Final answer:
The perimeter of a rectangle with length -2x + 3y - 10 and width -10x + 8y + 3 is represented by the algebraic expression -24x + 22y - 14.
Step-by-step explanation:
The perimeter of a rectangle can be found using the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. To find the perimeter of the given rectangle with a length of -2x + 3y - 10 and a width of -10x + 8y + 3, we first double each of the length and width and then sum them up as shown in the step-by-step calculation:
- Double the length: 2(-2x + 3y - 10) = -4x + 6y - 20
- Double the width: 2(-10x + 8y + 3) = -20x + 16y + 6
- Add them up to get the perimeter: P = (-4x + 6y - 20) + (-20x + 16y + 6) = -24x + 22y - 14
Thus, the perimeter of the rectangle is represented by the algebraic expression -24x + 22y - 14.