CPhill

x^2+11x+1=0  subtract 1 from both sides

x^2 + 11x  =  - 1        take (1/2) the coefficient on x, (11), square it and add to both sides..so (11/2) = 121/4 and we have

x^2 + 11x + 121/4 = -1 + 121/4      factor the left side and simplify the right

(x + 11/2)^2 = 117/4        take the ± square root of both sides

x + 11/2  = ±(√117)/2      subtract 11/2 from bot sides and note that √117 = √(13*9) =3√13....so we have..

x = [ - 11 ± 3√13] / 2

The largest value that "a" can assume is 2.....

Make that check payable to "Melody S."......late of Windsor, NSW.....!!!!

In lieu of that......it can also be re-routed to "Chris P"......late of Shreveport, LA......

P(G(a))  = 4 + 2√[(4-3x) +2] = 4 + 2√(6-3x )

Note that (6 - 3x) must be ≥ 0

So......

6 - 3x ≥ 0   add 3x to both sides

6 ≥ 3x        divide both sides by 3

2 ≥ x   →   x ≤ 2

So....."a" cannot be  > 2

SSS

SAS

AAS

ASA

And he's not "lion," either !!!!

Purr - fect !!!!

f^-1 (50) = 7

f^-1 (10) = 3

f^-1 (26) = 5

So ......

f^-1 (7 x 3 + 5) = f^-1 (21 + 5) = f^-1 (26) = 5

f(f(1)) = (x-1)(x-2)

First....we want to find f(1),,,,this just says to "plug" 1 into the function and evaluate

So we have

(1-1)(1-2) = (0)(-1) = 0

Now.... f(f(1))  ... says we want to take this result and "plug"  it  back into the function, again...so we have

f(f(1)) = f(0) = (0-1)(0-2) = (-1)(-2) = 2

The second isn't too bad..we have

 (b)  sinpcosp= 1/2

Note that sinpcosp is really just (1/2)(2)sinpcosp   = (1/2)sin(2p)

So we have

(1/2)sin(2p) = 1/2        multiply through by 2

sin(2p) = 1

Since sinp = 1 at  90 and 450, then sin(2p) = 1 at 45 and 225

A y intercept of 3 means the point (0, 3)...

Now note something.......we could find the slope arithmetically, but think about this....from (0,3) to (2, -4)...y changes by -7 and x changes by 2......and that's the definition of the slope....so...our slope is -7 / 2 

Now....using the point slope form, we have

y - y1 = m(x - x1)     where m is the slope and (x1, y1) is a point on the line....(let's use (0, 3))

So we have

y - 3 = (-7/2)(x - 0)

y - 3 = (-7/2)x      add 3 to both sides

y = (-7/2)x + 3

And there you go !!!