Question

1. how many sides will the next figure in the sequence have? a. 5 b. 6 c. 7 d. 8 2. if a number is divisible by 4, then it is divisible by 2. if a number is divisible by 2, then it is even. which of the following conclusions is true? a. a number that is divisible by 4 is even. b. an even number is not divisible by 4. c. a number that is divisible by 4 is not even. d. an even number is always divisible by 4. 3. the number of sides and the sum of the interior angles are given for each of the polygons shown below. shape number of sides sum of interior angles 3 180° 4 360° 5 540° if the pattern continues, what would be the sum of the interior angles of a polygon with 6 sides? a. 900 b. 1080 c. 720 d. 1260 4. which of the following counterexamples shows that the conjecture is false? if a number is divisible by 3, then the number is odd. a. 15 b. 7 c. 21 d. 12

Explanation:

Step1: Analyze question 1

Since no sequence of figures is shown, we cannot answer this question.

Step2: Analyze question 2

If a number is divisible by 4, it is divisible by 2 (because 4 = 2×2). And if a number is divisible by 2, it is even. So a number divisible by 4 is even.

Step3: Analyze question 3

The formula for the sum of interior - angles of a polygon is $(n - 2)\times180^{\circ}$, where $n$ is the number of sides. For $n = 6$, we have $(6 - 2)\times180^{\circ}=4\times180^{\circ}=720^{\circ}$.

Step4: Analyze question 4

We need to find a number divisible by 3 that is even. 15 and 21 are odd and divisible by 3. 7 is not divisible by 3. 12 is divisible by 3 and is even, which is a counter - example to the statement "If a number is divisible by 3, then the number is odd".

Answer:

1. A. A number that is divisible by 4 is even.
2. C. 720
3. D. 12