Find the missing side length BM. Round your answer to the nearest tenth.

Length of side BM is 30 yd

Step-by-step explanation:

⇒ ∠B + ∠M + ∠S = 180°

⇒ 35° + 102° + ∠S = 180°

∴ ∠S = 180° - 137° = 43°

Law of sines ⇒ a/sin A = b/sin B = c/sin C

Here, let BM be a then, sin A = sin S = sin 43° = -0.83

Also, b = 18 yd, then sin B = sin 35° = -0.43

⇒ BM/-0.83 = 18/-0.43

⇒ BM = -0.83 × 18/-0.43 = 14.94/0.43 = 34.74 yd = 30 yd (rounded to nearest tenth)

Step-by-step explanation:

Looking at the triangle, to determine BM, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. From the triangle, m∠S = 180 - (102 + 35) = 43°

Therefore, applying the rule,it becomes

18/Sin35 = BM/Sin43

Cross multiplying, it becomes

BM × Sin 35 = 18 × Sin 43

BM × 0.5736 = 18 × 0.6820

0.5736BM = 12.276

Dividing the left hand side and the right hand side of the equation by 0.5736, it becomes

0.5736BM/0.5736 = 12.276/0.5736

BM = 21.4

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be