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777dan777 [17]
3 years ago
8

I need help on these questions please! Quickly too

Mathematics
1 answer:
ale4655 [162]3 years ago
5 0
By definition, a rational number is a precise number: or in other terms, we know its exact value. Irrational numbers are number that has endless digits on the right of the decimal points: in other terms, we can't know its exact value.

First question:
√2.5 = 1.58113.... It's endless, so irrational.
-√64 = -8 it's a whole number, so rational.
4√5 = 8.94427.... Endless, so irrational.
√14.4 = 3.7947... Endless so irrational.

So -√64 is the rational number.

Second:
7.885 is rational because has a defined number of digits after the decimal points.
π² = 9.8696.... Endless, so irrational.
√0.144 = 0.3794.... Endless, so irrational
√91 = 9.5393.... Endless, so irrational

So 7.885 is the rational number.

Third:
-7.8 bar: You can notice the line over the 8, this means that there's an infinite number of 8 after the decimal points. So it's 7.88888888888.... Endless, so irrational.
√25 = 5, whole number so rational
25.8125 Has a definite number of digits after the decimal point, so is rational.
√0.025 = 0.1581... Endless, so irrational.

So -7.8 bar and √0.025 are irrational.

Fourth:
π= 3.1415... Endless, so irrational.
1.425 has a definite number of digits after the decimal point, so rational.
√50 = 7.0710.... Endless, so irrational
√-4 Doesn't exist. Finding the square root of a negative number is mathematically impossible.

So 1.425 is the rational number.

Fifth:
√10 = 3.1622..... Endless, so irrational.
√100 = 10, a whole number so rational.
√1000 = 31.6227..... Endless, so irrational
√100000 = 316.2277...... Endless, so irrational.

√100 is the rational number.

Hope this helps!! :D And I hope you understood the lesson a bit more xD
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charle [14.2K]
The answer is:  [C]:  -0.7, ⅕, 0.35, ⅔ .
________________________________________
Explanation:
_________________________________________
<span>
Note that in this correct Answer choice "C" given, we have the following arrangement of numbers:
_____________________________________________________
   </span>→ -0.7, ⅕, 0.35, ⅔ ; 
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We are asked to find the "Answer choice" (or, perhaps, "Answer choices?") given that show a set of numbers arranged in order from "least to greatest"; that is, starting with a value that is the smallest number in the arrangement, and sequentially progressing, in order from least to greatest, with the largest (greatest) number in the arrangement appearing as the last number in the arrangement.
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Note the EACH of the 4 (four) answer choices given consists of an arrangement with ONLY one negative number, "- 0.7".  Only TWO of the answer choices—Choices "B" and "C"—have an arrangement beginning with the number, "-0.7 ";  So we can "rule out" the "Answer choices: [A] and [D]".
________________________
Let us examine: Answer choice: [B]: <span>-0.7, 0.35, ⅕, ⅔ ; 
</span>_________________________
Note: The fraction, "⅕" = "2/10"; or, write as: 0.2 .
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          The fraction, "⅔" = 0.6666667 (that is 0.6666... repeating; so we often               see a "final decimal point" rounded to "7" at some point.
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Through experience, one will be able to automatically look at these 2 (two) fractions and immediately know their "decimal equivalents".
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Otherwise, one can determine the "decimal form" of these values on a calculator by division:
_________________________
→ ⅕ = 1/5 = 1 ÷ 5 = 0.2
_________________________
→ ⅔ = 2/3 = 2 ÷ 3 = 0.6666666666666667
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For Answer choice: [B], we have:
______________________________
→   -0.7, 0.35, ⅕, ⅔ ; 
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→ So, we can "rewrite" the arrangement of "Answer choice [B]" as:
___________________________________________
    →  -0.7, 0.35, 0.2, 0.666666667 ;
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    → And we can see that "Answer choice: [B]" is INCORRECT; because
"0.2" (that is, "⅕"), is LESS THAN "0.35".  So, "0.35" should not come BEFORE "⅕" in the arrangement that applies correctly to the problem.
_______________________________________
Let us examine: Answer choice: [C]:  -0.7, ⅕, 0.35, 0.666666667 .
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→ Remember from our previous— and aforementioned—examination of "Answer Choice: [B]" ; that:
____________________________ 
→ ⅕ = 0.2 ;   and:
→ ⅔ = 0.666666667
_______________________
So, given:
____________
→ Answer choice: [C]: -0.7, ⅕, 0.35, ⅔ ; 
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→ We can "rewrite" this given "arrangement", substituting our known "decimal values for the fractions:
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→ Answer choice: [C]: -0.7, 0.2, 0.35, 0.666666667 ;
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→ As mentioned above, this sequence starts with "-0.7", which is the ONLY negative number in the sequence; as such, the next positive number is correct.  Nonetheless, "0.2" (or, "(⅕") is the next number in the sequence, and is greater than "-0.7". The next number is "0.35. "0.35" is greater than "⅕" (or, "0.2"). Then next number is "(⅔)" (or, "0.666666667").
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____________________________
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Answer:

1.50S + 2.50P > 20

Step-by-step explanation:

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