Unit 5 Linear Equations Geometry in Construction

Transcription

1 Unit 5 Linear Equations Geometry in Construction Name 1. Each sentence tells a person s location relative to a house. Choose the graph that shows the person s distance from the house as time goes by. a) Stephanie walked towards the house. b) Joe walked away from the house. c) Erika walked a circle around the house. 2. Logan travels on his bike 500 ft in 10.8 seconds. What is his miles per hour? 3. Graph 2 x 1 on the number line given. Page 1

2 4. Each sentence tells the location a person is from the job site. Match the graph to the sentence. a) We walked at a steady pace toward the job site. b) My sister ran away from the job site but came back when my parents called. c) My father stood for a very long time in front of the job site. d) Afterward, we raced down the hill away from the job site. 5. Shay needs to design a storage building. The county codes say the length must be twice its width. She has 132 feet of wall (perimeter). What should the dimensions of the storage building? Page 2

3 6. Sarah s hourly pay is directly proportional to the number of hours she works. Sarah earns $184 for working 8 hours. How much will Sarah earn if she works 17 hours? 7. Everyone at one time has heard crickets chirp. For some crickets, the relationship between the number of chirps per minute and the air temperature is linear. When the air temperature is 20 C, these crickets chirp 124 times per minute. When the temperature is 27 C, they chirp 170 times per minute. a) Graph this information with x representing the temperature.. b) What is the slope of the line passing through the two points given? c) Write an equation of the line in the y = mx + b form. d) Predict the temperature using your equation if you hear 140 chirps. e) This equation has limited use. Explain the problem with this equation. f) What is the real world meaning of the slope? Page 3

4 8. The graph below shows the price of the stock of Alpine Lumber Company. a) Explain what the y intercept of the graph represents. b) Explain what the x intercept of the graph represents. 9. Alex s Car Rental rents cars for $25 per day plus a charge of $0.10 per mile. Create a graph that models the cost of a one-day rental from Alex s Car Rental. Write a linear equation. Page 4

5 10. Ryan s hourly pay is directly proportional to the number of hours he works. Ryan earns $114 for working 6 hours. How much will Ryan earn if he works 23 hours? 11. The graph below shows the population of Poduck, Colorado from 1986 to Draw a line of best fit to represent the line. 12. Three points lie on the same line. If the coordinates of two points are (0,-2) and (1,0), which of the following coordinates could represent the third point. Use the grid to help you find your answer if needed. (2,1) (-1,-3) (-2,-6) (0,-1) Circle one Page 5

6 13. Ashley earns money doing jobsite cleanup. She has two different methods of charging her customers, depending on the job. Graph if needed Method 1: A flat fee of $7.00 per hour Method 2: An initial fee of $21.00 plus $3.50 per hour a) Write an equation to represent each. b) For how many hours must Ashley clean so that the money she earns from the two methods is the same. 14. Dillon made a blanket for his grandmother. The blanket is 4 ft. by 3 ft. Now Dillon wants to make a blanket for his mother that will double the dimensions. How will the area of the blanket for Dillon s mother compare to the area of the blanket Dillon made for his grandmother. 15. Suppose you can have granola or wheat flakes for cereal with a choice of strawberries, bananas, peaches, or blackberries. How many ways can you have cereal for breakfast? 16. Suppose you can make an outfit from six sweaters, four pairs of jeans, and two pairs of shoes. How many outfits can you make? Page 6

7 17. Find the number of possible ways of answering a quiz with a true-false question followed by a multiple choice question with 4 choices. 18. Find the slope of the line passing through the points. The answers are not the same. a) (5, 90) (5, 93) b) (8, -10) (6, -10) 19. Find the number of possible license plates you can have if the first 3 spots are letters and the next 3 spots are digits. 20. Suppose you roll a regular six sided die (single of dice) three times. How many outcomes can you have? (Order matters in this game) 21. As a home decorator, Cassandra has 4 pictures to hang on the living room wall on 4 wall anchors. How many ways can she hang the pictures? 22. You have a choice of 10 paint colors for walls, 6 floor coverings, and 3 cabinet/trim packages. How many combinations do you have to choose from? 23. Stephanie went to the hardware store. She took $ with her. She spent $ What percent of the $ was NOT spent by Stephanie? Page 7

8 24. When in Canada, Whitney drove 93 miles which is the same as 150 kilometers. She also knows that 0 miles is 0 kilometers. a) Write an equation to represent this linear relationship. b) How many kilometers is 70 miles? 25. The circumference of a manhole cover is 8 feet. What is the area of the manhole cover? 26. Find the area of the regular hexagonal gazebo if each side is 6 feet? Hint: Use special triangle information to find the apothem. 27. Solve each equation for y (get y alone). a) 7x - 3y = 22 b) 5x + 4y = -12 c) 2x y = Find the slope of the line passing through a) (7, -9) (10, -12) b) (5, -15) (5, -17) Page 8

9 29. The roof line of a house starts 12 feet above the ground and has a slope of 1 4. If you are standing inside the house 6 feet from the wall, how high is the roof at that point? 30. Write an equation in the slope-intercept form (y = mx + b) for a line that passes through each pair of points. a) (8,1), (-2,3) b) (5,7),(1,9) 31. Find the slope and y-intercept of the graph of each equation. a) y = -3x + 7 b) 2x + y = -4 c) x = 3y A complete cycle of a traffic light takes 70 seconds. During each cycle, the light is red for 25 seconds, yellow for 10 seconds, and green for 35 seconds. What is the probability the light will NOT be yellow if a car randomly arrives at the traffic light? Page 9

10 33. Shown are two camping cottages. The floor area in both is 64 sq ft. The height of the wall in each is 8 feet with the total building height at 12 feet. a) Find the surface area of each. b) Find the volume of each. c) Which one is more efficient for heating? Why? 34. Dylan wants to build an awning over his porch. He wants the slope of the awning to be 5. The porch is 8 feet deep, and the roof line is 14 feet above the porch. He 12 draws this sketch to help his plan. a) How long will the awning be from the roof line to the porch support posts? b) How tall will the posts be that hold up the front of the awning? Page 10

11 35. The dimensions are doubled to get the larger deck shown below. a) Find the area of the small deck. b) Find the area of the large deck using proportions. 36. Very hot or very cold temperatures can affect the length of a steel tape measure. A surveyor can find out how the length of the tape measure changes by using a formula. For a tape calibrated at 68 F, the formula is: Change in the length of the tape = L(T 68) where L is the original length of the tape and T is the temperature at which the surveyor uses the tape. Suppose a 100 tape is used at a temperature of 16 F. Use the formula to find the length of the tape. 37. For each of the solids, find a) Area of the base. b) The volume if the 3D Height of each is 6. Page 11

12 38. Are these two rectangular concrete pads similar? Explain. 39. The graphs show the distance of a person from a fixed point for 4 second interval. Answer both questions for each graph. i. Is the person moving toward or away from the point? ii. Is the person speeding up, slowing down, or moving at a constant speed? 40. The figure below shows a cross-sectional drawing of the Great Pyramid and a crosssectional drawing of a casing block. a) Explain why the right triangle shown in the casing block is similar to the right triangle shown in the Great Pyramid. b) Determine the value of x in the casing block. Page 12

13 41. How many combinations of tools can you have if you can choose between 2 hammers, 5 tape measures, and 2 chalk lines? Assume you need one of each. 42. Suppose you can make a work uniform from three shirts, two pairs of pants, and two pairs of boots. How many ways can the uniforms be formed? 43. Using the graph below, how many buses do you need for a) 45 students b) 125 students c) 180 students 44. Find the volume of wood contained in 1 linear foot of a) 2 X 6 b) 2 X 12 (this is defined as 1 board foot) Page 13

14 45. Explain what the slope 90 pounds per square inch means. How many pounds per square foot would this be? 46. A liquid is poured into a large tank at the jobsite at the constant rate of 10 ml per second. A gauge on the tank recorded the height of the liquid in the tank as a function of time and plotted the data on the graph below. Describe the shape of the tank for each time listed. a) Time between 3 seconds and 6 seconds b) Time between 6 seconds and 12 seconds c) Time between 12 seconds and 18 seconds 47. Which slope is the steepest? -.70, 7, or 75% What is the probability of a dart landing in the middle circle if there is no skill involved? The diameter of the inner circle is 2 inches. Page 14

15 49. Study the graph to answer the questions. a) Which company is the best deal? b) What is the real world meaning of the y intercept of Bee Rental? 50. Write an equation of the line passing through the data points. a) (4, 12) (-6, 20) b) 3 steel posts weigh 3.75 lbs and 8 steel posts weigh 10 lbs 51. Graph 2x 3y What is half of 10 2? Be careful the answer is not 2 5. Page 15

16 53. Ryan is delivering building supplies and has got the prices of 3 truck rental companies. Assume Ryan only needs the truck for one day. The prices are listed below. A-1 Rental: $56 per day plus $1.75 per mile Super Rental: $26 per day plus $2.25 per mile Loveland Rental: $30 per day plus $2.05 per mile a) Write a linear equation for the rates for one day given by each company. b) Graph the 3 equations. Hint: the x axis should be scaled so each unit is 5 c) If his delivery is 48 miles, which company is cheapest? d) When would A-1 Rental be the cheapest? 54. If you roll 2 dice, what is the probability that you will get at least one six? 55. Write the pricing (linear) equation for spindles given a 36 inch costs $1.29 while a 42 inch costs $1.49. Page 16

17 56. Find the mean for the following data. Each of 3 students were able to install 100 shingles each in 30 minutes while each of 5 students were able to install 75 shingles each in 30 minutes. 57. Joe is filling a tank. He starts when it is 5 feet deep. It rises 1.5 inches per minute. a) Explain how the equation y= 1.5x + 60 represents the filling of the tank. b) If the tank is 10 feet deep, when will it be full? 58. Renae is working as a laborer at the local construction site. She has realized that not all of the money she earns, will be paid to her. Taxes, dues, and insurance premiums are deducted from her check. She has observed that when she works for 21 hours, her paycheck is $183 while if she works for 30 hours, her paycheck is $263. Write a linear equation to represent the situation. 59. Which of the graphs below best matches each of the following stories? a) Rusty had just left home when he realized he had forgotten his tools, so he went back to pick them up. b) Things went fine until Rusty had a flat tire. c) Rusty started out calmly, but sped up when Rusty realized he was going to be late for work. Page 17

18 60. When Jessie turns on the oven, it gradually heats up from room temperature to whatever temperature she set. Suppose that you set the oven control to 450. Which graph best matches this situation? 61. Find the missing angle. 62. Cassandra earns 10% of the sales of the building materials that she sells plus a $500 salary per week. Write an equation. 63. The table shows a linear relationship between actual temperature and approximate wind chill temperature when the wind speed is 20 miles per hour. a) Write an equation to represent this situation. b) If the temperature is 0 when you go to work, what is the wind chill temperature? Page 18

19 64. Describe in terms of speed how you would walk to produce a similar graph. a) b) 65. Write the equation of a line that passes through (1, -9) and (-3, 3) 66. In the graph, which line shows the best approximation of the line of best fit? Page 19

20 67. A speedometer knows how fast the car is going by measuring the number of times that each wheel turns. a) The tires on a car have a diameter of 18 inches. How far does the car go for 1 complete turn of a wheel? Hint: circumference b) Find the number of times that each wheel turns when the car travels 1 mile (5280 feet). c) If the tire travels 1 mile in 1 hour (1 mph), find the number of revolutions per minute (rpm) of the wheel. d) Complete the table below. e) Graph the data from the table with x representing mph. f) Write an equation to represent the graph. Page 20

21 68. Use the graph to answer the questions. a) What is the cost to rent the plumbing equipment for 6 hours? b) What does the y intercept mean (real life) in this graph? c) What is the independent variable? d) What is the slope of the line and what does the slope of the line mean (real life) in this problem? 69. The chart shows how the cost of the end of the year Geometry in Construction banquet, c, depends on the number of people attending the party, n. Which equation represents this relationship? Circle one. c = 20n c = 30n c = 40n c = 50n Page 21

22 70. Calculate the pressure (pounds per square foot) for each. a) A box weighs 100 pounds. The area of the bottom of the box is 20 square feet. b) A box weighs 250 pounds. The dimensions of the bottom of the box are 4 feet by 3 feet. c) A cylinder of concrete weighs 500 pounds. The base of the cylinder has a diameter of 1 foot. 71. A water tank is 7 feet in diameter and 12 feet high when filled to capacity. The tank, when empty, weighs 500 pounds. If a cubic foot of water contains 7.48 gallons and 1 gallon of water weighs 8.34 lbs. a) Find the number of gallons the tank holds. b) Find the weight of the tank and water. 72. The foundation that the tank (#71 above) sits on is made up of two parallel concrete beams set on the ground. The beams are each 2 feet wide and 8 feet long. Calculate the weight that each of the beams holds and then calculate what the pounds per square foot the foundation holds. Page 22

23 73. Match and describe the graph that best fits the situation. Situation A: During the first few years, the number of deer on the island increased by a steady percentage. As food became less plentiful, the growth rate started slowing down. Now, the number of births and deaths is about the same. Situation B: In the Northern Hemisphere the amount of daylight increases slowly from January through February, faster until mid-may, and then slowly until the maximum in June. Then it decreases slowly through July, faster from August until mid-november, and then slowly until the year s end. Situation C: Your cup of tea is very hot. The difference between the tea temperature and the room temperature decreases quickly at first as the tea starts to cool to room temperature. But when the two temperatures are close together, the cooling rate slows down. It actually takes a long time for the tea to finally reach room temperature. 74. The following diagrams show two casing blocks from the Great Pyramid. Find x. a) b) Page 23

24 75. Find the probability of each outcome if the spinner is spun. Reduce a) white b) M c) vowel d) gray e) Gray B f) consonant g) not gray h) not white i) A or B 76. Find the odds of each outcome if the spinner above is spun. a) B b) vowel c) gray d) not white e) U or B f) white or gray g) I or gray h) white i) black A 77. Write a linear equation for the data. Prices for 5/4 X 6 decking boards. Page 24

25 78. Two line segments are drawn by Mr. Moore on the overhead. One is 4 inches long and the other is 10 inches long. The line segments show up as 12 inches and 30 inches long on the screen. a) Complete the table given the same situation as mentioned above. Graph the data if needed for part b. b) Write an equation in the y = mx + b form. 79. Maria must work exactly 8 hours on Saturday to paint a shed and to install a faucet. List out 10 possible combinations of ways to split the work time between the shed and the faucet. 80. For the problem above, write an equation using p for painting and f for faucet. Graph paint time faucet time Page 25

26 81. Betsy has at most 8 hours on Saturday to paint a shed and to install a faucet. List out 10 possible combinations of ways to split the work time between the shed and the faucet. 82. For the above problem, write an inequality using p for painting and f for faucet. Graph that inequality. Paint time Faucet time 83. Trent and Jonathan have at least 8 hours of roofing work to do. List out 10 combinations of ways to split the work time between Trent and Jonathan. 84. Write an inequality to represent the above situation with t for Trent s work time and j for Jonathan s work time. Graph. Jonathan s time Trent s time Page 26

27 85. Marissa has at most $3000 to spend on carpet and tile. List 5 combinations of ways to split the money between the carpet and the tile. 86. Write an inequality for the problem above using c for carpet and t for tile. Graph carpet $ tile $ 87. Mr. Moore and Mr. Burke have at most 180 minutes a day to split between Geometry and Construction. List 5 combinations of ways time can be split between Geometry and Construction. 88. Write an inequality that represents the problem above. Use g for geometry time and c for construction time. Graph Geometry Construction Page 27

28 89. Find the midpoint of the segments that have endpoints as follows: a) (5,4) (-6,3) b) (-1,4) (3,-6) c) (-3,6) (7,0) 90. Find the slope of the segments above. a) b) c) 91. Find the distance between the endpoints of each segment in #89 a) b) c) 92. Find the missing endpoint if one endpoint is (5,-8) and the midpoint is (4,-2). 93. Complete the table for the outcomes for finding the sum of rolling a red die and a green die 94. Find the probability of each outcome if a pair of dice are rolled. Reference the table above. Reduce. a) an odd number on the red die b) a sum of 6 c) a sum of 2 d) an even sum e) a sum less than 8 f) a sum greater than 12 g) both dice are the same number h) the most occurring sum Page 28

29 95. Find the odds of each outcome if a bag contains 4 blue marbles, 2 green marbles, and 5 red marbles. Reduce a) choosing a blue marble b) choosing a green marble c) choosing a green or red marble d) choosing a red or blue marble e) not choosing a green marble f) not choosing a red or blue marble 96. The volume of the scale model of a home is 1200 cu inches. The scale is 1:40. What is the volume of the actual home? 97. One die is rolled. Find the probability of the compound event. Reduce a) P (a 5 or a 3) b) P ( an even or 3) c) P ( a 1 or a 2) d) P ( a multiple of 2) e) P ( a 1 or a number > 3) f) P ( an odd or an even #) 98. Two dice are rolled. Find the probability of each compound event. Reference the table in #93. Reduce a) P ( an odd number and an even number) b) P ( two odd numbers) c) P ( a 6 and a number <4) d) P (an even and a 5) e) P ( a number <3 and a number >3) f) P (a 1 and a 1) 99. How many toll free numbers can be made with an 800 area code? 100. How many phone numbers can Hensel Phelps have if their number must start with ? Page 29

30 101. A die is rolled and a coin is tossed. Find the probability of the compound event. Reduce a) P (even number and heads) b) P (4 and tails) c) P (a number divisible by 2 and tails) d) P (a multiple of 3 and tails) e) P (a number >1 and heads) f) P ( a number >6 and tails) 102. A card is drawn from a standard 52 card deck. Find the probability be careful! Face card is king, queen, jack. Reduce a) P(queen or four) b) P(ace or heart) c) P(red card or jack) d) P(black card or king) e) P(spade or heart) f) P(even number card or red card) g) P(face card or ace) h) P(black card or club) i) P(heart or red card) j) P(red and queen) k) P(ace and club) l) P(black king) 103. After watching a nail driving competition, 28% of the students could hit the nail head without missing. a) What is the probability that a student will hit the nail head? b) What is the probability that a student will miss the nail head? 104. A fascia board was cut as shown. What should the angle of the other cut be if you want the ends parallel? Page 30

31 105. The equation of a line is y = 3x + 5. a) What is the slope of a line parallel to it? b) What is the slope of a line perpendicular to it? 106. Write the equation of a line parallel to the line above but passing through (4,5) Write the equation of a line perpendicular to y = -2x 5 and passing through (1,-3) Find the missing angles formed by the section of the massive road system shown below a= b= c= d= e= f= g= h= j= k= m= n= Page 31

32 109. Find the mean, median, and mode of the following construction skilled staff salaries rounded to the nearest $100 (source : US Dept. of Labor) Carpenter $38700 Brickmason $46500 Concrete finisher $35800 Plumber $47200 Electrician $41800 Painter $33300 Drywall installer $34000 Equipment operator $42200 Steel worker $ What is the linear equation of the pricing formula for 4 X 4 posts? An 8 foot 4 X 4 cost $9 while a 10 foot 4 X 4 cost $ Graph a) y 5x 1 b) y 5x 1 Page 32

33 112. Find the missing angles of the road system shown below. a= e= j= b= f= k= c= g= m= d= h= 113. What is the angle of the ramp shown below. Page 33

34 114. A ramp is built as shown in the graph below. a) Find the length of the ramp. b) Find the slope of the ramp. c) Find the equation of the line containing the ramp. d) Find the midpoint of the ramp e) Find the slope of a support perpendicular to the ramp f) Find the equation of a line that is perpendicular to the ramp passing thru (5,5). g) Find the equation of a line that contains the handrails (parallel) passing thru (5,5) 115. Write an equation for the price of gravel. Gravel cost $15 per ton with a $120 delivery charge Write a linear equation for a line passing through (4, -8) and ( 6, -12) A customer has decided to triple all the dimensions of a warehouse (width, length, height). If the smaller warehouse cost $20,000 to build, what would be a good estimate for the new warehouse? Page 34

35 118. Tony the roofer is building the last (end) truss for a house. The house is 16 wide and has a 4/12 pitch. Find the length of the supports if each support is 24 apart A plumber routing pipe through a home as shown below. What angle must the plumber use to keep the pipe parallel? 120. Find the missing measurements of the windows below if the area of each is 144 sq inches. Assume sides that look congruent are and side that look perpendicular are Find the volume of these buildings. Page 35

36 122. Find the measure of each interior angle of a regular hexagon room Find the length of the support given the triangular structures are similar Find the probability that a dart thrown at these dart boards will land in the shaded region. Assume the dart will hit the dart board. a) b) c) d) Page 36

37 125. A bridge is being engineered. A sketch is shown below on a coordinate graph. Concern yourself only with the part of the bridge on the coordinate graph. a) Find the length of the bridge. b) Find the slope of the bridge. c) Find the equation of the line containing the bridge. d) Find the midpoint of the bridge. e) Find the slope of a support perpendicular to the bridge. f) Find the equation of a support that is perpendicular to the bridge through the midpoint. g) Find the equation of a line that contains the guardrails (parallel) passing one unit above the bridge floor Simplify. Do not use decimals. a) 2 60 b) c) What is the linear equation for the pricing formula for Logan s Paint? One gallon costs $11, (1,11) and five gallons cost $35 (5, 35). Page 37

38 128. Find the length of the support in the cathedral room (trapezoid) of the ski lodge shown The rectangular foundation is shown. What should be true about the diagonals give a specific length A customer has decided to triple the length and width of a warehouse (but not the height). If the smaller warehouse cost $20,000 to build, what would be a good estimate for the new warehouse? 131. Find the mean, median, and mode of the following construction professional staff salaries rounded to the nearest $100 (source : US Dept. of Labor) Architect $70300 Construction Manager $78300 Civil Engineer $46000 Electrical Engineer $79700 Drafter $45300 Surveyor $53400 Surveying Tech $30800 Mechanical Engineer $71100 Page 38

39 132. Angles a and b are congruent. The child is 4 feet tall. To the nearest tenth of a foot, what is the height of the building? 133. The spinner has been spun and has landed on a number that is odd. What is the probability that it has landed on 5? 134. What is the longest distance in a rectangular room that is 24 by 30 by 8? 135. Triangles ABC and EDC are similar right triangles. To the nearest tenth, what is AB, the distance across the river? Page 39

40 136. The radius and height of the smallest cylinder are each 2 in. Each cylinder has double the radius and double the height of the one to its left. What is the volume of the largest cylinder? 137. Find the area of the circular room sections (shaded part). a) b) 138. If two people were born in December, what is the probability that they were born on the same day? Hint: And or Or? 139. Your estimate for the cost of a job is $28,000. Your competition bid 10% less. What did the competition bid? Katrina wrecked 275,000 homes on the Gulf Coast. What is that number in scientific notation? Page 40

41 141. Graph y 2x Graph 2 y x You travel 60 mph for 1 hour and 50 mph for 2 hours. What is the mean speed? 144. Ace Rental charges $75 per hour for a backhoe. If you rent it for part of an hour, they round up to the whole hour. Example: 45 minutes would be a charge of 1 hour, while 70 minutes would be a charge of 2 hours. Graph the step function for 3 hours. 145.Write the equation of a line passing through (6,4) and (-8, 11) Page 41

42 146. Solve a) 3x 6 15x b) 3x 6 15x 147. How many feet of wall do I need to enclose a square room with 144 sq ft. and a circle room with 144 sq feet.? 148. Given the average weight of the blocks shown below. Is the median, mean, or mode the best representative average? 5.2 lb 5.2 lb 4.8 lb 2.3 lb 2.1 lb 149. This weekend Amber plans to call her friend in Denver. She can call either Friday evening or Saturday afternoon. The cost is $0.10 per minute Friday, or $0.07 per minute Saturday. If Amber plans to keep the cost below $2.50, about how many minutes (round to the nearest minute) longer can she talk on Saturday? Explain a) What is the equation of a line passing through (3,400) with slope of zero. b) Hollie charges $400 to install carpet for any number of rooms in a house. Write an equation to represent what Hollie charges Find the value of x. Page 42