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.

Complete Question

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?

a) substitute values for a and c into the original pythagorean theorem equation.

b) divide both sides of the equation by two, then determine the principal square root of both sides of the equation.

c) determine the principal square root of both sides of the equation.

d) divide both sides of the equation by 2.

c) determine the principal square root of both sides of the equation.

Step-by-step explanation:

Pythagoras Theorem for a right angled triangles states that:

a²+ b²= c²

But for an Isosceles Triangle, where two sides of the triangle are equal, we have:

a²+ a² = c²

By combining like terms

2a² = c²

We square root both sides of the equation.

√2a² = √c

√2a² = c

The final step will prove that the length of the hypotenuse, c, is StartRoot 2 EndRoot times the length of each leg = √2a² = c is Option c.

x = 1

y = - 2

Step-by-step explanation:

The given system of equations is expressed as

x - 3y = 7 - - - - - - - - - - - - - 1

-x + 5y = -11 -- - - - - - - - - - - - - 2

Since the coefficients of x on both rows are equal and the signs are opposite, we would add equation 1 to equation 2. It becomes

2y = - 4

Dividing the Left hand side and the right hand side of the equation by 2, it becomes

2y/2 = - 4/2

y = - 2

Substituting y = - 2 into equation 1, it becomes

x - 3 × - 2 = 7

x + 6 = 7

x = 7 - 6 = 1