32) then one side is a fourth of that perimeter 

(20x + 32) divided by 4 equals (5x + 8) and that's your answer 

_.

HA LOL

$30,000  x  0.042 = $1,260 will be deducted from their gross pay for "FICA"

Solve for x:
2 x^(1/3) = x^(1/3) + 7

Subtract x^(1/3) from both sides:
x^(1/3) = 7

Raise both sides to the power of three:
 
x = 343

Expand    [(3x+2y)^2(3x-2y)^2]^3

531441 x^12 - 1417176 x^10 y^2 + 1574640 x^8 y^4 - 933120 x^6 y^6 + 311040 x^4 y^8 - 55296 x^2 y^10 + 4096 y^12  (7 TERMS).
 

x^2 + 6x + 5 = 0... how would i solve for this?   

Chris, you swapped places with the 6 and the 5. 

X² + 6X + 5 = 0 

This factors to (X+5)(X+1) 

So  X = –5  and  X = –1 

_.

What is the maximum number of interior right angles that can be used to form a 9-sided polygon   

If it has to be a regular nonagon, the answer is none, of course. 

If it can be any shape at all, I can make one with 7 right angles. 

I wish I knew how to draw on this site, I'd show you an example. 

_.

Why did I take Ap Physics?   

I don't know about you, but I took it because the alternative was Biology ... ugh, the frogs ...

_.

Clyde's lightest pumpkins show that they are \(10\frac{3}{4}.\) Koen's heaviest pumpkins weigh \(17\frac{2}{4}\) each. Thus, \(17\frac{2}{4}\cdot2=35.\) Then, Clyde's pumpkins subtracted from Koen's pumpkins will be \(35-10\frac{3}{4}=\boxed{24\frac{1}{4}}.\)

We know the ratio from gifts to books to cards is 4:3:9. We know that there are 45 books sold. Thus, 45/3=15. Multiply each term in the constant ratio by 15. So, the ratio is now 60:45:135. Thus, they sold \(\boxed{60}\) gifts, and \(\boxed{135}\) cards. There total would be \(\boxed{195}.\)