CPhill

a =   √ [ 224.7^2 - 189.2^2  ] ≈  121.2

We don't know which angle is the right angle

If it's C   we have that 

cos 28  =   a / 54.8

Multiply both sides by 54.8

54.8 cos 28  =  a ≈    48.385

If A is the right angle, we have that

cos 28  =  54.8 / a  rearrange as

a  = 54.8 / cos 28  ≈  62.06

We can use the sine here

sin 35  = h / 15      where h is the ramp height

Multiply both sides  by 15

15 * sin 35  = h  ≈  8.6 ft

Yep....good job, Rauhan....!!!

Note, NSS....the two roots are  are x = -1 and x  = 1

And when x  = 0.....y is negative

Notice that letting x = 0   in the first equation means that y  = -2...this means that the point (0, -2)  should be on the graph....but this point clearly isn't on the graph

And letting x = 0   in the second and fourth equations, means that y is positive.....and that's not possible on the graph when  x = 0

So....the third equation must be correct.....!!!

5 * 8^4x = 376

Divide both sides by 5

8^(4x)  =  376/5

Take the log of both sides

log 8^(4x)  =  log (376/5)   = log (72.5)    and we can write

(4x) log 8  =  log (72.5)     divide both sides by   4 log8

x =  log (72.5) / [ 4 log (8) ]

log ₄ 25  = x

When  we have log_a b  = x  ....we can solve this with the change of base theorem  which says that

x  = log b / log a

So....this evaluates to

log 25 / log 4  ≈  2.32

Exactly....!!!!

We have a decagon ....the sum of the interior angles in a decagon is  (10 - 2)*180  =

1440°

[ Hint : The 80°  exterior angle means a 360 - 80  = 280°  interior angle  ]

So we have that

[ 107 + 126 + 325 + 125 + 95 +  x + 90 +  280 + 47 + 130 ]  = 1440

Rearrange as

1440 - [ 107 + 126 + 325 + 125 + 95 +  90 +  280 + 47 + 130 ]  = x

1440 - [ 1325 ]  =  x

115°  =  x

The functions are inverses of each other

The graphs of functions are symmetric to each other over the line y = x