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.

-6b - 3 = 9 + b
-6b = 9 + b + 3
-6b - b = 9 + 3
-7b = 12
b = \( \frac{12}{-7} \)
b = -1\(\frac{5}{7}\)

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

The area of a parallelogram is equal to its length x width:

a = l x w
a = a x b
a = 1 x 6
a = 6

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

9b + z = 9
z = 9 - 9b

then substitute the result (9 - 9b) into the second equation:

2b + 3(9 - 9b) = -8
2b + (3 x 9) + (3 x -9b) = -8
2b + 27 - 27b = -8
2b - 27b = -8 - 27
-25b = -35
b = \( \frac{-35}{-25} \)
b = 1\(\frac{2}{5}\)