To find the value of z in triangle XYZ, we can utilize the law of sines. We know the following:
1. The measure of angle XYZ is 51 degrees.
2. The measure of angle YZX is 76 degrees.
3. The length of side XZ is 2.6 units.
From these angles, angle XZY can be calculated, and then we can apply the law of sines to determine z.
Thus, we proceed to solve for z using the sine relationship in the triangle.
We will round the result to one decimal place.
A(w) = -w² + 100w
Step-by-step explanation: Initially, we need to express the length (l) of the rectangular area in terms of the width (w). Given that the total perimeter of the rectangle is 200 feet implies that 2(w + l) = 200, leading to l = 100 - w. Hence, the area A can be given as width multiplied by length: A = w * l = w * (100 - w) = -w² + 100w. Consequently, A(w) = -w² + 100w.