According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 6² + 1²
c² = 36 + 1
c² = 37
c = \( \sqrt{37} \)

An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

z² - 5z + 11 = z + 2
z² - 5z + 11 - 2 = z
z² - 5z - z + 9 = 0
z² - 6z + 9 = 0

Next, factor the quadratic equation:

z² - 6z + 9 = 0
(z - 3)(z - 3) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, (z - 3) must equal zero:

If (z - 3) = 0, z must equal 3

So the solution is that z = 3

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

2z - 9 = \( \frac{z}{-2} \)
-2 x (2z - 9) = z
(-2 x 2z) + (-2 x -9) = z
-4z + 18 = z
-4z + 18 - z = 0
-4z - z = -18
-5z = -18
z = \( \frac{-18}{-5} \)
z = 3\(\frac{3}{5}\)

You need to find the value of b so solve the first equation in terms of y:

-8b + y = -6
y = -6 + 8b

then substitute the result (-6 - -8b) into the second equation:

-9b + 4(-6 + 8b) = -7
-9b + (4 x -6) + (4 x 8b) = -7
-9b - 24 + 32b = -7
-9b + 32b = -7 + 24
23b = 17
b = \( \frac{17}{23} \)
b = \(\frac{17}{23}\)