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).

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

-9a - 4z = -7a - 7z - 6
-9a = -7a - 7z - 6 + 4z
-9a + 7a = -7z - 6 + 4z
-2a = -3z - 6
a = \( \frac{-3z - 6}{-2} \)
a = \( \frac{-3z}{-2} \) + \( \frac{-6}{-2} \)
a = 1\(\frac{1}{2}\)z + 3

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• 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°)

Applying these relationships starting with y° = 154, the value of x° is 154.

The volume of a cylinder is πr²h:

v = πr²h
v = π(9² x 5)
v = 405π