The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

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:

y² + 8y - 2 = 4y + 3
y² + 8y - 2 - 3 = 4y
y² + 8y - 4y - 5 = 0
y² + 4y - 5 = 0

Next, factor the quadratic equation:

y² + 4y - 5 = 0
(y - 1)(y + 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 1) or (y + 5) must equal zero:

If (y - 1) = 0, y must equal 1
If (y + 5) = 0, y must equal -5

So the solution is that y = 1 or -5

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 7cm + 9cm + 9cm = 25cm

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\( \sqrt{2} \)

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(7²) + 2π(7 x 8)
sa = 2π(49) + 2π(56)
sa = (2 x 49)π + (2 x 56)π
sa = 98π + 112π
sa = 210π