To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

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

p = x + y + z
p = 6cm + 9cm + 6cm = 21cm

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

3a + y = 5
y = 5 - 3a

then substitute the result (5 - 3a) into the second equation:

2a + 6(5 - 3a) = 2
2a + (6 x 5) + (6 x -3a) = 2
2a + 30 - 18a = 2
2a - 18a = 2 - 30
-16a = -28
a = \( \frac{-28}{-16} \)
a = 1\(\frac{3}{4}\)

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 2² + 3²
c² = 4 + 9
c² = 13
c = \( \sqrt{13} \)