A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

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

9a + y = 2
y = 2 - 9a

then substitute the result (2 - 9a) into the second equation:

a + 6(2 - 9a) = 5
a + (6 x 2) + (6 x -9a) = 5
a + 12 - 54a = 5
a - 54a = 5 - 12
-53a = -7
a = \( \frac{-7}{-53} \)
a = \(\frac{7}{53}\)

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.

a - 7 = \( \frac{a}{-1} \)
-1 x (a - 7) = a
(-1 x a) + (-1 x -7) = a
-a + 7 = a
-a + 7 - a = 0
-a - a = -7
-2a = -7
a = \( \frac{-7}{-2} \)
a = 3\(\frac{1}{2}\)

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 15 as well and sum (Inside, Outside) to equal 8. For this problem, those two numbers are 3 and 5. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 8y + 15
y² + (3 + 5)y + (3 x 5)
(y + 3)(y + 5)