Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
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Textbook Question
Chapter 10.4, Problem 6P
a. Fold and cut paper to make an isosceles triangle that has one side that is 5 inches long and two sides that are 10 inches long. Describe your method, and explain why it must create an isosceles triangle.
b. Fold and cut paper to make an isosceles triangle that has one side that is 10 inches long and two sides that are 7 inches long. Describe your method.
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Given: AABE ~ ACDE.
Prove: AC bisects BD.
Note: quadrilateral properties are not permitted in this proof.
Step
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Reason
AABE ACDE
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Vertical angles are congruent
try
Type of Statement
A
E
B
D
C
10-2
Let A =
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and b =
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Denote the columns of A by a₁, a2, a3, and let W = Span {a1, a2, a̸3}.
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a. Is b in {a1, a2, a3}? How many vectors are in {a₁, a₂, a3}?
b. Is b in W? How many vectors are in W?
c. Show that a2 is in W. [Hint: Row operations are unnecessary.]
a. Is b in {a₁, a2, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your
choice.
○ A. No, b is not in {a₁, a2, 3} since it cannot be generated by a linear combination of a₁, a2, and a3.
B. No, b is not in (a1, a2, a3}
since b is not equal to a₁, a2, or a3.
C. Yes, b is in (a1, a2, a3} since b = a
(Type a whole number.)
D. Yes, b is in (a1, a2, 3} since, although b is not equal to a₁, a2, or a3, it can be expressed as a linear
combination of them. In particular, b =
+
+
☐ az.
(Simplify your answers.)
(1) (14 points) Let a = (-2, 10, -4) and b = (3, 1, 1).
(a) (4 points) Using the dot product determine the angle between a and b.
(b) (2 points) Determine the cross product vector axb.
(c) (4 points) Calculate the area of the parallelogram spanned by a and b. Justify
your answer.
1
Chapter 10 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Ch. 10.1 - Tiffany says that the angle at A in Figure 10.29...Ch. 10.1 - Given that the indicated lines in Figure 10.30(a)...Ch. 10.1 - Given that the indicated lines in Figure 10.30 (b)...Ch. 10.1 -
Ch. 10.1 - Ed the robot is standing at point A and will walk...Ch. 10.1 - Draw a map that shows the following route leading...Ch. 10.1 - In your own words, give a clear, logical...Ch. 10.1 - Figure 10.33 shows a rectangle subdivided into...Ch. 10.1 - Given that the lines In Flgure 10.34 marked with...Ch. 10.1 - Determine the sum a+b+c+d+e+f of the angles in the...
Ch. 10.1 - Given that the lines marked with arrows in Flgure...Ch. 10.1 - Determine the sum of the angles at the star...Ch. 10.2 - Figure 10.46 9 depicts sun rays traveling toward 3...Ch. 10.2 - Figure. 10.48 shows a cross-section of Joey's toy...Ch. 10.2 - Figure. 10.49 shows a sketch of a room that has a...Ch. 10.2 - Many people mistakenly believe that the seasons...Ch. 10.2 - Refer to Figure 10.50 , 10.51 , 10.52 , and 10.53...Ch. 10.2 - 'Department store dressing rooms often have large...Ch. 10.2 - 'A concave mirror is a mirror that curves In, like...Ch. 10.2 - A convex mirror Is a minor that curves out, so...Ch. 10.2 - A convex mirror is a mirror that curves out, so...Ch. 10.3 - Smallville Is 7 miles south of Gotham. will is 8...Ch. 10.3 - A new mall is to be built to serve the towns of...Ch. 10.3 - A radio beacon indicates thata certain dolphin is...Ch. 10.3 - A new Giant Superstore is being planned somewhere...Ch. 10.3 - Part 1 of Class Actlvlty 10O on circle designs...Ch. 10.4 - Students sometimes get confused about the...Ch. 10.4 - Draw a Venn diagram or other clear diagram showing...Ch. 10.4 - Draw a Venn diagram or other clear diagram that...Ch. 10.4 - a. Describe how four children could use 4 pieces...Ch. 10.4 - Figure 10.85 shows a method for constructing...Ch. 10.4 - a. Fold and cut paper to make an isosceles...Ch. 10.4 - Draw a line segment AB that is 4 inches long. Now...Ch. 10.4 - a. Use a ruler and compass to help you draw a...Ch. 10.4 - Is there a triangle that has one side of length 4...Ch. 10.4 - Create two different rhombuses, both of which have...Ch. 10.4 - Prob. 11PCh. 10.4 - In a paragraph, discuss how the detinition of...Ch. 10.4 - Give instructions telling Robot Rob how to move...Ch. 10.4 - Give instructions telling Automaton Annie how to...Ch. 10.4 - a. Flgure 10.87 shows 3 pairs of parallel line...Ch. 10.4 - a. Given a parallelogram with angles a, b, c. and...Ch. 10.4 - What is wrong with the diagram for the problem In...Ch. 10.4 - Given a right triangle that has angles a, b, and...Ch. 10.4 - Use the idea of walking and turning around a shape...Ch. 10.4 - a. Determine the angles in a regular pentagon....
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