Warm Up
Simplify each expression.
a. (3x + 10)(3x - 5) =
b. (x - 5)2 =
c. (2x - 1)(x2 - 5x - 7) =
d. (3x - 5)(-x2 - 2x + 2) =
The image below represents the bed of a cargo truck. The truck has a height, h, of (3x) feet, a length, l, of 8 feet, and a width, w, of (30 + 4x) feet.
What it the capacity of the truck bed as a function of x?
Write a simplified algebraic expression to represent the volume.
V(x) =
The degree of the volume is
The leading coefficient of the volume is
The constant term of the volume is
A company uses a cargo delivery truck to transport the loads of woodchips to the schools for their playgrounds. There are two differentsized trailers connected to the truck. Both trailers will be filled with bags of woodchips to enhance the outdoor learning spaces, or playgrounds. The first trailer can transport x2 + 8x + 3 cubic feet at full capacity, and the second trailer can transport x2 + 3 cubic feet at full capacity. The truck makes 15 trips back and forth to the warehouse to refill the truck at full capacity with bags of woodchips in each trailer for each trip in order to satisfy the order for all schools.
Create an expression to calculate the total capacity of bags of woodchips, in cubic feet, transported across the 15 trips.
The degree of the combined volume is
The lead coefficient of the combined volume is
The constant of the combined volume is
The Playground
The playground for each school will include the following shape to incorporate all of the playground equipment. What is the area of the space requiring wood chips? Each side is measured in feet.
The area of the playground is
Suppose that x = 3. What is the area of the playground?
Area =
We need to cover the playground with woodchips. Woodchips come in bags. Each bag includes 2 cubic feet of woodchips. One 2 cubic foot bag covers 3 square feet. The desired depth of woodchips is 8”, how many bags does the playground require to adequately cover the space?
