Answer:
D). 
Step-by-step explanation:
<u>STEP 1a:</u> Find the last angle of the triangle. ( which is angle A)

<u>STEP 1b:</u> Solve the equation for A by adding 90 and 45.

<u>STEP 1c:</u> Then Move all terms not containing A to the right side of the equation by subtracting 135 from both sides of the equation

<u>STEP 1d:</u> Subtract 135 from 180.

STEP 2a: Find side b next.
STEP 2b: The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

STEP 2c: Substitute the name of each side into the definition of the cosine function.

STEP 2d: Set up the equation to solve for the adjacent side, in this case b.

STEP 2e: Substitute the values of each variable into the formula for cosine.

STEP 2f: Cancel the common factor of 2.

HOPE THIS HELPS!
P(sum = 6) = 5/36 ; P(sum = 12) = 1/36
expected payoff = (5/36)(5) + (1/36)(9) = $0.94
Answer:
4x-11
Step-by-step explanation:
open parentheses: 4x-8-3
solve: 4x-11
The equivalence

means that n-5 is a multiple of 12.
that is
n-5=12k, for some integer k
and so
n=12k+5
for k=-1, n=-12+5=-7
for k= 0, n=0+5=5 (the first positive integer n, is for k=0)
we solve 5000=12k+5 to find the last k
12k=5000-5=4995
k=4995/12=416.25
so check k = 415, 416, 417 to be sure we have the right k:
n=12k+5=12*415+5=4985
n=12k+5=12*416+5=4997
n=12k+5=12*417+5=5009
The last k which produces n<5000 is 416
For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,
thus there are 417 integers n satisfying the congruence.
Answer: 417