Question 470280: 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?
Answer by karaoz(32)   (Show Source):
You can put this solution on YOUR website!
Wow! How about pasting the whole exam paper into one question? I believe your chances of getting an answer to your question will greatly improve if you decide to post questions one by one. Anyway, here are the answers for your first question. Answers to your second question will be very difficult to figure out without the graph of the backyard.
1.a.
The main trick here is to define a variable, say m, to stand for "the money I am willing to spend on the project". The rest is simple:
$6,000 <= m <= $10,000.
The only thing to ponder for a second are the symbols <=. Should they both be <= or should one of them be <, or should they both be <. Always check these details since the formulation of these types of sentences in English can be sometimes quite tricky. An easy way to figure this out is asking yourself questions like: "Is $6,000 acceptable according to the sentence given?" If yes, then symbol <= is fine there. If not but anything else greater than $6,000 is, then you need to use < symbol instead of <=. The same way with the other edge. "Is $10,000 acceptable?" If yes, <= symbol should be fine. Here, both symbols should indeed be <=.
1.b.
This is about money. Budget is $2500. So whatever you need to buy the total must be less than or equal to $2500. In other words, "bunch of staff <= $2500". So, what is this "bunch of stuff" for us? Apparently, rocks and trees. In particular we need 30 tons of rock while each ton is $60. This will cost us 30*$60 = $1800. Then we want some trees, with each tree being priced at $84. We do not know how many trees to buy but we know that:
$1800 + $84*T <= $2500
Simplifying this inequality, we can get:
$84*T <= $700,
from where we have:
T <= 8.3333...
Hence the maximum number of trees you can buy is 8 (Assuming you cannot buy 1/3 of a tree for a third of a price).
1.c.
Yes, 5 trees would be a solution to the above inequality since substituting T = 5 into the inequality T < 8.333... does not invalidate the inequality.
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