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Wow.... you must have po'd a moderator!  Haha

  Did you switch computers?  Change browsers?  Delete cookies?     ......Just thoughts..

(5x+5)/(x+1)+(x-2)/(x+1)=(6x+3)/(x+1)=(3(2x+1))/(x+1)

solved

I have been registered for about a year i think and ive never seen it until today

Pretty sure, after you have been registered user for a while it stops the recaptcha thingie.....I have not seen it in quite some time....granted, it was most annoying initially.

you sir have made my day

*omega facepalms into a different universe where everything is made of gelatin*

You’re not. You’re a tank—it’s official.

We can write :

a^(6/4) * b^(3/4)  / c^(2/4)  =

a^(3/2) * b^(3/4) / c^(1/2)      multiply top/bottom by c^(1/2)

a^(3/2)*b^(3/4) *c^(1/2)  / c

Note, Manuel, we could also write this as

a^(3/2) * b^(3/4) * c^(-1/2)

Thanks but the radical sign extends to the c² too

\(\sqrt[4]{a^6}\)  b^3 / c^2

= (a^6)^1/4  b^3 /c^2

= a^6/4  b^3 c^-2

= a^3/2  b^3 c^-2

or

\(\sqrt[4]{a^6b^3}\)  /  c^2

=  (a^6)^1/4   (b^3)^1/4   c^-2

= a^3/2    b^3/4  c^-2

Thank you!!! <3

Note that

Every dimension of the largest rectangular solid is twice that of the "intermediate" rectangular solid

So....they are similar (and proportional)

And every  dimension of the largest rectangular solid is four times that of the smallest rectangular solid......So they are similar (and proportional)

But, by Euclid....two things that are similar to a third are also similar themselves....thus the "intermediate" rectangular solid and the smallest rectangular solid are similar to each other

So....all three objects are similar  (and proportional) to each other

I'm going to guess that this is supposed to be  1 + 1/4  lbs per day  =

5/4 lbs per day

So....the number of days that a 35 lb bag will last is

35 / [ 5/4 ]  =

35 * 4/5   =

(35/5) * 4  =

7 * 4   =

28 days

Actually, EP....the lack of brackets/parentheses in many of the problems leave them open to interpretation.....yours might have been just as "correct" as others

Guess I 'overthunked' that one, huh?   The other way seemed too easy   

Very well done, heureka  !!!

Manuel says that this is actually 

a^-2 + a^-1b - b²/ (a²b^-1 )

So we have

a^-2 + a^-1b   - b²* b * a^-2

a^-2 + a^-1b - b³*a^-2       factor out   a^-2

a^-2  [ 1  + ab - b³ ]

Thank you!

Thank you!!

Second one :

4x - 20  + x   =  180

5x - 20  =  180     add 20 to both sides

5x  = 160    divide both sides by 

x  = 32°

Third one :

116 + x   = 180     subtract  116 from both sides

x  = 64

So A = 2(64) - 40  =  128 - 40  =  88°

Last one :

x + 10  + x + 24  =  180

2x + 34  =  180      subtract 34 from both sides

2x  = 146         divide both sides by 2

x  = 73

So

A + C  = 180

(x + 15) +   C   =  180

(73 + 15) + C  = 180

88 + C   =  180  subtract 88 from both sides

C  = 92°

114 pounds of dog food a day!!?   That is not a dog, it is a very large BEAR!

Anyway....

35 lbs  /  114 lbs/ day = .307 day   = 7.36 hours   (if dog-bear eats at a steady rate all day)

Opposit angles in a quadrilateral add to 180 (supplementary)

1. 3x+6   +   x+2  = 180

     4x = 172

       x = 43        A= 3x+6 = 3 x 43   + 6 = 135 degrees

2 and 3 are similar

4 all of the angles in a quadrilateral add to 360   

So(I think  ) the cost of the 500 chairs would be   

500 * $70  +   $ 10 * { .01(500)(.4)  + .02(500)(.35)  +  .03(500)(.25) } = $ 35,092.50  

(are you sure about your posted 'correct' answer?....my answer has the '0' and '9' transposed...hmmmmm)