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Each tile is  4 x 6 / 12 x 12 = 24/144 =  1/ 6 sq ft/tile

9ft x 12 ft = 108 sq ft

108 ft²  / 1/6 ft²/ tile = 648 tiles

corrections::::    ∠Y = tan-1(5 / 12)    

A right triangle has side lengths 5, 12, and 13.  The angle bisector is drawn from the vertex with the right angle to the other side.  What is the length of the angle bisector?

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∠Y = tan^-1(3 / 12)              ∠X = 180 - (45 +∠Y)

AN / 12 = sin(Y) / sin(X)

AN = [12 * sin(Y)] / sin(X) = 4.991341987

Let  the  distance  between the center of   one of the smaller semicircles and the  red  circle  =  1 + r

Let  radius of  one of the semicircles   = 1

Let  the  distance  form the  center of the small red circle to the diameter of the  large semicircle  = 2 - r

These form a right triangle such that

1^2 + (2-r)^2  = (1 + r)^2   simplify

1  +  4  - 4r  + r^2  =  1  + 2r  + r^2

4  = 6r

r = 4/6  = 2/3

A semicircle with radius 2 and two semicircles with diameter 2 are drawn as shown.  The red circle is tangent to all three semicircles.  Find r.

r = 0.666666667     or     2/3

Rewrite  as

6t^2  - 41t   +  30  =   0

(6t   -  5)  ( t - 6)    =   0

Set each  factor to 0  ad  solve for  t    gives

t = 5/6     and  t  = 6

So

6 - 5/6   = 

[36 - 5 ] / 6  =

31/6

Let AB  =12, BC  =13  and AC   = 5

Let the angle  bisector divide the  hypotenuse  into  segments x and  13 - x

And we have the  relationship

5 / x =  12/ ( 13 - x)

5 ( 13 -x)  = 12x

65  - 5x  = 12 x

65  = 17x

x =  65/17

And  

sin 45  / (65/17)  =  sin BCA / bisector length

(1/sqrt (2)  / (65/17)  = ( 12/13)  /  bisector  length

bisector legth  =   (12/13) (65/17)  *sqrt (2)  =   (60/17)sqrt (2)

3(-4)  + 5(7)  +  (5) (-1)   =  

-20   +  35    - 5   =

10

5 / 12  =  13/ x     cross-multiply

5x  =  13 * 12

5x   = 156        divide both sides  by  5

x   =156/5  = 31.2  miles  =    31 miles

1.  Each side of the square  =    22/sqrt (2)

So.....the perimeter =  4 *  22/sqrt (2) =  88/sqrt (2)  =  88 sqrt (2) / 2  =  44 sqrt (2)

2.    One  of the sides  of the triangle  =  (1/sqrt (2) )  ( 16  + 8/sqrt (2)  ) =  16/sqrt (2)  + 8/2  =

16 sqrt (2) / 2  + 4  =     8sqrt (2)  + 4

So the perimeter  = 2 [ 8sqrt (2)  + 4 ]   +   16  + 8/sqrt (2)   =

16sqrt (2) + 8  +  16  + 8sqrt (2) / 2   =

16sqrt (2)  +  8  + 16  +  4sqrt (2)  =

24  +   20 sqrt (2)

13 in / 5/12 in/mile   = 13 * 12/5 miles  = ........ miles

The product  of  the roots in the first equation  = 2

So   ab   = 2

And  

(a  + 1/b)  =  [ ab + 1 ] / b

(b + 1/a)   = [ ab + 1 ] / a

And  the  product of these  roots   = q

So

[ ab + 1 ]  [ ab + 1]                     [2 + 1 ]  [ 2 + 1]

_________________      =        ____________   =      9/2   =    q  

           ba                                            2

We need to solve this

-6t^2  - 7t  +  45  =  25

-6t^2    -7t  +  20   =   0

(-2t - 5)  ( 3t - 4)  = 0

Only the econd factor produces a  positive  result  for t

3t  - 4   =   0

3t   = 4

t =  4/3    seconds

Thx, jugoslav....!!!!

We have the points  (4,-7)  and (0, -6)  on the  graph

Slope    of the line through  these ponts   =     [ -6 - - 7 ]  /  [ 0 -4 ] =    -1/4    =  m

We have the form

y = mx  +  b

Where  m  = the slope   b =  the y intercept  =  -6

So we have that

y  = (-1/4)x  - 6

If the line of symmetry  is  x =2.....then this is the x coordinate of the  vertex

We have the form

y =  a(x - h)^2  + k         where  h  is the  x oordinate of the vertex ....we need to find a  and k thusly

1  = a  (1 - 2)^2  +  k   →  1  = a  +  k

-1  = a  (5 - 2)^2  + k  → -1  = 9a + k

Subtract  the second equation from the first

2  = -8a

a = 2/-8  = -1/4

And   1 =  -1/4  +  k

k  = 1 + 1/4  = 5/4

So  we  have that

y  =(-1/4) ( x - 2)^2 +  5/4

y = (-1/4)  ( x^2  -4x  + 4) + 5/4

y = (-1/4)x^2  + x  -1  +  5/4

y  = (-1/4)x^2  + x  + 1/4

a = -1/4    b  =  1     c   =   1/4

And their sum is     1

Two more add-ons cost 6.25-5.25 = 1.00   or 50 cents each

   so the base sandwich costs  5.25 - 3(50) = 3.75    (the y intercept)

Three....

Rate =   1/12 tank  / 1/3 hour =  1/12 * 3/1 = 3/12 tank/hr

1 tank  /  3/12 tank /hr = 12/3 hr = 4 hours

(4+8) = .......

If the wholesale price of the bike = P

Then the markup before sale        =1.30P

Bike sold at 20% discount =1.30P x 0.8 =1.04P - Or, 4% above wholesale price that Ande will pay.

Some info missing....how much $ did store  pay at wholesale for said bike?

6x   =  4 (x+22)

2x = 88

x = 44  m/hr   for the trip up  at 6 hrs = 264 miles

4C2  *  6C3 = ........

sorry nut I still can not solve it