Question 1. Determine whether the biconditional statement is true or false. If false, give a counterexample. An angle is a straight angle if and only if it is not acute.

A. false; m∠1 = 180°, ∠1 is not an acute angle
B. true
C. false; m∠1 = 63°, ∠1 is not a straight angle
D. false; m∠1 = 102°, ∠1 is not a straight angle

Question 2. Determine whether the biconditional statement is true or false. If false, give a counterexample.

An angle is a right angle if and only if it is not obtuse.

1. false; m∠1 = 70°, ∠1 is not a right angle
2. false; m∠1 = 90°, ∠1 is not an obtuse angle
3. true
4. false; m∠1 = 120°, ∠1 is not a right angle

1. B. true

2. 2. false; m∠1 = 90°, ∠1 is not an obtuse angle

Step-by-step explanation:

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b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

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