What is the length of AB?

A.12
B.9
C.6
D.3

Option A:

The length of AB is 12.

Solution:

Given ABC is a triangle.

∠A = 50° and ∠B = 50°

AB = 4x and BC = 2x + 6

To find the length of AB:

∠A = 50° and ∠B = 50°

So, ∠A = ∠B

In triangle, sides opposite to equal angles are equal.

⇒ AB = BC

⇒ 4x = 2x + 6

Subtract 2x from both sides.

⇒ 2x = 6

Divide by 2 on both sides.

⇒ x = 3

AB = 4x

     = 4 × 3

     = 12

AB = 12

Hence option A is the correct answer.

The length of AB is 12.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is