PLS HELP 30 POINTS If ∠P is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for p.

Law of Cosines, all sides are known
Law of Cosines, two sides and the included angle are known
Law of Sines, all sides are known
Law of Sines, two angles and the included side are known

Step-by-step explanation:

Let's just get to the answer. It is the second one. Two sides and the included angle are known. It is very important to know that the angle is included. The law of cosines cannot be used if that angle is not included.

p^2 = r^2 + q^2 - 2rq*cos(P)

A: not true. You are looking for one of the sides.

B: the answer

C: You are not going to use the law of Sines at all

D: Same as C

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step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1