Using the same data table (x,y): (1,2), (2,8), (3,18), (4,32), (5,50), identify the type of mathematical function that best describes y as a function of x based on the pattern in the data.

From the data table (x,y): (1,2), (2,8), (3,18), (4,32), (5,50), select the algebraic equation that best expresses y as a function of x.

Using your selected equation for the data above, what is the predicted value of y when x=6?

Use the equation $$2x + (2x+3) + (2x+6) = 45$$ to solve for x. What is the value of $$x$$ ?

In the equation $$2x + (2x+3) + (2x+6) = 45$$ , remove the parentheses to write the equation in terms of individual terms. Which property justifies this step?

After grouping and combining the $$2x$$ terms and the constants in $$2x + (2x+3) + (2x+6) = 45$$ , what simplified equation results?

To go from $$6x + 9 = 45$$ to $$6x = 36$$ by subtracting 9 from both sides, which justification should be cited?

From $$6x = 36$$ , divide both sides by 6 to isolate $$x$$ . Which justification should be cited for this step?

A gardener plants one sunflower seed on day 1 and then triples the number of seeds planted each subsequent day for 10 days. Based on this pattern, what type of functional relationship best models the number of seeds planted, y, as a function of the day, x (1 through 10)?

A gardener plants one sunflower seed on day 1 and then triples the number of seeds planted each subsequent day for 10 days. Which explicit formula correctly models the number of seeds planted on day x?

On the provided graph grid where x represents the day (1 through 10) and y represents the number of seeds, which set of ordered pairs shows the correct points to plot for days 1 through 4, given that the gardener triples the number of seeds each subsequent day starting from one seed on day 1?

A hexagon lies in the xy-coordinate plane with the vertices A(1,2), B(3,4), C(5,3), D(5,0), E(3,−2), and F(1,−1). The hexagon is dilated by a scale factor of 2 with the origin as the center of dilation. Choose the coordinates of the vertices of the resulting figure.

Using the original hexagon with vertices A(1,2), B(3,4), C(5,3), D(5,0), E(3,−2), and F(1,−1), the figure is reflected over the line y = x. Choose the coordinates of the vertices of the resulting figure.

Using the original hexagon with vertices A(1,2), B(3,4), C(5,3), D(5,0), E(3,−2), and F(1,−1), the figure is rotated 180° counterclockwise about the origin. Choose the coordinates of the vertices of the resulting figure.

Using the original hexagon with vertices A(1,2), B(3,4), C(5,3), D(5,0), E(3,−2), and F(1,−1), the figure is translated up 3 units and right 4 units. Choose the coordinates of the vertices of the resulting figure.

The original hexagon is reflected over one of two intersecting lines; then the image is reflected over the other intersecting line. Describe a single transformation that results in a congruent image.

A second hexagon in the xy-coordinate plane has vertices A′(2,4), B′(6,8), C′(10,6), D′(10,0), E′(6,−4), and F′(2,−2). Describe a series of transformations that prove this hexagon is similar to the original hexagon with vertices A(1,2), B(3,4), C(5,3), D(5,0), E(3,−2), and F(1,−1).

A three-dimensional solid shown is a sphere with radius $$6\text{ cm}$$ . Calculate the volume of the sphere.

A cone has the same radius as the sphere’s base, $$6\text{ cm}$$ , and a height of $$12\text{ cm}$$ . Calculate the volume of the cone.

Using the given dimensions (sphere radius $$6\text{ cm}$$ ; cone radius $$6\text{ cm}$$ and height $$12\text{ cm}$$ ), explain how the volume of the sphere compares to the volume of the cone.