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# mat116_appendix_d

CSU - Dominguez hills

GPA 3.0

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Date Created: 11/16/15

Axia College Material 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 doityourself 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 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 6000 and no more than 10000 on your landscaping project a Write an inequality that demonstrates how much money you will be willing to spend on the project Let X be the amount that you are willing to spend We know that x has to be no more than 10000 so we know that x S 10000 We also know that x has to be no less than 6000 so we know thatx 2 6000 Putting these together we have 6000 S x S 10000 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 2500 Write an inequality that illustrates the problem and solve Express your answer as an inequality and explain how you arrived at your answer Let y be the number of trees We know that each ton costs 60 and we need 30 tons of rocks so the amount spent on rocks is 30x 60 1800 Then that leaves 2500 1800 700 to spend on trees If each tree is 84 then we know that the amount spent on trees is 84x 32 We only have 700 to spend so we must have 84X y 700 Dividing through by 84 on each side we have y S 833 So the most number of trees we can buy is 8 since y has to be a whole number less than 833 Therefore the solution as an inequality is y S 8 MAT 116 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 6 1 Would 5 trees be a solution to the inequality in part b Justify your answer M MhUTIDIIIII Yes 5 would be alright since 84x5 2 420 which is less than the 700 left to spend after buying the rocks m 00 GI Cable line 5 39 Hillllllv39Vlll NI al l l l l l l39quotl l l l 24 22 2D 18 1B444218 B 4 2 a l The coordinate graph of the backyard shows M lal olt39mlhl Waterline I V I What are the coordinates of Tree A Plant B Plant C Patio D Plant E Plant F To find the coordinates of the points just count along the X axis and then up along the y axis So for point A we move left along the x axis to 20 until we39re right below it Then we move up until we hit the point So the point A is at x 20 and y 20 or in coordinates as 2020 The point B is at x 20 and y 4 or 20 4 The point C is at 10 14 The point D is at 1212 The point E is at amp 8 The point F is at 18 12 The water line is given by the equation 2 y x 12 3 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 410 We want to know if the point 4 10 is on the line What we do is set x 4 and see 2 what value of y is when 2 x 12 2x12 933 3 3 3 3 The answer is Yes it would not lie directly on the line but it would be close to the water line What is the slope and y intercept of the line in part b How do you know MAT 116 When we have a line in the form y mxb then the slope is m and the y intercept is b 2 Here m andb 12 We know that because when x increases by 1 the value of y 3 2 decreases by E We know that the y intercept is at 12 since when x O the line passes through y 12 Suppose you want to add a sprinkler system and the location of one section of the sprinkler line can be described by the equation y x 4 Complete the table for this equation What objects might be in the way as you lay the pipe for the sprinkler The point 8 8 is on the sprinkler line and it39s also the location of one of the plants at point E Also if the line extends very far to the left then it goes through the point 26 which looks like it39s on the trees MAT 116

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