5. GEOMETRY The volume of a rectangular pyramid is one third the product of the area of its base and its height. Find
an expression for the volume of a rectangular pyramid whose base has an area of 3x2 + 12x + 9 square feet and
whose height is x + 3 feet.

x³ + 7x² + 15x + 9

Step-by-step explanation:

Given that the volume (V) of a rectangular pyramid is

V = A h ( A is the area of base and h the height ), then

V = (3x² + 12x + 9)(x + 3) ← factor out 3 from A

   = × 3(x² + 4x + 3)(x + 3)

   = (x² + 4x + 3)(x + 3)

Each term in the second factor is multiplied by each term in the first factor, that is

x² (x + 3) + 4x(x + 3) + 3(x + 3) ← distribute parenthesis

= x³ + 3x² + 4x² + 12x + 3x + 9 ← collect like terms

= x³ + 7x² + 15x + 9

Thus the expression for the volume is

V = x³ + 7x² + 15x + 9

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.