MAT 116 Algebra 1A

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

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 be willing to spend on the project.

b) 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 cost \$60 and each tree is \$84, what is the maximum number of trees you can buy with a budget for rock and trees 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 5 trees be a solution to the inequality in part b? Justify your answer.

2. 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?

b) The water line is given by the equation
.
Suppose you want to put a pink flamingo lawn ornament in your backyard, but 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) Suppose 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?

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1. What is your question? If the copy and paste method did not work, you need to type out all the information and the question.

Please repost with the complete inquiry.

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2. Initial Budget:
\$80,000 loan from family
\$38,250 small business loan from bank
All loans to be repaid in 10 years

1. You have recently found a location for your bakery and have begun implementing the first phases of your business plan. Your budget consists of an \$80,000 loan from your family and a \$38,250 small business loan. These loans must be repaid in full within 10 years.
a) What integer would represent your total budget?

b) Twenty-five percent of your budget will be used to rent business space and pay for utilities. Write an algebraic expression that indicates how much money will be spent on business space and utilities. Do not solve.

c) How much money will rent and utilities cost? Explain how you arrived at this answer.

d) Suppose an investor has increased your budget by \$22,250. The investor does not need to be repaid. Rather, he becomes part owner of your business. Will the investor contribute enough money to meet the cost of rent and utilities? Support your answer, and write an equation or inequality that illustrates your answer.

e) This equation illustrates your remaining funds after paying for rent and utilities. How much money is left? Explain how you arrived at your answer.

\$38,250 + \$80,000+ \$22,250-0.25(\$80,000 + \$38,250) =

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3. 1) you are planning to spend no less than \$6,000 and no more than \$10,000 on your landscaping project.
Q1: write an inequality that demonstrates how much money you will be willing to spend on the project.
A1: 6,000 greater than > and equal = to 10,000

Q2: 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 cost \$60 and each tree is \$84, what is the maximum number of trees you can buy with a budget for rock and trees 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.

A2: 30(60) + 84x = 2500
1800 + 84x = 2500
subtract both sides by 1800 to get:
-1800 + 84x = 2500-1800
84x = 700
divide both sides by 84 to get:
x = 8.33

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4. Complete the table for this equation.

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

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5. estimates the price of gasoline in January of each year (Bureau of Labor Statistics, 2006).
a) Do you expect the lines to be intersecting, parallel, or perpendicular? Explain your reasoning.

b) Use the equations of the lines to determine if they are parallel. What did you find?

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6. grkbsoq zejvxopl xdtiwa kadphnf gtimfyquz koargjnbp ovkwc

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7. at a local community college,it costs \$500 to enroll in a morning section of algebra course. suppose that thevariable n stands for the number of students who enroll. then 500n stands for the total amount of money collected for this course. how much is collected if 46 students enroll? 82 students? 240 Students?

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8. If 46 students enrolled, the amount collected will be 500(46) = \$23000
if 82 enrolled,
500(82) = \$41000 and if 240 enrolled
500(240) = \$120,000

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9. A driver who drives at a speed of r mph for t hr will travel a distance d mi given by d = rt mi. How far will a driver travel at a speed of 61 mph for 5 hr? What is the distance traveled?

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10. Mat/116 Algebra 1 A

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11. b) 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 cost \$60 and each tree is \$84, what is the maximum number of trees you can buy with a budget for rock and trees of \$2,500? Write an inequality that illustrates the problem and solve (c)c) Would 5 trees be a solution to the inequality in part b? Justify your answer

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12. Math 116, Week 4 Checkpoint, Graphing Equations

Graph the equation and identify the y-intercept.
y = ½ x

Graph the equation and identify the y-intercept.
y = 5x – 5

Graph the equation and identify the y-intercept.
y + x = -5

Graph the equation and identify the y-intercept.
x + 2y = 8

The value, v, of a shopkeeper's inventory software program is given by v = -1/2t + 4, where t is the number of years since the shopkeeper bought the program. What is the program worth 9 years after it is first purchased?
Plot the point with the given t-value, 4.

Find the y-intercept and x-intercept for the equation.
4x + 3y = 48
(Type an ordered pair.)

Use the intercepts to graph the equation.
x + 2y = 4

Find the intercepts and then use them to graph the equation.
5y – 15 = 5x

Find the intercepts and then use them to graph the equation.
y = -5 – 5x

Graph the equation.
y = 6

Graph the equation by plotting points.
21 – 3y = 0

Graph the line containing the given pair of points and find the slope. (7,0) and (2, -2)

Find the slope, if it exists, of the line containing the points (-2, ½) and (-6, ½).
m =
(Simplify your answer. Type as integer or fraction. Type N if the slope is undefined.)

A roof raises 1.2 feet vertically and 12.9 feet horizontally. What is the grade of the roof?
The grade of the roof is %.

Find the slope, if it exists.
y = -5x + 8
m =
(Simplify your answer. Type as integer or fraction. Type N if slope is undefined.)

Find the slope, if it exists.
3x – y = 7
m =
(Simplify your answer. Type as integer or fraction. Type N if slope is undefined.)

Find the slope, if it exists.
y = -2.17x
m =
(Simplify your answer. Type an integer or a decimal. Type N if the slope is undefined.)

Find the slope, if it exists.
2x – 4y + 17 = 0
m =
(Simplify your answer. Type an integer or a fraction. Type N if the slope is undefined.)

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13. V = 1/5 ð t^2 s

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