Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°–45°–90° triangle) Prove: In a 45°–45°–90° triangle, the hypotenuse is StartRoot 2 EndRoottimes the length of each leg. Triangle X Y Z is shown. Angle X Y Z is 90 degrees and the other 2 angles are 45 degrees. The length of X Y is a, the length of Y Z is a, and the length of X Z is c. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this isosceles triangle becomes a2 + a2 = c2. By combining like terms, 2a2 = c2. Which final step will prove that the length of the hypotenuse, c, is StartRoot 2 EndRoot times the length of each leg? Substitute values for a and c into the original Pythagorean theorem equation. Divide both sides of the equation by two, then determine the principal square root of both sides of the equation. Determine the principal square root of both sides of the equation. Divide both sides of the equation by 2.

Prove that (x-2)is factor of p (x)=2x³-3x²-17x+30

Ascientist studied a population of workers to determine whether verbal praise and/or tangible rewards affect employee productivity. in the study, some workers were offered verbal praise, some were offered tangible rewards (gift cards, presents, and some were offered neither. the productivity of each participant was measured throughout the study by recording the number of daily tasks completed by each employee. which inference might the scientists make based on the given information? a.) the number of daily tasks completed by each employee may influence the dependent variable, which is whether the employee receives verbal praise, tangible rewards, or neither. b.) verbal praise and/or tangible rewards may influence the independent variable, which is the number of daily tasks completed by each employee. c.) verbal praise and/or tangible rewards may influence the dependent variable, which is the number of daily tasks completed by each employee. d.) the dependent variables, which are verbal praise and tangible rewards, may influence the number of daily tasks completed by each employee.

What is the perimeter of an isosceles triangle with each leg measuring 2x+3 and the base measuring 6x-2?