Geometry I Unit Quiz 2

Two lines are defined by the following equations:
\(3y-9x=21\)

\(3y+x=-6\)

What is the degree measure of the angle formed by the intersection of the two lines?

A line segment that serves as the diagonal of one face of a cube has a length of \(6\sqrt{2}\). What is the volume of the cube?

Lines \(y_1\), \(y_2\), and \(y_3\) have the following equations:

\(y_1=-x+4\)

\(y_2=\frac{3}{5}x-\frac{4}{5}\)

\(y_3=-2\)

What is the area of the region bounded by these lines?

A perfectly spherical balloon with a volume of \(36\pi\) is expanded so that the radius doubles. What is the volume of the resulting perfectly spherical balloon? (Note: for spheres, volume \(=\frac{4}{3}\pi r^3\)

The sides of a triangle measure \(8\), \(12\), and \(x\). Which one of the following is a possible value of \(x\)?

If \(AB\) is parallel to \(DC\), \(AD\) is parallel to \(BC\), \(AB=6\), \(AD=4\), and angle \(DAB=120\) degrees, what is the area of \(ABCD\)?

A polygon has the same interior angle measure as that of seven triangles combined. How many sides does the polygon have?

A chiliagon has \(1000\) sides. What is the total measure of the exterior angles of a chiliagon?