Question

1. which is a counterexample to this conjecture? \the square of a number is always greater than the number\.

a. 0.4
b. 2
c. -1
d. 2.1

given the image, choose the correct reason for each statement of the proof.

1. statement 3: ( 4x + 20 = 180 )

a. substitution property
b. angle addition postulate
c. division property of equality
d. simplify
e. subtraction property of equality

1. which is the contrapositive of the statement:

\if a number is even, then it is divisible by 2.\
a. if a number is not divisible by 2, then it is not even.
b. if a number is divisible by 2, then it is even.
c. if a number is not even, then it is not divisible by 2.

Explanation:

Step1: Analyze each option for the first question

• For option A: \(0.4^2 = 0.16\), and \(0.16<0.4\).
• For option B: \(2^2 = 4\), and \(4 > 2\).
• For option C: \((-1)^2=1\), and \(1>-1\).
• For option D: \(2.1^2 = 4.41\), and \(4.41>2.1\).

Step2: Analyze the second question

• The Angle Addition Postulate states that if two angles are adjacent, then the sum of their measures is equal to the measure of the larger angle. Here, \(x+(3x + 20)=4x + 20\) (a straight - angle is \(180^{\circ}\)), so the reason for \(4x + 20=180\) is the Angle Addition Postulate.

Step3: Analyze the third question

• The contrapositive of a statement “If \(p\), then \(q\)” is “If not \(q\), then not \(p\)”. For the statement “If a number is even (\(p\)), then it is divisible by 2 (\(q\))”, the contrapositive is “If a number is not divisible by 2 (not \(q\)), then it is not even (not \(p\))”.

Answer:

1. A. 0.4
2. B. Angle Addition Postulate
3. A. If a number is not divisible by 2, then it is not even.