CPhill

(2-1/x))/(x+3)  ....we could use the quotient rule here, but I always tend to forget it, so I prefer to write the denominator as a ( -1 ) power and just use  the product / chain rules....so we have

 y = (2 - x^-1) (x + 3)^-1

y ' =  x^-2(x + 3)^-1 - (2 - x^-1)(x +3)^-2

Which we could simplify as  (x+ 3)^-2 [ x^-2 (x + 3) - 2 + x^-1 ] = (x+ 3)^-2 [ 2x^-1 + 3x^-2 - 2 ]

[Note....there are several other acceptable forms ]

Let Jenny's age be N

And Manuel's age = N + 5

So we have

3/4 (N + 5)  = N  simplify

(3/4)N + 15/4  = N    subtract (3/4)N from both sides

15//4 = (1/4)N    multiply both sides by 4

15 = N 

And  Manue's age  is 15 + 5 = 20

x^2-12x+20=0         let's factor this

(x -10) (x -2) = 0     and setting each factor to 0, we have the solutions that x = 10 and x = 2

Not that Melody needs anyone to defend her, but she's a person of many fine qualities.....and even if "answering questions" were all she did, that would be enough.....but......she also looks after the forum in many hidden ways we never see.....we are very lucky to have Melody here  (even if she is a little "barky" at times)...LOL!!!

(-a^0 * a^3)^5

Gotta' be a little careful, here ....  a^0 = 1  but that "-" in front of it makes it negative !!!  ...so we have

(-1 * a^3)^5      and by a property of exponents, we have

(-1)^5 * (a^3)^5  =

-1 * a^15 =

-a^15

Hit the nCr button on the lower left and type in 10, 3....just like that...!!!

Ah....thank you for that correction, Anonymous...that's what I get for being in a hurry...!!!

Let's do this...using x - y = 6   ..... we can just rearrange it and  say that y = x - 6

Now...in  x^2 + y^2 = 26, let's substitute what we just got for y...so this gives us

x^2 + (x -6)^2  = 26  simplify

x^2 + x^2 - 12x + 36 = 26

2x^2 - 12x + 10 = 0    divide through by 2

x^2 - 6x + 5 = 0     factor

(x -5 ) ( x -1)  = 0    so setting each factor to 0 , we find that x = 5  or x =1

And using y = x -6    when x =5 , y = -1  and when x = 1, y = -5

So..our solutions are (5, -1) and (1, -5)

Unless you're asking to factor this...then it becomes.... 30(3x + 4)

1:24 means  that the "real" car is 24 times as long as the model

So

24 x 7.5 =

24 x ( 7 + 1/2) =

168 + 12 =

180 in =

15 ft

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Edit ....24 (7 + 1/4) = 168 + 6  = 174 in = 14 ft 6 in = 14.5 ft

Thanks to Anon, again, for spotting my error...