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y =  18x^2  -48x  - 77

The  line of symmetry is given by :

x =  -(-48)  / (2 (18) )  =    48 /36 =     4 / 3

2√15 =  √60

2√6 = √24

So....the  other leg measures   √ [ 60 - 24 ]  = √36  = 6

The larger  angle will be opposite this side

We need  the  arctan here  [ remember  that the inverse functions return an angle value  ] 

So

arctan (  6 / √24)  ≈  50.77°

sin (-pi/12)  =  sin (-15°)  =   -sin (15°) =  -sin ( 45°  - 30°) =

-  [ sin 45 cos 30  -  sin 30 cos 45 ]  =

- [ √2/2 * √3/2   -  1/2 * √2/2]  =

- [ √6  - √2 ] / 4  =

[ √2  - √6]  /  4     [exact value  ]

Perimeter =  2 (W + L)

And L  = 2W - 8

So

38 = 2 ( W  + 2W - 8)     simplify

Divide both sides by 2

19 = (3W  - 8)     add 8 to both sides

27 = 3W     divie both sides by 3

9 = W

And

L = 2(9)  - 8 =  18 - 8   =   10

Using Dragan's  illustration.....

AP    =  2

And 

sin (60°)  = PF /  AP

sin(60°)  = PF / 2  ⇒   PF  = √3

But CF is a median of  triangle  ABC  and  the PF  is 1/3 of the altitude FC  = 3√3   = √27

And  using the Pythagorean Theorem

CB  =√ [ FC^2  + FB^2 ]=   √ [27 + 1 ]  =   √28  =   2√7  =   CA

So  the perimeter  =  CB + CA  + AB =    2√7  + 2√7 +  2  =    4√7  + 2

Let   N  be  the  number of  55 lb boxes

Then  110 - N = the number of  30  lb boxes

So  we  have  that

55N + 30 (110 - N)  = 4800      simplify

55N  +  3300 - 30N  = 4800

25N  +  3300  =  4800   subtract 3300 from both sides

25N  = 1500   divide both sides by  25

N = 60  =  number  of 55 lb boxes

110 - N  =  110 - 60 =  50  = number of 30 lb boxes

Let  P  be  the pounds of raspberries  sold

Then P + 13  =  the pounds of bananas sold

So

1.75P  + 3.25 (P + 13) =  227.25    simplify

1.75P  + 3.25 P  +  42.25  =  227.25

5P + 48.75 = 227.25     subtract 42.25 from both sides

5P = 185      divide both sides by  5

P =  37 lbs of raspberries

Hey guest! Im pretty sure the scale factor is when you find two corresponding sides then use the ratio right? Well im pretty sure the scale factor in this question is 6:9 which can be simplified into 2:3. Which means that the scale factor is 2:3? I think.

Edges  of a prism  =

3 times   the  base  edges

So

3 * base edges =   99       divide  both sides by 3

base  edges  =  33 =  edges of pyramid's base

The  pyramid  will  have  the same number of  faces  as  base edges = 33 

Hey guest! Lets start! First the way I learend it is that you first make it all that he bought kid tickets. If he only bought kid tickets it would cost him $58.50. Then you subtract 69.50 and 58.50 which gets you 11. Then you subtract 9.25 from 6.50 to get 2.75. Then you divide 11 by 2.75 which gets you 4! That means that he bought 4 adult tickets! Lets see if we are correct!

4*9.25=37. Then 6.50*5=32.5. 37+32.50=69.50! So he bought 4 adult tickets!

Just a mis-read....should  be  30 instead of 32  and  82  instead of  80

Thanks to EP for the correct answer   !!!!

An investment declines in value by 5% each month. By what percentage does its value decline in a year? (Round your answer to two decimal places.)

Let A  be   the value of the investment at the beginning  of the year

At the  end of the year, the investment will be worth 

A(.95)^12  ≈  .54036 A  

So......the %  decline in one year =  1 -.54036  ≈   45.964% ≈  45.96%

Welcome!!! :D

Thanks, Cal   !!!!

The  lagest   possible rectangle will be  a  square with  a diagonal of 2

The side of this square  =   2/√2

So......the area of this square =  (2/√2)^2 =  4/2  =  2 units^2