Answer:

Step-by-step explanation:
Existence of Triangle



Answer:
Infinite
Step-by-step explanation:
3(4x + 1) - 2
= 12x + 3 - 2 (Multiply the sum in the bracket by 3)
= 12x + 1 (Simplify)
This means that:
12x + 1 = 3(4x + 1) - 2
is the same as
12x + 1 = 12x + 1
Hence, anything that is used to substitute x is correct.
Answer:
C
Step-by-step explanation:
C is only right answer among a to d
Answer:
5507.79 feet
Step-by-step explanation:
To find the height of the mountain, we can draw triangles as in the image attached.
Let's call the height of the mountain 'h', and the distance from the first point (31 degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(34) = h/x
tan(31) = h/(x+1000)
tan(31) is equal to 0.6009, and tan(34) is equal to 0.6745, so:
h/x = 0.6745 -> x = h/0.6745
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.6745 + 1000) = 0.6009
h = 0.6009 * (h/0.6745 + 1000)
h = 0.8909*h + 600.9
0.1091h = 600.9
h = 600.9 / 0.1091 = 5507.79 feet