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y  = ( x + 6)^2   -  2      add 2 to both sides

y + 2  =  ( x + 6)^2       take  the positive root

√ [y  + 2] =  x  +  6        subtract 6 from both sides

√[ y + 2]  -  6  = x           "swap"   x and y

√[x + 2]  - 6  = y        [this is the inverse ]

The domain of the inverse  is   [-2, infinity )

It is a DEcreasing value

slope = rise/run   =   -449500 / 36 = -12486.11   per year

1960   450000    27 years later?

450000 - 27 (12486.11) =112875 cases in 1987

You can find the formula here: https://en.wikipedia.org/wiki/Standard_deviation

There are 7 ways to choose the geometry textbook at one end, then 6 ways to choose the geometry textbook at the other end.  Then there are 9 ways to choose the second textbook, 8 ways to choose the third textbook, and so on.  But then there are 4 ways to choose the algebra textbook, so there are 7*6*9!*4 = 60963840 ways that work.

Log 36....or log 35?

The number of ways is 4*7*7*8! = 7902120.

Triangle   4

Triangle 1  hypotenuse  =sqrt (2)

Triangle 2  hypotenuse = sqrt (3)

Triangle  3 hypotenuse = sqrt (4)  = 2

Area of triangle 4 =    (1/2) * (  hypotenuse of  Triangle 3)  * ( 1 ) =   (1/2) *  2 * 1 =    1

What makes you think you are wrong? You were actually correct! The other answer was wrong. Thank you!

thank you all!

61328.

Nice, heureka and Gadfly   !!!!

Thanks, Alan  !!!!

maybe they're testing the website? Like Testing 1-2-3??

(3+36+x)/3  = (3 * 36 * x)^1/3  + 13

Solve by whatever method to find x = 54

Let L be the center of circle S, and let F be the center of circle T.  Since LA = AF = 1 and LF = sqrt(2), triangle LAF is a 45-45-90 triangle.  This means angle ALF is 45 degrees.  By symmetry, angle BLF is also 45 degrees.

Then angle ALB = angle ALF + angle LBF = 45 + 45 = 90 degrees, so arc AB is 90 degrees.  Since angle APB subtends arc AB, angle APB is 90/2 = 45 degrees.  Then by Poncelet's Theorem, triangle PCD is a 45-45-90 triangle, so angle PCD is 90 degrees.  Then angle ACD is 90 degrees, which implies that CD is a diameter of circle T.

I hope this helps, too.

Got it. Thanks Melody!

thank you!

1/2 way between those endpoints is the center      (h,k) =  (   -1,-4 )

 The total distance between the points is the DIAMETER = sqrt 288

     1/2 of which is th radius = sqrt(72)

Circle form = 

 (x-h)^2 + (y-k)^2 = r^2

(x+1)^2 + (y+4)^2 = 72

Here's a graph:

https://www.desmos.com/calculator/0dkqbxgyxy

I just dont understand this, its the last question and i need help.

These are the solutions for x:
x≈2.5908
x≈-4.5065
x≈-0.04216 - 0.71563 i
x≈-0.04216 + 0.71563 i

So, it looks like the 3rd choice from the top is the accurate one [1 positive and 3 negatives].

Is this a test question?   You should not be looking for answers to test questions here....

-4 -1 - 7x = -4x-14        gather like terms,   add 7x to both sides and add 14 to both sides...that should almost give ya your answer....

Solve for n:
(n + 5)/(n + 8) = 6/(n + 1) + 1

Bring 6/(n + 1) + 1 together using the common denominator n + 1:
(n + 5)/(n + 8) = (n + 7)/(n + 1)

Cross multiply:
(n + 1) (n + 5) = (n + 7) (n + 8)

Expand out terms of the left hand side:
n^2 + 6 n + 5 = (n + 7) (n + 8)

Expand out terms of the right hand side:
n^2 + 6 n + 5 = n^2 + 15 n + 56

Subtract n^2 + 15 n + 56 from both sides:
-9 n - 51 = 0

Factor constant terms from the left hand side:
-3 (3 n + 17) = 0

Divide both sides by -3:
3 n + 17 = 0

Subtract 17 from both sides:
3 n = -17

Divide both sides by 3:
 
n = -17/3