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3 years ago

Classify the numbers as rational or irrational

Mathematics

2 answers:

zmey [24]3 years ago

7 0

Answer and explanation:

irrational - doesn't have an integer answer or repeating decimal

rational - has a repeating pattern

irrational - numbers forever never repeating

rational = -7

rational = 2/5

irrational means the number can't be made into a fraction

Hope this helps! :)

Morgarella [4.7K]3 years ago

4 0

Answer:

$-\sqrt{13}$ = Irrational

43.95 (repeat sign) = Rational

-3π = Irrational

-√49 = Rational

6/15 = Rational

Step-by-step explanation:

Note:

A rational number can be defined as any number that can be expressed or written in the p/q form, where 'p' and 'q' are integers and q is a non-zero number. An irrational number on the other hand cannot be expressed in p/q form and the decimal expansion of an irrational number is non-repeating and non-terminating.

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The square root of a negative number is imaginary.

Natural Number Test

A number is natural if it is one of the counting numbers (greater than 0), i.e., 1,2,3,4,5,...

Since NAN is not both positive and a counting number, NAN is not a natural number

Whole Number Test:

Whole Numbers are positive numbers, including 0, with no decimal or fractional parts

Since NAN is not both ≥ 0 and an integer, NAN is a not a whole number

Integer Test

The number is an integer if it is a whole number (no fractions or decimals) positive or negative including the number 0, ...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...

Since NAN is not a positive or negative number (no decimals or fractions), NAN is not an integer

Rational Number Test

The number NAN is rational if it is an integer or decimal

A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.

Irrational Number Test:

An irrational number is a number that cannot be expressed as a ratio between two integers and is not an imaginary number.

Since NAN is the square root of a negative number, it is imaginary

Imaginary Numbers are not rational

Imaginary

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43.95 ⇒ With repeat sign over 43.95

The decimal places repeat an infinite amount of times and when a decimal repeats it's rational.

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Pi is a Greek letter (π), and one of the most well-known mathematical constants.

It is the ratio of a circle's circumference to its diameter which is always constant.

pi (π) approximately equals 3.14159265359... and is a non-terminating non-repeating decimal number.

Hence 'pi' is an irrational number.

Any number with pi is considered irrational.

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The square root of a negative number is imaginary.

Natural Number Test

A number is natural if it is one of the counting numbers (greater than 0), i.e., 1,2,3,4,5,...

Since NAN is not both positive and a counting number, NAN is not a natural number

Whole Number Test:

Whole Numbers are positive numbers, including 0, with no decimal or fractional parts

Since NAN is not both ≥ 0 and an integer, NAN is a not a whole number

Integer Test

The number is an integer if it is a whole number (no fractions or decimals) positive or negative including the number 0, ...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...

Since NAN is not a positive or negative number (no decimals or fractions), NAN is not an integer

Rational Number Test

The number NAN is rational if it is an integer or decimal

A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.

Irrational Number Test:

An irrational number is a number that cannot be expressed as a ratio between two integers and is not an imaginary number.

Since NAN is the square root of a negative number, it is imaginary

Imaginary Numbers are not rational

Imaginary

But is rational as it equals -7.

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Rational because the decimal terminates:

6/15 = 0.4/0.40...

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Mademuasel [1]

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3 years ago

2x + 3y = 17<br> 5x + 6y = 32<br><br> Usibg method if elimination

lions [1.4K]

Answer:

Solution (-2, 7)

Step-by-step explanation:

2x + 3y = 17 (1)

5x + 6y = 32 (2)

Using elimination method

Multiply (-2) to the equation (1)

-4x - 6y = -34

Now you have 2 new equations

-4x - 6y = -34

5x + 6y = 32

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x = -2

Substitute x = -2 into 2x + 3y = 17

2(-2) + 3y = 17

- 4 + 3y = 17

3y = 21

y = 7

Solution (-2, 7)

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3 years ago

What is the sum of all of the perfect squares between

Nonamiya [84]

Answer:

(-138) is the answer.

Step-by-step explanation:

Perfect square numbers between 15 and 25 inclusive are 16 and 25.

Sum of perfect square numbers 16 and 25 = 16 + 25 = 41

Sum of the remaining numbers between 15 and 25 inclusive means sum of the numbers from 17 to 24 plus 15.

Since sum of an arithmetic progression is defined by the expression

$S_{n}=\frac{n}{2}[2a+(n-1)d]$

Where n = number of terms

a = first term of the sequence

d = common difference

$S_{8}=\frac{8}{2} [2\times 17+(8-1)\times 1]$

= 4(34 + 7)

= 164

Sum of 15 + $S_{8}$ = 15 + 164 = 179

Now the difference between 41 and sum of perfect squares between 15 and 25 inclusive = $41-179$

= -138

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3 years ago

. Two bicyclists, Sarah and Emily, depart from the same location. Sarah heads N55°E at an average speed of 6 km/hr. Emily heads

Liula [17]

Answer:

The distance between them after 30 minutes is 6.5 km.

Step-by-step explanation:

Speed = $\frac{distance}{time}$

Sarah's speed = 6 km/hr = 1.6667 m/s

Emily's speed = 10 km/hr = 2.7778 m/s

The measure of angle between their bearings = $105^{o}$

After 30 minutes (1800 seconds);

distance = speed x time

Sarah would have covered a distance = 1.6667 x 1800

= 3000 m

= 3 km

Emily would have covered a distance = 2.7778 x 1800

= 5000 m

= 5 km

The distance between them, a, can be determined by applying the cosine rule;

$a^{2}$ = $b^{2}$ + $c^{2}$ - 2bcCos A

= $5000^{2}$ + $3000^{2}$ -2(5000 x 3000) Cos 105

= $5000^{2}$ + $3000^{2}$ -2(5000 x 3000) x (-0.2588)

= 2.5 x $10^{7}$ + 9 x $10^{6}$ + 7764000

= 41764000

a = $\sqrt{41764000}$

= 6462.5073

a = 6462.5 m

The distance between them after 30 minutes is 6.5 km.

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3 years ago