Question 1 (0.5 points) Given a = 31, A = 84 degrees, and b = 20, use the Law of Sines to solve for B. Round
your answer to the nearest degree, and enter the number only. Note: The figure is
not drawn to scale.

39.91 degrees.

Step-by-step explanation:

Formula

Sin(A)/a = Sin(B) / b

Givens

Solution

Sin(84)/31 = Sin(B)/20

20*Sin(84) / 31 = Sin(B)

Sin(B) = 0.6416

B = 39.91 degrees.

This looks like it is right, but you should check. Let h be the height opposite angle A.

h/20 = sin(39.91)

h = 20*sin(39.91)

h = 12.83

31 has to be longer than that amount (which it is.) So there is one solution.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions