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For f(x) to be defined, we need both x^2 + 3x - 4 and x^2 + 9x + 20 to be nonzero, so the values of x not in the domain are -4, 1, and -5.

y - b = m(x - a)

(y - b)/m = x - a

a = x - ^(y-b)/_m 

like that?

Let a and b be real numbers such that a + b = - 1 . Compute  \(a^2-b^2+a-b\).

Hello Guest!

\(a + b = - 1\ |\times (a-b)\\ a^2-b^2=-a+b\\ \color{blue}a^2-b^2+a-b=0\)

  !

The denominator x^2 - 3x - 4 can't be 0, so the domain is (-inf,-1) U (-1,4) U (4,inf).

The y coordinates are 3 and 1.

3 - 1 = 2

1 - 3 = -2

2 is greater so the answer is 2.

-x  - 3    =  0                x/2  +  1    = 0

-x  = 3                          x/2  =  -1

x = -3                           x  =  -2

The  first  value  of x    is in the  domain   of  - x - 3

The second  value of   x   is NOT  in the domainn  of  x/2  +  1

So .....

-3

cross multiply the left side

gx^2 -g 4x + hx + 5 h  =  x^2 -2x+10         so    g = 1   h = 2      take it from here !

I'll save this one for later...

First 2x + 2y = 180     (angles next to each other in a parallelogram are supplementary)

x+y = 90

then   x+y + 180 -2z  = 180            (sum of angles in a triangle)

            90   = 2z

               z = 45^o

12/7  *  -29/3    =  -116/7  ≈  -16.xxx

Ceiling  -16.xxx =  -16

And

 -29/3   = -9.xxx 

Floor  -9.xxx   = -10

So

12/7 * -10  =  -120/7  = - 17.xxx

Floor  =   -17.xxx   =  -18

So

-16  -  (-18)   =  

-16  +  18  =  

2

What a clever little Claire.

You get all your homework done for you and you don't have to learn a thing.

Hint  :    2* EF   =  BD

Welll.... we found that

x = 3/13 a

2 = 3/13 a

a = 26/3

40 days / 5 days/ half life = 8 half lives

13 mCi * (1/2 )⁸   = .05 mCi

x^3 + 14x^2  +  13x    take out the GCF    =  x

x ( x^2  + 14x + 13)            note ..in the parentheses  the last term  = 13  = 13 * 1       and  the middle term  = 13 + 1  = 14

So....this gives us the clue that  the correct factorization is

x ( x + 13)  ( x + 1)

Let the initial  number of  students  = N

Then in 1997  there  were  2N

And in 1998  there were    2(2N)   =  4N

% increase   =   [ Number in 1998  - Number in 1997  ]  / [ Number in 1997  ]   x  100%

So

[ 4N  - 2N ]  / [ 2N ]       x 100%  =

2N  / 2N  x   100%   = 

1   x  100%   =

100%  increase

(4 - 5i)(-5 + 5i) = (4)(-5) + (4)(5i) + (-5i)(-5) + (-5i)(5i) = -45 + 45i.

The area of trapezoid EFGH is 22.

1) If you start writing out the next terms of the pattern, you'll see that, well, there is a pattern.

13, 28, 520, 133, 55, 250, 133...

The 100th term would be 133. 

x   =   t  - 3    →    t   =  x +  3       (1)   

y  = 2t^2    - 1            (2)

Sub (1)  into  (2)  for  t

y  = 2 ( x + 3)^2   -  1     simplify

y  =2  (x^2  + 6x  + 9)  -  1

y  = 2x^2  + 12x  + 18   -1

y  = 2x^2  + 12x +  17

Note  that  in  t  is  on  [-2, 2]

Then  x  is on  t  -3   =     -2 - 3    =  -5      and   2 - 3    = -1

So  x  is  on the  interval  [ -5, -1 ]

The other angle would have to be 80 degrees.

1/x + 1/y  =  3   →   ( y + x)  / xy   =  3  →   (y + x)   / 3    = xy       (1) 

1/x  - 1/y   =  -7  →  (y  - x) / xy   = - 7 →    ( y   -  x)  /  -7  = xy     (2)

Setting (1) , (2)   equal....we  have  that

(y + x)  / 3    =    (y - x)  / -7              cross-multiply

-7 ( x +y)   =  3 ( y - x)

-7x  - 7y   = 3y   - 3x

-10y  =  4x

y = (-4/10) x

y  =  ( -2/5 ) x....sub this  back into    1/x + 1/y =  3

1/x   +  1/ [(-2/5) x ] =  3

1/x  -  5/2x  = 3

  ( 1  -5/2)  /x  = 3

(-3/2) / 3  =  x

-1/2   = x

So

y  = (-2/5) (-1/2)  =  1/5

x +  y    =     -1/2   + 1/5   =     - 5/10  +  2/10  =    -3 / 10

1. 1/a^2 + 1/b^2 + 1/c^2 = 11/8.

2. (x - ab)(x - bc)(x - ac) = 6x^3 - 20x^2 + 8x - 4.

3. The possible values of a are 1 and 3.

The value of k is -8.