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Axia College Material
MAT116 Application 2Instructor: Rachelle Williams
Landscape Design
Landscape designers often use coordinate geometry and algebra as
they help their clients. In manyregions, landscape design is a
growing field. With the increasing popularity of do-it-yourself
televisionshows, however, many homeowners are becoming amateur
landscape artists.
Suppose you are a homeowner getting ready to sell your home. You
realize that there are somelandscaping problems that you want to
address so that your home will sell quickly and you can get thebest
price. Since deciding to landscape your backyard, you have realized
there are many things toconsider, such as budget, time, and
space.
Application Practice
Answer the following questions. Use Equation Editor to write all
mathematical expressions and equations(and to show all work).
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 $5,500 and no more
than $10,500 on your landscapingproject.
a) Write an inequality that demonstrates how much money you will
be willing to spend on theproject. Use x as the variable in your
inequality.
b) Suppose you want to cover the backyard with decorative rock
and plant some trees as the firstphase of the project. You need 34
tons of rock to cover the area. If each ton cost $55 and eachtree
is $91, what is the maximum number of trees you can buy with a
budget for rock and trees of$3,100? Write an inequality that
illustrates the problem and solve that inequality. Show all
work.Express your answer as an inequality.
This means that the most trees you can buy is13 trees.
c) Would 9 trees be a solution to the inequality inpart b?
Explain your answer.
Yes, it would satisfy the equation because themost you can buy
is 13, and the least you can buyis 0, so 9 is between these to, so
it works.
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Mathematical Work: - Yes
2. The coordinate graph of the backyard shows the location of
trees, plants, the patio, and utility lines. (Ifnecessary, 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 coordinates of Tree A are: (-20, 20)The coordinates of Plant
B are: (-20, 4)The coordinates of Plant C are: (-8, -14)The
coordinates of Patio D are: (12, 12)The coordinates of Plant E are:
(8, -8)The coordinates of Plant F are: (18, -12)
b) The cable line is given by the equation
45
2 xy .
Suppose you want to put a pink flamingo lawn ornament in your
backyard, but you want to avoidplacing it directly over the cable
line, in case you need to excavate the line for repairs in the
future. Could you place it at the point (-4, 2)? Explain your
answer.
Yes, you could place it on (-4, 2). Just by looking at the
picture it looks as if it would notwork but if you actually plug in
-4 for x in the equation, you find out the y is actually 2.4, not
2. So,(-4, 2) is not a point on the line, thus the ornament can be
placed on (-4, 2).
() ()
c) What is the slope and y-intercept of the line in part b?
Explain how you found the slope and the y-intercept.
The slope is 2/5, and I figure it out by looking at the
coefficient of x, which is 2/5, so that is theslope.
The y intercept is 4, and I knew that by finding the b ( y = mx
+ b, y = (2/5)x + 4)
d) Suppose you want to add a sprinkler system and the location
of one section of the sprinkler linecan be described by the
equation
143
1 xy .
Complete the table for this equation. Show all work.
x y (x,y)
-9 17 (-9, 17)
-6 16 (-6, 16)
-3 15 (-3, 15)
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12 10 (12,10)
24 6 (24, 6)
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e) What objects might be in the way as you lay the pipe for the
sprinkler? Explain your answer(s).
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The tree A will get in the way of the pipe of the sprinkler.
First of all, that points lies on this line, so it willcome in the
path. No other points lies on that line.A = (-18,20)
( )
[ ( ) ]
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