options: Define trigonometric ratios and solve problems involving right triangles.

Understand and apply the Pythagorean Theorem.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Explain volume formulas and use them to solve problems.

Prove geometric theorems.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Prove theorems involving similarity.

Analyze, compare, create, and compose shapes.

Visualize relationships between two-dimensional and three-dimensional objects.

Make geometric constructions.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Find arc lengths and areas of sectors of circles.

Classify two-dimensional figures into categories based on their properties.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Understand and apply theorems about circles.

Use coordinates to prove simple geometric theorems algebraically.

Reason with shapes and their attributes.

Apply geometric concepts in modeling situations.

Apply trigonometry to general triangles.

Experiment with transformations in the plane.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Solve real-world and mathematical problems involving area, surface area, and volume.

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

Translate between the geometric description and the equation for a conic section.
problem_activity: Task
Janine is planning on creating a water-based centerpiece for each of the 30 tables at her wedding reception. She has already purchased a cylindrical vase for each table. The radius of the vases is 6 cm and the height is 28 cm. She intends to fill them half way with water and then add a variety of colored marbles until the waterline is approximately three-quarters of the way up the cylinder. She can buy bags of 100 marbles in 2 different sizes, with radii of 9 mm or 12 mm. A bag of 9 mm marbles costs \$3 and a bag of 12 mm marbles costs \$4.
If Janine only bought 9 mm marbles how much would she spend on marbles for the whole reception? What if Janine only bought 12 mm marbles? (Note: $1\text{ cm}^3 = 1\text{ ml}$)
Janine's parents, who are paying for the wedding, have told her she can spend at most $d$ dollars on marbles.  Write a system of equalities and/or inequalities that she can use to determine how many marbles of each type she can buy.
Based on your answer to part (b), how many bags of each size marble should Janine buy if she has \$180 and wants to mix in as many small marbles as possible.


correct_option_index: 3