CPhill

(1/2)   of   the  base  length  =   6/sqrt 3  =   6sqrt 3 / 3  =   2 sqrt 3

So....the  area  =  (1/2) base * height =   2sqrt 3 *  6    =     12 sqrt 3   units^2

NVM.....EP's  answer  below  is  the correct  one.....

Slope  =  ( 5 - - 11)  /( -4 - 1)   =  16 / -5   =  -16/5

Equation

y  =  (-16/5)(x -1)  -  11                multiply through by  5

5y  =  -16( x - 1)  -  55

5y  = -16x  + 16  -  55

5y  =  - 16x  -  39          divide through  by  -39      and  rearange  as

(-5/39)y - ( 16/39)x  =  1

x / ( -39/16)  +  y / ( -39/5 )  =   1

a  =  -39/16

6|4−3d|−2|d+5| > 9

We have two equations to solve

abs  ( 24 - 18d)  - abs ( 2d + 10)  > 9

We can write                                 

24 - 18d -  ( 2d + 10) > 9                   18d - 24  - ( 2d + 10) > 9

14  - 20d  >  9                                   16d   -  34 >  9

-20d  >  9 -  14                                  16d  >  43

-20 d >   -5                                           d >   43/16

d <   -5/-20

d < 1/4

So....the solution set is

(-inf , 1/4)  U  (43/16, inf)

If  10  dropped  and the  number  who  took neither increased from 27  to 31.....then 4 who dropped  must have only been taking  Chinese......then  the  other  6  must  have  been  taking Spanish and Chinese

So....the  number  who  take only Spanish  must increase by 6

Here's  the  shortcut :

25*24*23* .....* 2 * 1   =  25!

Divide  25  / 5    and discard  any  remainders =   5

Divide 25 / 5^2    and discard any remainders =   25  /  25  =  1

Add  the  whole  numbers  =   5 + 1  =  6 trailing zeroes

Another  example

300!

300 / 5   =    60

300/5^2   =   300/ 25   =  12

300/5^3 =   300/125  =  2  + 50/125

Add the whole numbers =   60 + 12 + 2    =   72 trailing zeroes

cos Q   =  QP  / QR   .....so....

.4  =  10  /  QR

QR  =  10   / .4       =       25  cm

1. Graph the function f(x) = -sec(x/4)+3 on the interval [-2pi,6pi]

The  " -"    flips  the  normal  secant   graph over  the x axis

The (x/4)   lengthens  the  normal period  by  a  factor  of  4

The " +3 "  shifts everything  up  by 3 units

Here's  the  normal graph   and  the  transformed graph on  [-2pi, 6pi]

https://www.desmos.com/calculator/ptwct2d3ec

Let  the  number of  marbles  that Kamal  had  in the  beginning=  K

Then  Jason had (128 - K)

Let the  number  of  marbles  that  Jason gave away =  G

Then the  number of marbles  that Kamal  gave away =  3G

And  the number that  Kamal had left = K  - 3G

And  we  know that, from Jason's point of view

What  he started with - what  he gave away =  what he had left

(128 - K)  -  G   = G - 4  simplify

(128 - K)   =  2G - 4

128  + 4  -  2G   = K   

132  -  2G     =    K       (1)

And  from  Kamal's   point of  view  we have  that

3 times  what  he  had left = what Jason had left

3(K - 3G)  =  G -  4       (2)

Sub  (1)  into (2)

3  (  132 - 2G - 3G)  =  G - 4

396 - 15G  = G  -  4

400  =  16G

G = 400/16  =   25

What Jason started with   =  2G  - 4   =  2*25 - 4   =  46

No prob  !!!