HEART OF MATHEMATICS
4th Edition
ISBN: 9781119760061
Author: Burger
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Question
Chapter 4.4, Problem 26MS
To determine
To find: The number of tiles needed for the room.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
You work at a restaurant that has 20 tables. Each table has a set of salt and pepper shakers on it that are in the shape of square pyramids . How much salt do you need to fill all the salt shakers ?
Maluwa has 9 identical tiles. When she counts the total number of sites on the tiles, she gets 72. Draw a picture of what her tile could look like, and name the shape
This map of six square blocks shows the location of Mae’s house (M), her grandfather’s house (G) and the library (L). How many different routes can Mae take to walk from her house to the library to get a book and then to her grandfather’s house for lunch, assuming she does not walk more than a total of 7 blocks?
Chapter 4 Solutions
HEART OF MATHEMATICS
Ch. 4.1 - The main event. State the Pythagorean Theorem.Ch. 4.1 - Two out of three. If a right triangle has legs of...Ch. 4.1 - Hypotenuse hype. If a right triangle has legs of...Ch. 4.1 - Assesing area. Suppose you know the base of a...Ch. 4.1 - Squares all around. How does the figure below...Ch. 4.1 - Operating on the triangle. Using a straightedge,...Ch. 4.1 - Excite your friends about right triangles....Ch. 4.1 - Easy as 1,2,3? Can there be a right triangle with...Ch. 4.1 - Sky high (S). On a sunny, warm day, a student...Ch. 4.1 - Sand masting (H). The sailboat named Sand Bug has...
Ch. 4.1 - Getting a pole on a bus. For his 13th birthday,...Ch. 4.1 - The Scarecrow (ExH). In the 1939 movie The Wizard...Ch. 4.1 - Rooting through a spiral. Start with a right...Ch. 4.1 - Is it right? (H) Suppose someone tells you that...Ch. 4.1 - Tfrain trouble (H). Train tracks are made of...Ch. 4.1 - Does everyone have what it takes to be a triangle?...Ch. 4.1 - Getting squared away. In our proof of the...Ch. 4.1 - The practical side of Pythagoras. Suppose you are...Ch. 4.1 - Pythagorean pizzas (H). You have a choice at the...Ch. 4.1 - Natural right (S). Suppose r and s are any two...Ch. 4.1 - Well-rounded shapes. Suppose we have two circles...Ch. 4.1 - A Pythagorean Theorem for triangles other than...Ch. 4.1 - With a group of folks. In a small group, discuss...Ch. 4.1 - Double trouble. Suppose you know a right triangle...Ch. 4.1 - K-ple trouble. Suppose you have a right triangle...Ch. 4.1 - Padding around. You have a rectangular patio with...Ch. 4.1 - Pythagoras goes the distance. Plot the points (5,...Ch. 4.1 - Ahoy there! (H) Your exotic sailboat, which you...Ch. 4.2 - Standing guard. Draw the floor plan of a gallery...Ch. 4.2 - Art appreciation. State the Art Gallery Theorem.Ch. 4.2 - Upping the ante. How many guards do you need for a...Ch. 4.2 - Keep it safe. At what vertices would you place...Ch. 4.2 - Puttoing guards in their place. For each floor...Ch. 4.2 - Guarding the Guggenheim. The Art Gallery Theorem...Ch. 4.2 - TriangulatIng the Louvre (H). Triangulate the...Ch. 4.2 - Triangulating the Clark. Triangulate the floor...Ch. 4.2 - Tricolor me (ExH). For each triangulation, color...Ch. 4.2 - Tricolor hue. For each triangulation, color the...Ch. 4.2 - One-third. Write the number 6 as a sum of three...Ch. 4.2 - Easy watch. Draw a floor plan of a museum with six...Ch. 4.2 - Two watches (S). Draw the floor plan of a museum...Ch. 4.2 - Mirror, mirror on the wall. Consider the floor...Ch. 4.2 - Nine needs three (H). Draw a floor plan for a...Ch. 4.2 - One-third again (ExH). If a natural number is...Ch. 4.2 - Square museum (S). If a museum has only...Ch. 4.2 - Worst squares (H). Draw examples of museums with...Ch. 4.2 - Pie are squared. The circumference of a circle of...Ch. 4.2 - I can see the light. Suppose you are in a...Ch. 4.2 - Less than. Youve tnangulated your polygon and...Ch. 4.2 - Greater than. Youve triangulated your polygon and...Ch. 4.2 - Counting the colors. Your polygon has 40 vertices....Ch. 4.2 - Only red. Twelve of your polygons vertices have...Ch. 4.2 - Totaling triangles. If a polygon has n sides, it...Ch. 4.3 - Defining gold. Explain what makes a rectangle a...Ch. 4.3 - Approximating gold. Which of these numbers is...Ch. 4.3 - Approximating again. Which of the following...Ch. 4.3 - Same solution. Why does the equation l1=1l have...Ch. 4.3 - X marks the unkonw (ExH). Solve eachh equation for...Ch. 4.3 - A cold tall one? Can a Golden Rectangle have a...Ch. 4.3 - Fold the gold (H). Suppose you have a Golden...Ch. 4.3 - Sheets of gold. Suppose you have two sheets of...Ch. 4.3 - Circular logic? (H). Take a Golden Rectangle and...Ch. 4.3 - Growing gold (H). Take a Golden Rectangle and...Ch. 4.3 - Counterfeit gold? Draw a rectangle with its longer...Ch. 4.3 - In the grid (S). Consider the 1010 grid at left....Ch. 4.3 - A nest of gold. Consider the figure of infinitely...Ch. 4.3 - Comparing areas (ExH). Let G be a Golden Rectangle...Ch. 4.3 - Do we get gold? Lets make a rectangle somewhat...Ch. 4.3 - Do we get gold this time? (S) We now describe...Ch. 4.3 - A silver lining? (H) Consider the diagonal in the...Ch. 4.3 - Prob. 20MSCh. 4.3 - Going platinum. Determine the dimensions of a...Ch. 4.3 - Golden triangles. Draw a right triangle with one...Ch. 4.3 - Prob. 23MSCh. 4.3 - Prob. 24MSCh. 4.3 - Prob. 25MSCh. 4.3 - Power beyond the mathematics. Provide several...Ch. 4.3 - Special K. As a student at the University of...Ch. 4.3 - Special x. Find all values of x satisfying the...Ch. 4.3 - In search of x. Solve each equation for x:...Ch. 4.3 - Adding a square. Your school Healthy Eating garden...Ch. 4.3 - Golden Pythagoras (H). If you have a Golden...Ch. 4.4 - To tile or not to tile. Which of the following...Ch. 4.4 - Shifting Into symmetry. Shown below are small...Ch. 4.4 - Prob. 3MSCh. 4.4 - Prob. 4MSCh. 4.4 - Symmetric scaling (ExH). Each of the two patterns...Ch. 4.4 - Build a super. Draw a 1,2,5 right triangle in the...Ch. 4.4 - Another angle. Look at the 5-unit super-tile you...Ch. 4.4 - Super-super. Surround your 5-unit super-tile with...Ch. 4.4 - Expand forever (H). If you continue the process of...Ch. 4.4 - Prob. 10MSCh. 4.4 - Expand again. Take your 4.unit equilateral...Ch. 4.4 - One-answer supers. Here is a Pinwheel Pattern. For...Ch. 4.4 - Prob. 14MSCh. 4.4 - Many answer supers (H). Shown here are pictures of...Ch. 4.4 - Fill er up? (ExH) For each tile below, could...Ch. 4.4 - Prob. 18MSCh. 4.4 - Prob. 19MSCh. 4.4 - Prob. 20MSCh. 4.4 - Penrose tiles. Roger Penrose constructed two tiles...Ch. 4.4 - Expand forever. Why does any shape that can be...Ch. 4.4 - Super total. Recall that the Pinwheel Triangle has...Ch. 4.4 - Prob. 26MSCh. 4.4 - XY-tiles. The trapezoidal tile on the left has one...Ch. 4.4 - School spirit. Your dorm bathroom is tiled using...Ch. 4.4 - T-total (H). Suppose you start with one small...Ch. 4.5 - Its nice to be regular. What makes a polygon a...Ch. 4.5 - Keeping it Platonic. What makes a solid a regular...Ch. 4.5 - Countem up. How many faces, edges, and vertices...Ch. 4.5 - Defending duality. Explain why the cube and the...Ch. 4.5 - The eye of the beholder. Suppose you have models...Ch. 4.5 - Drawing solids. Draw each solid by completing the...Ch. 4.5 - Count. For each of the regular solids, take the...Ch. 4.5 - Soccer counts (ExH). Look at a soccer ball. Take...Ch. 4.5 - A solid slice (S). For each regular solid, imagine...Ch. 4.5 - Siding on the cube. Suppose we start with the...Ch. 4.5 - Cube slices (H). Consider slicing the cube with a...Ch. 4.5 - Dual quads (S). Suppose you have a cube with edges...Ch. 4.5 - Super dual. Suppose you take a cube with edges of...Ch. 4.5 - Self-duals. Suppose you have a tetrahedron having...Ch. 4.5 - Not quite regular (ExH). Suppose you allow...Ch. 4.5 - Truncated solids. Slice off all the vertices of...Ch. 4.5 - Stellated solids. Take each regular solid and...Ch. 4.5 - Prob. 24MSCh. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.5 - Here we celeb rate the power of algebra as a...Ch. 4.6 - Walkind the walk. Here are three walks from corner...Ch. 4.6 - Missing angle in action. The triangles below are...Ch. 4.6 - Slippery X. A triangle is drawn on a sphere. Can...Ch. 4.6 - A triangular trio. The sphere below has three...Ch. 4.6 - Saddle sores. The triangle at right is drawn on a...Ch. 4.6 - Travel agent. In each of the following three...Ch. 4.6 - Travel agent. In each of the following three...Ch. 4.6 - Travel agent. In each of the following three...Ch. 4.6 - Latitude losers (H). In each of the following...Ch. 4.6 - Latitude losers (H). In each of the following...Ch. 4.6 - Latitude losers (H). In each of the following...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Spider and bug. For each pair of points on the...Ch. 4.6 - Big angles (H). What is the largest value we can...Ch. 4.6 - Many angles (S). Draw three different great...Ch. 4.6 - Quads in a plane. Measure the sum of the angles of...Ch. 4.6 - Quads on the sphere. Below are quadrilaterals on...Ch. 4.6 - Parallel lines (ExH). On a plane, if you draw a...Ch. 4.6 - Cubical spheres (ExH). Take a cube. Put a point in...Ch. 4.6 - Tetrahedral spheres. Lets do a similar calculation...Ch. 4.6 - Dodecahedral spheres. This Mindscape is the same...Ch. 4.6 - Total excess. Using the observations from the...Ch. 4.6 - What is the sum of the three angles? Why? Consider...Ch. 4.6 - What is the sum of the angles of your triangle? Is...Ch. 4.6 - Removing a slice of the pie. Complete the...Ch. 4.6 - Conjuring up a conjecture. Make a conjecture about...Ch. 4.6 - Tetrahedral angles. What is the sum of the angles...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.6 - Here we celebrate the power of algebra as a...Ch. 4.7 - At one with the univers. Below is a sketch of a...Ch. 4.7 - Are we there yet? Why does the information x=4 not...Ch. 4.7 - Plain places. Plot the following points in the...Ch. 4.7 - Big stack. If you take a huge number of sheets of...Ch. 4.7 - A bigger stack. If you take a huge number of...Ch. 4.7 - On the level in two dimensions. Pictured in the...Ch. 4.7 - On the level in two dimensions (S). Pictured in...Ch. 4.7 - On the level in four dimensions. Pictured in the...Ch. 4.7 - Tearible 2s. In the pictures below, describe how...Ch. 4.7 - Dare not to tear? For the figures in the Tearible...Ch. 4.7 - Unlinking (H). Using the fourth dimension,...Ch. 4.7 - Unknotting. Describe how you would unknot the...Ch. 4.7 - Prob. 13MSCh. 4.7 - Edgy hypercubes (H). Produce drawings of the...Ch. 4.7 - Prob. 15MSCh. 4.7 - Prob. 16MSCh. 4.7 - Doughnuts in dimensions. Suppose we have a...Ch. 4.7 - Assembly required (S). As promised in the...Ch. 4.7 - Slicing the cube. Take a 3-dimensional cube...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...Ch. 4.7 - Here we celebrate the power of algebra as a...
Knowledge Booster
Similar questions
- On the map, Seattle. Portland, and Boise form a triangle whose sides are shown in the figure below. If the actual distance from Seattle to Boise is 400 miles, find the distance from Seattle to Portland.arrow_forwardOn a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides the shown in the figure below. The actual distance from Los Angeles to Las Vegas is 270 miles. Find the distance from San Francisco to Las Vegas.arrow_forwardFind the largest area possible if the association has 1200 feet of fencing available.arrow_forward
- One side of a rectangle is 2 cm longer than a second side. If the area is 35cm2, find the dimensions of the rectangle.arrow_forwardThe paper company is millon boxes of notebook paper to a supply store. The dimensions of each pack of notebook paper by 10.5 inches by 8 inches by 3 inches Paula putting 12 sacks or paper in each Box. If she has the choice of 3 boxes below, Which one should she choose? Show how you found the answer A.Box 1: 13 inches by 35 inches x 32 inches B.Box 2: 30 inches x 34 inches x 65 inches C.Box 3: 25 inches x 35 inches x 50 inchesarrow_forwardYou have a large brown wall in your yard. You are going to use part of that wall to enclose a rectangle and separate it into three pens as shown below. You have $6720 to spend on fencing to enclose this rectangular area. You also want to make THREE pens as shown below. You are also using the wall as one horizontal side of the area so you do NOT need to provide fencing on that side. The cost of the outside fencing (in purple) is Ş4.00 per foot and the two vertical fences inside the pen (in green) costs $7.00 per foot. You desire to enclose the largest possible area you can. What is the largest total area you can enclose? Do NOT use calculus to solve this problem. Use your graphing calculator or a Desmos graph to help answer it at the end of your work. largest area = O feetO square feetO dollars per footO dollars per square foot Did you indicate the units also? IN TERMS OF THE WORK THAT YOU NEED TO SHOW: All variables must be defined. (in words or pictures) All work must be neat and easy…arrow_forward
- The figures A and B are similar. Figure A has an area of 48 square feet and one of the side lengths is 6 feet. Figure B has an area of 75 square feet. Find the missing corresponding side lengtharrow_forwardKlara is building a fence in her backyard. The sides of the fence will form a right triangle with her home. The legs (base and height) of the triangle will be the fence material and the remaining side (hypotenuse) will be formed by her home. In other words, she only needs fencing for the legs of the triangular region. The diagram below provides a sketch to help you visualize the fence. The proportions of the side lengths are not necessarily representative of the actual side lengths. Fence Given that she only has 150 feet of material for the fence, what is largest area she can enclose? Enter your answer to the nearest whole number. Fence Housearrow_forwardThe areas of two squares differ by 7 sq ft and their perimeters differ by 4 ft. Determine the sum of their areas.A. 25 sq ft B. 27 sq ft C. 28 sq ft D. 22 sq ftarrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Elementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice University
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,