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Given:

It is given that the lines AB and DE are parallel.

We need to determine the value of x.

Value of x:

Let us use the property of similar triangles.

Thus, using the similar triangles, the corresponding sides of the triangle is given by

Substituting AB = 10, ED = 6, BC = 14 and CD = x in the above expression, we get;

Cross multiplying, we have;

Thus, the value of x is 8.4

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b