The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

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.

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(3²) + 2π(3 x 2)
sa = 2π(9) + 2π(6)
sa = (2 x 9)π + (2 x 6)π
sa = 18π + 12π
sa = 30π

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

9b + y = -5
y = -5 - 9b

then substitute the result (-5 - 9b) into the second equation:

-3b + 4(-5 - 9b) = 1
-3b + (4 x -5) + (4 x -9b) = 1
-3b - 20 - 36b = 1
-3b - 36b = 1 + 20
-39b = 21
b = \( \frac{21}{-39} \)
b = -\(\frac{7}{13}\)