Final answer:
After utilizing the properties of an isosceles trapezoid and equations for its sides, we found that the length of segment AB is -38 units and the length of segment BD is 22 units.
Step-by-step explanation:
To find the values of segments AB and BD in an isosceles trapezoid, we utilize the given expressions for these segments and the properties of an isosceles trapezoid. With AB = x+5, and given that CD = 3*-11, which simplifies to -33, we can deduce that AB also equals -33, due to the fact that in an isosceles trapezoid the top and bottom sides (bases) are equal in length. Thus, x+5 = -33, solving for x we get x = -38. For segment BD we are given BD = 2y + 10, and AC = 5y - 8. Since AC and BD are diagonals of the isosceles trapezoid and they bisect each other, it implies that AC = BD. Therefore, 5y - 8 = 2y + 10. Solving for y, we subtract 2y from both sides to get 3y - 8 = 10, and then add 8 to both sides to get 3y = 18. Dividing by 3, we find that y = 6. Plug this value back into the expression for BD to get BD = 2(6) + 10 = 22.