Q23 Tell whether each statement is t... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 2: Q23 (page 35)

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$a^{2} > 9$ if $a > 3$ .

Short Answer

Expert verified

The statement " $a^{2} > 9$ if $a > 3$ ", " is true.

The converse of the given statement 鈥淚f $a^{2} > 9$ then $a > 3$ .鈥� is false.

Step by step solution

Step 1. Converse a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement 鈥淚f p, then q鈥� will be 鈥淚f q, then p鈥�.

Step 2. State whether the statement is true or not.

The statement " $a^{2} > 9$ if $a > 3$ ", Here the given statement is of the form q if p.

Here p is and q is $a^{2} > 9$ .

If $a > 3$ obviously $a^{2} > 9$ .

Therefore, the statement is true.

Step 3. Write the converse.

The converse is of the form "if q, then p鈥�

Therefore, the converse of the given statement is 鈥� 鈥淚f $a^{2} > 9$ then $a > 3$ .鈥�

Step 4. State whether the converse is true or not.

In order to verify if the converse is true or not let $a^{2} = 16$ such that $a^{2} > 9$ .

But $a = 卤 4$ .

That is a maybe 鈥�4 which is less than 3.

Therefore, the converse of the given statement is false.

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Statement	Reasons
1. A, M, and B have coordinated a, x, and b respectively; $b > a$ .	1. ?
2. $A M = x 鈭� a; M B = b 鈭� x$	2. ?
3. M is the midpoint of $\overset{炉}{A B}$ .	3. ?
4. $\overset{炉}{A M} 鈮� \overset{炉}{M B}$ , or $A M = M B$	4. ?
5. $x 鈭� a = b 鈭� x$	5. ?
6. $2 x =$ ?	6. ?
7. $x = \frac{a + b}{2}$	7. ?

91影视

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$a^{2} > 9$ if $a > 3$ .

Short Answer

Step by step solution

Step 1. Converse a conditional.

Step 2. State whether the statement is true or not.

Step 3. Write the converse.

Step 4. State whether the converse is true or not.

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91影视

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.a2>9if a>3.

Short Answer

Step by step solution

Step 1. Converse a conditional.

Step 2. State whether the statement is true or not.

Step 3. Write the converse.

Step 4. State whether the converse is true or not.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$a^{2} > 9$ if $a > 3$ .