Mathematics
Mathematics, 12.12.2019 03:31, heidibode

Prompt:
his interactive animation shows an image of a brick patio and a garden and grass area. the title "patio project" is shown and a "begin" button starts the animation. [click "begin."]

on-screen text and audio:

patio project: you have a small patio and want to improve it. you can build one of the following features: a fish pond, a planter box, or a fire pit. choose one of the projects, and drag it to the patio. [an image of an orange fish in water, a planter box with flowers, and a fire pit can be seen on the left side of the screen. any of the images can be dragged to the patio and a message pops up.]

fish pond: the patio is rectangular and has a total area of 24 square feet. you are building a rectangular fish pond and want the length of the pond to be twice the width. you also need to add a 1-foot border around the entire pond.

suppose the total area of the patio is represented by the polynomial 2x2 + 6x + 4, where x is the width of the fish pond.

planter box: the patio is rectangular and has a total area of 40 square feet. you are building a rectangular planter box and want the length of the box to be twice the width. you also need to add a 1-foot border around the entire planter.

suppose the total area of the patio is represented by the polynomial 2x2 + 6x + 4, where x is the width of the planter box.

fire pit: the patio is rectangular and has a total area of 24 square feet. you are building a rectangular fire pit and want the length of the fire pit to be twice the width. you also need to add a 1-foot border around the entire fire pit.

suppose the total area of the patio is represented by the polynomial 2x2 + 6x + 4, where x is the width of the fire pit.

questions:

your assignment: patio project
you have a small patio and want to improve it with a project. circle the project you picked:

fish pond planter box fire pit
making sense of the problem
make sense of the problem (3 points: 1 point for each answer)
what do you know?

what do you want to find out?

what kind of answer do you expect?

writing an equation
1. set your polynomial equal to the total area of your patio to create the equation. (1 point)

getting the right side of the equation equal to 0
2. use inverse operations to make the right side of the equation equal to 0. (2 points)

factoring the gcf out of the polynomial
3. factor the gcf out of the trinomial on the left side of the equation. (2 points: 1 for the gcf, 1 for the trinomial)

factoring the polynomial completely
4. factor the polynomial completely. (4 points: 2 points for each factor)

5. if a product is equal to zero, we know at least one of the factors must be zero. and the constant factor cannot be zero. so set each binomial factor equal to 0 and solve for x, the width of your project. (2 points: 1 point for each factor)

6. check your work. substitute the two values of x into the equation from question 2 to confirm that it equals zero. (2 points: 1 point for each value of x)

7. what are the dimensions of your project? remember that the width of your project is represented by x. (2 points: 1 point for each dimension)
width =

length =

8. draw a new picture of your patio that shows the dimensions of your project and the border. (2 points) check to confirm that the total area equals the area of your patio.

answer
Answers: 1

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Prompt:
his interactive animation shows an image of a brick patio and a garden and grass area...

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