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y = 2x + 13      the slope  = 2

The second line will be perp  when   the slope =  -1/2.....so.....

6y + ax = 6 + 5y - 3x          simplify as

y = -ax - 3x + 6

y = - (a + 3) + 6             the slope =  - (a + 3).....set this = -1/2

-1/2 = - (a + 3)

1/2 = a + 3

1/2 - 3  = a

1/2 - 6/2  =  a

-5/2 =  a

Substitute the first equation into the second equation for y

2 ( 11x + 14) - 4 =  ax + (11x + 14) - 6         simplify

1 ( 11x + 14) - 4 = ax - 6

11x + 14 - 4 = ax - 6

11x + 10 = ax - 6

11x = ax - 16

16 = ax - 11x

16 = x ( a  - 11)

16 / ( a - 11)  =  x

This will have no  solution  when a  = 11 because it will make the  denominator of 16 / ( a -11)  = 0

decimal point

See the following :

When P falls below the line segment ED, it will be closer to C than to A because any triangle ADC will be isosceles with AD = CD

The area of ECBD  is a trapezoid with  bases of 1 and 1/2  and height 1/2 so its area= (1/2) (1/2) ( 1 + 1/2) =

(1/4)(3/2) = 3/8

And the total  area of triangle ABC = (1/2)AC * BC =  (1/2) (1) (1) = 1/2

So....the probability that P is closer to C than A is   (3/8) / (1/2) = 6/8 = 3/4

\(4 * 6 + 9 * 3 + \frac{1}{2} * 16 * 7 + 3.14 * 2^2 * \frac{1}{2} = 113.28\)

First part

CP  = 10000 + 5* Q

CP = 5Q + 10000

Second part

CP = 10000 + 1000 * 5

CP = 10000 + 5000

CP = 15000

Call the distance  he  had hiked, D and  call the elevation , E

We have these equations

E = (7/13)D  - 44    →   E = (7/13)D - 44   →   E = (21/39)D - 132/3

E = (1/3)[  D  - 44]     →   E = (1/3)D - 44/3  →   E = (13/39)D -  44/3

Subtract the second equation from  the  first

0 = (8/39)D - 88/3

(8/39)D = 88/3

D = (39*88) /(3 * 8)  =  143

E =  (1/3)(143) - 44/3  =  33

Elevation = (7/13)x - 44

Elevation at the top = (1/3)(x - 44)

Since we know that when he reaches the top, the elevation would be equal to (7/13)x - 44, we can set up an equation:
(1/3)(x - 44) = (7/13)x - 44

To simplify this equation, we can multiply both sides by 3 to eliminate the fraction:
x - 44 = (21/13)x - 132

Next, we can isolate x by subtracting (21/13)x from both sides and adding 44 to both sides:
x - (21/13)x = -132 + 44

x = 143

The distance he reached the top of the mountain is 143.

YAY I BEAT CPhiII again !

3 / 4 - 1 / 2 = 1 / 4, so 1 / 4 of the people like both football and tennis. because 1 / 4 of the group is 35 friends, the whole group is 35 * 4, or 140 friends. 

We aren't very crafty. We just are having fun with this website. 

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You guys are too crafty !!!!

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Correct

f^-1(0)

Set the first function  = 0  

0 = 3- x

-3 = -x 

x = 3      

So f(3) =  0

Which means  that f^-1(0)  = 3

f^-1(6)

Set the second function  =  6

-x^3 + 2x^2 + 3x  = 6

By inspection , x =  2  ..... no good....x must be  > 3

So set the first function =  6

6 = 3 - x

x = 3 - 6

x = -3

So f(-3) = 6

Which means that  f^-1(6)  = -3

So

f^-1(0)  + f^-1(6)  =    3 + - 3 =  0