Density and Design Problems — Unit test Answers

An area reserved for a parking lot is 80 feet long and 77 feet wide. The stalls of the lot are at 90° angles to two one-way aisles. Each aisle is 80 feet by 10 feet. The three areas set aside for the parking spaces are congruent rectangles.

Which equation represents the circle described?The radius is 2 units. The center is the same as the center of a circle whose equation is x2 + y2 – 8x – 6y + 24 = 0.

Which shape could be thought of as being created by stacking congruent polygons?

A trapezoid, square, and semicircle are connected to form a composite figure. Trapezoid M D C K has base lengths of 8 millimeters and 4 millimeters. Square A B C D has side lengths of 2 millimeters. Line A B is the diameter of the semicircle and has a length of 4 millimeters.

A parabola and its focus are shown on the graph. The vertex of the parabola is at (0,0).

The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. A state had 424 earthquakes over a given time span and a land area of 71,300 square miles.What is the seismic activity density for this state? Round to the nearest ten thousandth, if necessary.

A composite figure is comprised of a square, trapezoid, and a rectangle. The square has side lengths of 10 centimeters. The trapezoid has base lengths of 8 centimeters and 14 centimeters. The height of the trapezoid is 4 centimeters. The rectangle has side lengths of 20 centimeters and 6 centimeters.

Every possible cross section of a three-dimensional figure is a circle. What is the figure?

A parabola can be represented by the equation x2 = 2y.

A point is on a circle if the distance from the center of the circle to the point is equal to the

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units.The center of the circle lies on the x-axis.The center of the circle lies on the y-axis.The standard form of the equation is (x – 1)² + y² = 3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The right isosceles triangle shown is rotated about line k with the base forming perpendicular to k. The perimeter of the triangle is 58 units.

Which three-dimensional figure has double the number of edges as faces?

A parabola with a vertex at (0,0) has a directrix that crosses the negative part of the y-axis.

The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. The table shows the land area and seismic activity density.

What is the radius of a circle whose equation is (x + 5)2 + (y – 3)2 = 42?

Which statements are true? Select three options.

A circle is shown. 4 radii are drawn. Chords are drawn to connect the radii points on the circle to form 2 triangles. The triangles have base lengths of 6 centimeters and the other 2 sides have lengths of 5 centimeters. The distance between the base of the triangle to the outline of the circle is 1 centimeter. Everything around the triangles is shaded.

3 shapes are combined to form a composite figure. A semicircle is on the bottom, and then a small rectangle connects the semicircle to a triangle.

A general formula for a parabola is x2=4py.What is the value of p in the equation x2=12y?