A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
13th Edition
ISBN: 9780135183885
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott, Barbara Boschmans
Publisher: PEARSON
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Chapter 12.4, Problem 9MC
To determine
a.
The value of x from the following figure.
To determine
b.
To show:
The smaller rectangle is also a golden rectangle.
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Pidgeonhole Principle
1. The floor of x, written [x], also called the integral part, integer part, or greatest integer, is defined
as the greatest integer less than or equal to x. Similarly the ceiling of x, written [x], is the smallest
integer greater than or equal to x. Try figuring out the answers to the following:
(a) [2.1]
(b) [2]
(c) [2.9]
(d) [2.1]
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it.
3. The general pidgeonhole principle states that, if you have N places and k items, then at least one
hole must have [] items or more in it. Try this out with
(a) n = 10 chairs and k = 15 students
(b) n = 10 chairs and k = 23 students
(c) n = 10 chairs and k = 20 students
4. There are 34 problems on these pages, and we…
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linearly independent
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The everything combined problem
Suppose that a computer science laboratory has 15 workstations and 10 servers. A cable can be used to
directly connect a workstation to a server. For each server, only one direct connection to that server can be
active at any time.
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2. How many stations can be used at one time?
3. How many stations can not be used at any one time?
4. How many ways are there to pick 10 stations out of 15?
5. (This one is tricky) We want to guarantee that at any time any set of 10 or fewer workstations can
simultaneously access different servers via direct connections. What is the minimum number of direct
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Chapter 12 Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Ch. 12.1 - Can you construct a triangle using the lengths...Ch. 12.1 - A triangle has two sides of length 10cm and 14cm....Ch. 12.1 - For the Figure below, answer the following Point C...Ch. 12.1 - In a circle with centre A and radius AB, let P be...Ch. 12.1 - In the following kite, congruent segments are...Ch. 12.1 - If the kite in exercise 5 were concave, do the...Ch. 12.1 - a. Are all rectangles whose diagonals are 19in....Ch. 12.1 - Explain why the quadrilateral ABCD is a kite.Ch. 12.1 - To draw the perpendicular to a line l through a...Ch. 12.1 - In the following drawing a compass is used to draw...
Ch. 12.1 - Prob. 11MCCh. 12.1 - a. find examples of congruent objects. c. Find...Ch. 12.1 - Prob. 13MCCh. 12.1 - Prob. 14MCCh. 12.1 - Prob. 15MCCh. 12.1 - Squares are constructed on the sides of ABC as...Ch. 12.1 - Prove that the triangles shown below on 55 dot...Ch. 12.1 - Prob. 18MCCh. 12.1 - A student claims that all squares are congruent...Ch. 12.1 - Joel claims that the following triangles are...Ch. 12.1 - On a test, a student wrote the answer as ABCD...Ch. 12.1 - Zara claims that in spite of the fact that every...Ch. 12.1 - Prob. 1NAEPCh. 12.1 - Which two figures are congruent? a. E and H b. F...Ch. 12.1 - Prob. 3NAEPCh. 12.1A - If CATDOG, which of the following, if any, is...Ch. 12.1A - In TRI and ABC, TRAB, RIBC, and ITCA. Which angle...Ch. 12.1A - a. Name two congruent triangles in the following...Ch. 12.1A - A truss used in house construction to strengthen...Ch. 12.1A - Prob. 5ACh. 12.1A - Prob. 6ACh. 12.1A - If line l is the perpendicular bisector of AC,...Ch. 12.1A - Prob. 8ACh. 12.1A - Prob. 9ACh. 12.1A - Prob. 10ACh. 12.1A - Prob. 11ACh. 12.1A - Prob. 12ACh. 12.1A - Prob. 14ACh. 12.1A - Prob. 15ACh. 12.1A - Prob. 16ACh. 12.1A - Prob. 18ACh. 12.1A - Prob. 20ACh. 12.1B - Prob. 1ACh. 12.1B - Prob. 2ACh. 12.1B - Prob. 3ACh. 12.1B - Prob. 4ACh. 12.1B - Prove that if the convex quadrilateral ABCD has...Ch. 12.1B - Find the measure of C in the following figure.Ch. 12.1B - Given that polygon ABCD polygon EFGH, complete the...Ch. 12.1B - Prob. 8ACh. 12.1B - For each of the following, determine whether the...Ch. 12.1B - Prob. 10ACh. 12.1B - Prob. 11ACh. 12.1B - Prob. 13ACh. 12.1B - Prob. 14ACh. 12.1B - Let ABCD be a square with diagonals AC and BD...Ch. 12.1B - Prob. 19ACh. 12.2 - MATHEMATICAL CONNECTIONS a. If you know 4 parts...Ch. 12.2 - Prob. 2MCCh. 12.2 - Prob. 3MCCh. 12.2 - Prob. 4MCCh. 12.2 - Prob. 5MCCh. 12.2 - Prob. 6MCCh. 12.2 - MATHEMATICAL CONNECTIONS Use the fact that the...Ch. 12.2 - MATHEMATICAL CONNECTIONS The marked angles and a...Ch. 12.2 - Prob. 10MCCh. 12.2 - MATHEMATICAL CONNECTIONS On a square geoboard or...Ch. 12.2 - MATHEMATICAL CONNECTIONS M and N are midpoints of...Ch. 12.2 - Prob. 13MCCh. 12.2 - Prob. 14MCCh. 12.2 - MATHEMATICAL CONNECTIONS A student asks why...Ch. 12.2 - Prob. 16MCCh. 12.2 - Prob. 17MCCh. 12.2 - Prob. 18MCCh. 12.2 - In the following regular pentagon, use the...Ch. 12.2 - If possible, construct a triangle that has the...Ch. 12.2 - MATHEMATICAL CONNECTIONS Construct an equilateral...Ch. 12.2 - MATHEMATICAL CONNECTIONS For each of the following...Ch. 12.2 - Mathematical Connections Explain how to construct...Ch. 12.2 - National Assessment of Educational Progress Sara...Ch. 12.2A - Draw each of the following figures using a...Ch. 12.2A - ASSESSMENT For each of the conditions in exercise...Ch. 12.2A - ASSESSMENT For each of the following, determine...Ch. 12.2A - Prob. 4ACh. 12.2A - List congruent triangles, if any, for each of the...Ch. 12.2A - Prob. 6ACh. 12.2A - If ABCDEF and ABC is given with the information...Ch. 12.2A - Prob. 8ACh. 12.2A - Given ADEC and BDBC, Prove ABDEBC.Ch. 12.2A - Prob. 10ACh. 12.2A - Prob. 11ACh. 12.2A - Prob. 12ACh. 12.2A - ASSESSMENT Classify each of the following...Ch. 12.2A - Prob. 15ACh. 12.2A - Prob. 16ACh. 12.2A - The game of Triominoes has equilateral-triangular...Ch. 12.2A - ASSESSMENT In the rectangle ABCD shown, X and Y...Ch. 12.2A - Prob. 20ACh. 12.2A - Prob. 21ACh. 12.2A - ASSESSMENT What minimum information is sufficient...Ch. 12.2A - Prob. 24ACh. 12.2B - Assessment Draw each of the following figures...Ch. 12.2B - Prob. 3ACh. 12.2B - Prob. 4ACh. 12.2B - Prob. 6ACh. 12.2B - ASSESSMENT Given circle O in the figure below,...Ch. 12.2B - Prob. 8ACh. 12.2B - Prob. 9ACh. 12.2B - Prob. 10ACh. 12.2B - Prob. 11ACh. 12.2B - Prob. 12ACh. 12.2B - ASSESSMENT a. Draw a pentagon with all sides...Ch. 12.2B - Prob. 15ACh. 12.2B - Prob. 16ACh. 12.2B - Prob. 17ACh. 12.2B - Prob. 18ACh. 12.2B - ASSESSMENT What minimum information sufficient to...Ch. 12.2B - Prob. 21ACh. 12.2B - Prob. 22ACh. 12.3 - Mathematical Connections Draw a line l and a point...Ch. 12.3 - Prob. 2MCCh. 12.3 - Mathematical Connections Construct a circle O and...Ch. 12.3 - Mathematical Connections Place three dots, A,B and...Ch. 12.3 - Mathematical Connections Lines l and m intersect...Ch. 12.3 - Mathematical Connections Given an angle and a roll...Ch. 12.3 - Mathematical Connections If two pieces of tape of...Ch. 12.3 - MATHEMATICAL CONNECTIONS Write a sample letter...Ch. 12.3 - MATHEMATICAL CONNECTIONS A student asked if a line...Ch. 12.3 - MATHEMATICAL CONNECTIONS A student wants to know...Ch. 12.3 - Mathematical Connections In the following figure,...Ch. 12.3 - Mathematical Connections Draw ABC. Then construct...Ch. 12.3 - Mathematical Connections Given two right...Ch. 12.3 - Mathematical Connections Find the value of x.Ch. 12.3 - MATHEMATICAL CONNECTIONS Consider ABC and DEF. It...Ch. 12.3 - Mathematical Connections The quadrilaterals shown...Ch. 12.3 - Mathematical Connections In figure, congruent...Ch. 12.3 - Mathematical Connections In the figure, OP is the...Ch. 12.3A - Prob. 2ACh. 12.3A - Prob. 3ACh. 12.3A - Prob. 4ACh. 12.3A - Prob. 5ACh. 12.3A - Prob. 6ACh. 12.3A - Prob. 7ACh. 12.3A - Prob. 8ACh. 12.3A - Prob. 9ACh. 12.3A - Prob. 10ACh. 12.3A - Prob. 11ACh. 12.3A - Prob. 12ACh. 12.3A - Prob. 13ACh. 12.3A - Prob. 14ACh. 12.3A - Use compass and straightedge to construct angles...Ch. 12.3A - Construct AB close to the bottom of a blank page....Ch. 12.3A - Prob. 18ACh. 12.3A - Construct a circle. Then construct an equilateral...Ch. 12.3B - Assessment Copy line segment AB shown below and...Ch. 12.3B - Assessment Construct an obtuse triangle and the...Ch. 12.3B - Prob. 5ACh. 12.3B - Prob. 6ACh. 12.3B - Prob. 7ACh. 12.3B - Prob. 8ACh. 12.3B - Prob. 10ACh. 12.3B - Assessment In the isosceles right triangle shown,...Ch. 12.3B - Prob. 12ACh. 12.3B - ASSESSMENT Explain why any rectangle can be...Ch. 12.3B - Prob. 14ACh. 12.3B - Prob. 15ACh. 12.3B - Prob. 16ACh. 12.4 - Do you think any two cubes are similar?Ch. 12.4 - Write a description of what it takes for two...Ch. 12.4 - If two isosceles triangle have non-base angles of...Ch. 12.4 - If two right triangles have hypotenuses that are...Ch. 12.4 - Prob. 5MCCh. 12.4 - Prob. 6MCCh. 12.4 - Prob. 7MCCh. 12.4 - Prob. 8MCCh. 12.4 - Prob. 9MCCh. 12.4 - How are the SSS and SAS similarity thoerems like...Ch. 12.4 - Prob. 11MCCh. 12.4 - Prob. 12MCCh. 12.4 - Prob. 13MCCh. 12.4 - Prob. 14MCCh. 12.4 - Prob. 15MCCh. 12.4 - Prob. 16MCCh. 12.4 - Arthuro writes that ABCTRI. Betty writes that...Ch. 12.4 - Prob. 18MCCh. 12.4 - Prob. 19MCCh. 12.4 - Prob. 20MCCh. 12.4 - Prob. 21MCCh. 12.4 - A student asks whether there is an ASA similarity...Ch. 12.4 - Prob. 1NAEPCh. 12.4 - Prob. 2NAEPCh. 12.4A - Prob. 1ACh. 12.4A - Prob. 2ACh. 12.4A - Prob. 3ACh. 12.4A - Prob. 4ACh. 12.4A - Prob. 5ACh. 12.4A - Prob. 7ACh. 12.4A - Prob. 8ACh. 12.4A - Prob. 9ACh. 12.4A - Prob. 10ACh. 12.4A - Prob. 11ACh. 12.4A - A photocopy of a polygon was reduced by 80 and...Ch. 12.4A - Sketch two hexagons with corresponding sides...Ch. 12.4A - Prob. 15ACh. 12.4A - Prob. 16ACh. 12.4A - In the following figure, find the distance AB...Ch. 12.4A - Prob. 18ACh. 12.4A - Prob. 19ACh. 12.4A - a. Examine several examples of similar polygons...Ch. 12.4A - The midpoints M,N,P,Q of the sides of a...Ch. 12.4A - Prob. 22ACh. 12.4A - Prob. 23ACh. 12.4B - School pictures come in 8in.by10in., 5in.by7in....Ch. 12.4B - Prob. 2ACh. 12.4B - Prob. 4ACh. 12.4B - Prob. 5ACh. 12.4B - Prob. 9ACh. 12.4B - Prob. 12ACh. 12.4B - Prob. 13ACh. 12.4B - Prob. 14ACh. 12.4B - To find the height of a tree, a group of Girl...Ch. 12.4B - Prob. 17ACh. 12.4B - Prob. 18ACh. 12.4B - Prob. 19ACh. 12.4B - Prob. 20ACh. 12.4B - a. In the figure, ABCD is a trapezoid, M is the...Ch. 12.4B - ABCD is a convex quadrilateral and M,N,P,Q are the...Ch. 12.4B - Prob. 23ACh. 12.4B - Prob. 24ACh. 12.CR - Each of the following figures contains at least...Ch. 12.CR - Prob. 2CRCh. 12.CR - Prob. 3CRCh. 12.CR - Prob. 4CRCh. 12.CR - Prob. 5CRCh. 12.CR - Prob. 6CRCh. 12.CR - Prob. 7CRCh. 12.CR - Prob. 8CRCh. 12.CR - Prob. 9CRCh. 12.CR - Prob. 10CRCh. 12.CR - A swimming pool is shown with a rectangular patio...Ch. 12.CR - Prob. 12CRCh. 12.CR - Prob. 13CRCh. 12.CR - Prob. 14CRCh. 12.CR - Prob. 15CRCh. 12.CR - Determine the vertical height of playground slide...Ch. 12.CR - Prob. 17CRCh. 12.CR - Prob. 18CRCh. 12.CR - Prob. 19CRCh. 12.CR - Prob. 20CRCh. 12.CR - Prob. 21CRCh. 12.CR - Prob. 22CRCh. 12.CR - Prob. 23CRCh. 12.CR - In real estate, lots that have more ocean frontage...Ch. 12 - Prob. 1NTCh. 12 - Prob. 2NTCh. 12 - Prob. 3NTCh. 12 - Prob. 4NTCh. 12 - Prob. 5NTCh. 12 - Are all right triangles in which the hypotenuse is...
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