CPhill

First one......let's get the area...first.....the easiest way to do this one is to divide the shape up into two triangles and a rectangle, thusly :

Notice that the area of the triangle on the left  = base * height  / 2  = 6 * 3  /2  = 9 units^2

And....by symmetry....the triangle on the right has the same area......and the area of the rectangle  = 4*6 = 24 units^2

So....the area  =  9 + 9 + 24  =  42 units^2

Perimeter....note that we only need to find EF because  the outer sides of the triangles are all equal

So EF   = sqrt [ (3 - 0)^2 + (7 - 4)^2 ]  = sqrt [ 9 + 9 ]  = sqrt (18)  =  sqrt (9) *sqrt (2)  = 3sqrt(2)

So....we have   4 * 3sqrt (2)  =  12 sqrt (2)  units

And the top and bottom sides of the rectangle are 4 units each

So...the perimeter  =  4 + 4 + 12sqrt (2)   =   8 + 12sqrt(2) units

We are choosing any 6 of 11  = C(11,6)  = 462

The common ratio is 2....so....

Sum   =   first term  [ 1 - common ratio^7 ]   / [ 1 - common ratio ]  =

(1/2) [ 1 - 2^7 ] / [ 1 - 2 ]    =

(1/2) [ -127] / [ -1]  =

(1/2) (127)  =

63.5

5/26 *4/25

You will get the same answer

4x - y = 3    ⇒  y = 4x - 3   (1) 

2x + 3y = 19    (2)

Put  (1) into (2)  for y  and we have

2x + 3(4x - 3)  = 19       simplify

2x + 12x - 9  = 19

14x - 9  =  19       add 9 to both sides

14x  = 28     divide both sides by 14

x  = 2

And using (1)  y  =  4(2) - 3  =  5

DOH...I wasn't thinking!!!

He has worn the same number.....so

(1/5)W = (5/8)B    multiply both sides by  5

W  = (25/8)B

So....he has 25 white and 8 black

So....after 5 days  he has worn  5 white  = (1/5) of the white   and  5 black  = 5/8 of the black

So.....he has worn   [ 5 + 5 ] / [ 25 + 8 ]  =  10 / 33  of the total

 Translate four units left and two units down

OK....just set the function =   108    and we have that

108  = -6t^2 + 51t        rearrange as

6t^2 - 51 t   + 108  =   0         divide through by 3

2t^2 - 17 t +  36  =  0        factor....if we can

(2t  - 9 ) (t - 4)  = 0

Set both factors to 0  and solve for t   and we get two times

t = 9/2 sec    and  t =  4 sec

So  9/2 sec is correct....

NVM....

OK man....!!!!