Landscape Design

Landscape designers often use coordinate geometry and algebra as they help their clients. In many regions, landscape design is a growing field. With the increasing popularity of do-it-yourself television shows, many homeowners are becoming amateur landscape artists.

Imagine you are a homeowner getting ready to sell your home. You realize there are some landscaping problems you want to address so your home will sell quickly and you can get the best price. After making this decision, you realize there are many things to consider when landscaping the backyard, such as budget, time, and space.

Application Practice

Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.

1. You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project.
a. Write an inequality that demonstrates how much money you will are willing to spend on the project.

b. For the first phase of the project, imagine you want to cover the backyard with decorative rock and plant some trees. You need 30 tons of rock to cover the area. If each ton costs $60 and each tree is $84, what is the maximum number of trees you can buy with a budget of $2,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.

c. Would five trees be a solution to the inequality in Part b? Justify your answer.

2. The coordinate graph of the backyard shows the location of the trees, plants, patio, and utility lines. If necessary, you may copy and paste the image to another document and enlarge it.
a. What are the coordinates of Tree A, Plant B, Plant C, Patio D, Plant E, and Plant F?

b. The water line is given by the equation

Imagine you want to put a pink flamingo lawn ornament in your backyard. You want to avoid placing it directly over the water line in case you need to excavate the line for repairs in the future. Could you place it at the point (-4,-10)?

c. What is the slope and y-intercept of the line in Part b? How do you know?

d. Imagine you want to add a sprinkler system and the location of one section of the sprinkler line can be described by the equation



Complete the table for this equation.

x y (x,y)
-1
-2
-4
2
8

e. What objects might be in the way as you lay the pipe for the sprinkler?

How would you like us to help you with this assignment?

well, it also has a graph with a landscape layout but it will not past into this is there another way i can submit it for help? I am looking for someone to help with a few assignments

I'm sorry, but there's no way to paste graphs in this forum. You should probably pay someone in your immediate locale to help you.

1a. The inequality that demonstrates how much money you are willing to spend on the project is:

$6,000 ≤ cost ≤ $10,000

b. Let's assume the maximum number of trees you can buy is represented by the variable 't.'

The cost of 30 tons of rock is given by:

Cost of rock = 30 * $60 = $1800

The cost of 't' trees is given by:

Cost of trees = t * $84

So the total cost of the project should be less than or equal to the budget of $2500:

Cost of rock + Cost of trees ≤ $2500

Substituting the values, we get:

$1800 + t * $84 ≤ $2500

To find the maximum number of trees, we need to solve for 't':

t * $84 ≤ $700

Dividing both sides by $84:

t ≤ $700 / $84

t ≤ 8.33

Since we cannot buy a fraction of a tree, the maximum number of trees you can buy with a budget of $2500 is 8.

c. To check if five trees would be a solution to the inequality in part b, we substitute 't' with 5 in the inequality:

$1800 + 5 * $84 ≤ $2500

$1800 + $420 ≤ $2500

$2220 ≤ $2500

Since $2220 is less than or equal to $2500, five trees would be a solution to the inequality in part b.

2a. Without the coordinates graph, it is not possible to determine the coordinates of Tree A, Plant B, Plant C, Patio D, Plant E, and Plant F.

b. To determine if the point (-4,-10) is above or below the water line represented by the equation, we substitute the x-coordinate (-4) into the equation and check if it satisfies the equation. If the equation is true when x = -4, then the point is above the water line.

Given the equation of the water line:

Substituting x = -4:

-10 = 2(-4) + 2

-10 = -8 + 2

-10 = -6

The equation is false, which means the point (-4,-10) is not above the water line.

c. The slope and y-intercept of the line in part b can be determined by comparing the equation to the standard form of a linear equation, y = mx + b.

The given equation is:

Comparing the equation to the standard form, we can see that the slope (m) is 2, and the y-intercept (b) is 2.

d. To complete the table for the equation , substitute the given x-values into the equation and calculate the corresponding y-values.

x y (x,y)
-1 4
-2 2
-4 -2
2 10
8 26

e. Based on the equation , the objects that might be in the way as you lay the pipe for the sprinkler would be any plants or structures indicated by the coordinates (x, y), where y is equal to or greater than the given equation.