The dotted line represents the mid segment of the trapezoid. Find the value of X

Given:

Given that the bases of the trapezoid are 21 and 27.

The midsegment of the trapezoid is 5x - 1.

We need to determine the value of x.

Value of x:

The value of x can be determined using the trapezoid midsegment theorem.

Applying the theorem, we have;

where b₁ and b₂ are the bases of the trapezoid.

Substituting Midsegment = 5x - 1, b₁ = 21 and b₂ = 27, we get;

Multiplying both sides of the equation by 2, we have;

Simplifying, we have;

Adding both sides of the equation by 2, we get;

Dividing both sides of the equation by 10, we have;

Thus, the value of x is 5.

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c