ElectricPavlov

https://web2.0calc.com/questions/your-dog-weights-5-times-as-much-as-your-cat-your

The vertical distance 300ft and the horizontal distance are the legs of a right traingle

the tangent of the 15^o  =  opp/adj = 300/horiz     horiz is what you are looking for

tan 15 = 300/horiz       solve for horiz

Find slope    = -2

y = -2x + 13   is the equation of the line

2x + y = 13     divide by 13

x / (13/2)  + y/13 = 1

Probably looks something like this

d = 5 c

d = c + 20       solve.....

a + 15 r = $ 70

a + 12 r = 61        Multiply this equatin by -1     -a - 12 r = -61    add it to the first equation

3 r = 9

r = $ 3       now you can use this value of 'r' to plug into either of the equations to find 'a'   admission cost

If they are parallel, they will have the same slope, m

   arrange the equations in the form   y = mx+b   to see if the 'm' s   are equal

    one  is in this form already    m = 5

2y-10x+3 = 0

2y= 10x-3

y = 5x - 3/2       Yep m= 5 on this one too......

81  +     ( 6/5x + 39 )   = 180^o         Solve for 'x'

After 1 1/2 hr hike A has travelled   1 1/2 x 6.2       Hiker B has travelled  1 1/2 x 5.4

  Use law of cosines to find the distance between the two hikers at this point

       then the tangent of  angle in question will be    .8 km / (distance between hikers)

First find the slope = m  =  (y1-y2)/(x1-x2) = (-5-1) / (-3-6) = 6/9 =  2/3

Now a line equation is   y = mx + b      y = 2/3 x + b

   sub in one of the points to find 'b'

     1 = 2/3 (6) + b

         b = -3

so you lie equation becomes   y = 2/3 x -3       but not in the form requested

    multiply through by 3

           3y = 2x -9      re-arrange

           2x - 3y = 9     You can finish !   

Divide both sides of the equation by 2

2/2 g = 26/2

g=13