Answer:
10 miles less
Step-by-step explanation:
To get the direct distance first, we use the pythagorean theorem. Distance from Ferris to Butte directly would be the hypotenuse. By solving for the hypotenuse, we have 25 miles. Now the distance used previously is 35 mile. Hence, it (35 - 25 = 10 ) miles less.
Answer:
x = -9, y = 6.
Step-by-step explanation:
-x + y = 15
-5x - 3y = 27
From the first equation:
y = x + 15.
Substituting for y in second equation:
-5x - 3(x + 15) = 27
-8x - 45 = 27
-8x = 72
x = -9.
Now plug x = -9 into equation 1
-(-9) + y = 15
y = 15 -9 = 6.
Answer: C) $462.96
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Thank you.
Answer:
Step-by-step explanation:
Given the expression cosec (x) = 4 and tan(x)< 0
since cosec x = 1/sinx
1/sinx = 4
sinx = 1/4
From SOH, CAH TOA
sinθ = opposite/hypotenuse
from sinx = 1/4
opposite = 1 and hypotenuse = 4
to get the adjacent, we will use the Pythagoras theorem
adj² = 4²-1²
adj² = 16-1
adj ²= 15
adj = √15
cosx = adj/hyp = √15/4
tanx = opposite/adjacent = 1/√15
since tan < 0, then tanx = -1/√15
From double angle formula;
sin2x = 2sinxcosx
sin2x = 2(1/4)(√15/4)
sin2x = 2√15/16
sin2x = √15/8
for cos2x;
cos2x = 1-2sin²x
cos2x = 1-2(1/4)²
cos2x = 1-2(1/16)
cos2x= 1-1/8
cos2x = 7/8
for tan2x;
tan2x = tanx + tanx/1-tan²x
tan2x = 2tanx/1-tan²x
tan2x = 2(-1/√15)/1-(-1/√15)²
tan2x = (-2/√15)/(1-1/15)
tan2x = (-2/√15)/(14/15)
tan2x = -2/√15 * 15/14
tan2x = -30/14√15
tan2x = -30/7√15
rationalize
tan2x = -30/7√15 * √15/√15
tan2x = -30√15/7*15
tan2x = -2√15/7
