Is the set of integers closed under division? Explain why or why not.

1 answer:

5 0

The set of integers is not closed under the operation of division because when an integer is divided by another, the results are not limited to only integers i.e. zero and decimals are possibilities

<h3>How to determine the true statement?</h3>

Integers are numbers without decimal points

When integers are divided, the possible results are:

Zero
Decimal
Integers

The decimal and the zero possibilities imply that the set of integers is not closed under the operation of division

This is so because when an integer is divided by another, the results are not limited to only integers i.e. zero and decimals are possibilities

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The hypotenuese of an isosceles right triangle is 16 inches. The midpoints of its sides are connected to form an inscribed trian

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Answer:

256/3 = 85 1/3 square inches

Step-by-step explanation:

The dimensions of the first inscribed triangle are 1/2 those of the original, so its area is (1/2)² = 1/4 of the original. The area of the original is ...

A = (1/2)bh = (1/2)(16/√2)(16/√2) = 64 . . . . square inches

The sum of an infinite series with first term 64 and common ratio 1/4 is ...

S = a1/(1 -r) . . . . . . for first term a1 and common ratio r

= 64/(1 -1/4) = 64(4/3) = 256/3 . . . . square inches

The sum of the areas of the triangles is 256/3 = 85 1/3 square inches.

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