## MAT 116 Week 4 Appendix D

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 , however , many homeowners are becoming amateur landscape artists

Suppose you are a homeowner getting ready to sell your home . You realize that there are some landscaping problems that you want to address so that your home will sell quickly and you can get the best price . Since deciding to landscape your backyard , you have realized there are many things to consider , such as budget , time , and space

Application Practice

Answer the following questions . If appropriate , use Equation Editor to show your work . First , save this to your hard drive by selecting Save As from the menu . Click the white space below each question to maintain proper formatting

You are planning to spend no less than 6 ,000 and no more than 10 ,000 on your landscaping project

Write an inequality that demonstrates how much money you are willing to spend on the project

Let us assume that the money spent on the project is equal to x

Since , money spent will be no less than 6 ,000 and no more than 10 ,000 therefore Combining both inequalities Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project . 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 Cost of one tree 84

Let us assume that the number of tree is equal to t , therefore Since , one cannot not buy a portion of a tree and there is not enough money to buy nine trees , therefore Would 5 trees be a solution to the inequality in part b ? Justify your answer . Because five is less than eight and the cost of five trees is also less than the cost of eight trees , so it will under budget of 700 for trees

The coordinate graph of the backyard shows the location of trees plants , the 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 Plant F

The coordinate of Tree A is (-20 , 20

The coordinate of Plant B is (-20 ,-4

The coordinate of Plant C is (-10 ,-14

The coordinate of Patio D is (12 , 12

The coordinate of Plant E is (8 ,-8

The coordinate of Plant F is (18 ,-12

b) The water line is given by the equation

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

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

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