Answer:
100.0 feet
Step-by-step explanation:
For an acute angle in a right triangle, the cotangent function is the ratio of the adjacent side to the opposite side:
cot(16°42') = (distance to goal)/(30 ft)
Multiplying by the denominator, we have ...
(distance to goal) = (30 ft)cot(16°42') = (30 ft)(3.33317) ≈ 100.0 ft
The football is 100.0 feet from the base of the goal.
_____
cot(16°42') = tan(73.3°)
Since the graph is a linear function, we're going to use the slope formula solve this:
Note I am replacing m with k

Inserting 2 points from the graph, let's use (1,8) and (2,16).

k=8
Answer:
a) 1/27
b) 16
c) 1/8
Step-by-step explanation:
a) 
One of the properties of the exponents tells us that when we have a negative exponent we can express it in terms of its positive exponent by turning it into the denominator (and changing its sign), so we would have:

And now, solving for x = 9 we have:

b) 
This is already a positive rational exponent so we are just going to substitute the value of y = 8 into the expression

c) 
Using the same property we used in a) we have:

And now, solving for z = 16 we have:

24% = 24/100 = 12/50 = 6/25
24% is 6/25 fraction of world's energy.