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You're OK  until  here   

y + 1   =       - 3

               _________

                (2 - y) - 1 

y + 1  =    -3

             ______

                1 - y

(1 + y) (1 - y)  =  - 3

-y^2  + 1  =   - 3                         

-y^2  + 4  =  0      multiply through by -1

y^2  - 4  =  0

y^2  =  4

y = 2                or  y  = -2

So

x + 2  = 2                                                  or       x   -  2  =  2

x = 0                                                                    x =   4

reject since  1/x  isn't defined

So     x =  4 , y  =  -2

1/4  +   1/-2   = 

1/4   - 2/4   =

-1/4

Hi CPhill,

thank you for the response, I guess I'm getting thrown off track with the fact that I thought the roots had to be squares themselves. my error, thank you kindly..

The  second  term  is                        The  third term  is

C(5,1)a^4 b  =  15                             C(5,2)a^3 b^2 =  50

5a^4b = 15                                         10a^3 b^2  =  50

a^4b  =  3                                             a^3b^2  =  5        (2)

b =  3 / a^4    (1)

Sub (1)  into (2)   and we  have

a^3 ( 3 / a^4)^2  =  5

9a^3 / a^8  = 5

9/5  =  a^8 / a^3

9/5  =  a^5

a  =  fifth root (9/5)=    (9/5)^(1/5)

The  frirst  term   =  C(5,0) [ (9/5)^(1/5)]^5   =   1 * (9/5)  =   9/5 

Hi catmg,

I've got it thanx, my mistake was I thought the first equation already had the factors, but the factors are really only established once the equation is equal to, or more, or less than 0..and not -3.  Thank you kindly.

Hi mworkhard222,

I've got it...thank you very much..

Basic angle chasing gives 10 degrees

This problem is answered here: https://web2.0calc.com/questions/find-constants-a-and-b-such-that-for-all-x-such-that

Essentially, you use partial fraction decomposition.

Thank you

Same guest here -- for some reason I see that there shows a 1 reply but I don't see the reply...

thank you!

1.4-6=-4.6, which is your answer.

cos(0.8) = 240000/x

0.999902524 = 240000/x

x = 240023.396521

= 240,023 miles

Notice though  that b^2  -4ac    is  under  a radical......so    sqrt (36)  =  6

So.....the roots will   be real,  rational   AND unequal

The number of zeros a number has is the same as the number of 10s it has. 

For example 200 has 2 tens. 2 * 10^2, so it has 2 zeros. 120 has 1 ten, 12 * 10, so it has 1 zero. 

The number of tens a number has is equal to the number of two and five pairs it has since 2*5 = 10. 

In the number above, there are 12 twos and 15 fives, meaning you can have 12 pairs of 2 and 5. 

So there are 12 zeros. 

=^._.^=

Hi mworkhard222,

thank you for the quick response...but please just tell me if you don't mind...

I thought the factors were already out there...meaning the (x+2) and the (2x-3)??

(x+2)(2x-3) =< -3

2x^2 + x - 6 =< -3

2x^2 + x - 3 =< 0

(2x+3)(x-1) =< 0 

If x > 1, both 2x-1 and x+1 will be positive causing x to not satisfy the equation. positive * positive = positive

If x < -1.5, both 2x-1 and x+1 will be negative causing x to not satisfy the equation. negative * negative = positive

So x has to be inbetween, x = [-1.5, 1]

=^._.^=

Hi there, 

i cant see ur steps but here are mine:

\(\left(x+2\right)\left(2x-3\right)\le-3\)

\(2x^2+x-3\le0\)

\(\left(x-1\right)\left(2x+3\right)\le0\)           (u get this by factoring \((x-1)(2x+3)\))

\(-\frac{3}{2}\le x\le 1\)                          (identify the interval)

  Thanx , Chris....I answered this incorrectly the other day....   I edited it after you showed how to calculate it .....( I incorrectly divided the result by 2 )

  .{3/4 * 2   +  1/4 * (-1) ]/2=625 

    I've seen this Q answered by Chris    his answer is :

{3/4 * 2   +  1/4 * (-1) ]= 1.25

The  function will be  negative   on the interval (2, 3)

This  implies  that we  have

(x - 2) ( x - 3)  > 0

x^2  - 5x  +  6   >   0

b =  -5      c  =  6

b +  c    =    1

Expected  value  =

Probability  of Winning * Amt  Won  -   Probability of Losing * Amt Lost  =

(3/4) ($ 2)   - (1/4) ($1)   =

1.50    -  .25   =

$1.25

Note that if PQ  =PR,  then  angles PRQ  and   PQR  =  x

So.....we  have  this system

2y + 3x  =  180       (1)

4y + 2x =  180   ⇒  2x =  180  -  4y   ⇒  x  =  90 - 2y      (2)

Sub (2)  into (1)   for  x

2y  + 3 ( 90 - 2y)  =  180

2y  +  270  -  6y  =  180

-4y = 180  - 270

4y   =  270  -  180  =  90°   =  angle  RPQ 

If DCB  = 40°......then BC  is  a transversal  cutting parallels CD  and  AB

So  angle CBA =  angle  DCB

And  since AC = BC,  then  angle  CAB  =  angle CBA  =   40°

So...angle  ACB =  180  - 2(40)  =  180 -  80   =  100°  

oh i just noticed my message didn't post! yes i got it