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 < sign and the answer on the other.

2b - 7 < -5 - 3b
2b < -5 - 3b + 7
2b + 3b < -5 + 7
5b < 2
b < \( \frac{2}{5} \)
b < \(\frac{2}{5}\)

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 = \( \sqrt{a} \) = \( \sqrt{36} \) = 6

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 = 6² + 6²
c² = 72
c = \( \sqrt{72} \) = \( \sqrt{36 x 2} \) = \( \sqrt{36} \) \( \sqrt{2} \)
c = 6\( \sqrt{2} \)

The volume of a cylinder is πr²h:

v = πr²h
v = π(9² x 1)
v = 81π

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

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

a + y = 8
y = 8 - a

then substitute the result (8 - 1a) into the second equation:

5a + 7(8 - a) = 1
5a + (7 x 8) + (7 x -a) = 1
5a + 56 - 7a = 1
5a - 7a = 1 - 56
-2a = -55
a = \( \frac{-55}{-2} \)
a = 27\(\frac{1}{2}\)