To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 5)(y + 2)
(y x y) + (y x 2) + (5 x y) + (5 x 2)
y² + 2y + 5y + 10
y² + 7y + 10

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 59° - 47° = 74°

So, d° = 47° + 74° = 121°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 59° = 121°

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 9 x 8 = \( \frac{72}{2} \) = 36

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

c² = a² + b²
c² = 6² + 6²
c² = 36 + 36
c² = 72
c = \( \sqrt{72} \)