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.

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

p = x + y + z
p = 10cm + 8cm + 12cm = 30cm

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

a² + 11a + 30 = 0
(a + 5)(a + 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 5) or (a + 6) must equal zero:

If (a + 5) = 0, a must equal -5
If (a + 6) = 0, a must equal -6

So the solution is that a = -5 or -6

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

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 1. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -2) and (2, 4) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = 1\(\frac{1}{2}\)x + 1