Which of the following numbers is rational? A. 4/5 B.√27 C.4.020020002000002.... D.√31
2 answers:
<em>Greetings from Brasil...</em>
First let's define the rational number....
→ Division between two numbers with the detail that the dividend or denominator cannot be zero
A/B or A ÷ B
where B ≠ 0
<em>(just for the sake of knowledge. If B = 0 we would have +∞ as an answer)</em>
<em>A ∈ ℤ</em>
<em>and</em>
<em>B ∈ ℤ* (B ≠ 0)</em>
In this way, when dividing A by B, we will obtain a whole number or a number with a decimal (finite decimal or periodic tenth)
Let's go to the alternatives
<h3>A = 4/5 = 0,8 <em> (finite decimal)</em></h3>4 ∈ ℤ and 5 ∈ ℤ*, so we have a rational number
B = √27 = 5.1961524227066318805823390245176
(There is no repetition of tithing periods (numbers after the point) - non-periodic tithe). So we have an Irrational Number
C = 4.020020002000002
There is no periodic tenth - Irrational Number
D = √31 = 5.5677643628300219221194712989185
Irrational Number - Non-periodic tithe
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Answer:
One of the sides is 6 cm and the other is 8 cm
Step-by-step explanation:
Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:
a + b + hypotenuse = 24
a + b + 10 = 24
a + b = 14
b = 14 - a
So now we can right the Pythagorean theorem as follows:
and from this expression in factor form to be zero a must be 6 or a must be 8.
Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)
or a = 8 (and therefore b = 14 - 8 = 6)