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4 years ago

A natural number is _____ a rational number. always sometimes never

Mathematics

2 answers:

olga nikolaevna [1]4 years ago

7 0

Answer:

always

Explanation:

1- Rational numbers:

Rational number is any number that can be written in the form of a fraction $\frac{a}{b}$ where both a and b are integers and b ≠ 0.

2- Natural numbers:

Natural number is a counting number (1,2,3,4,.....etc)

Now, we know that any number if divided by 1, the result would still be the same number ( $\frac{a}{1} = a$ )

This means that if any natural number is divided by 1, the result would still be the same natural number.

We can now conclude that natural numbers can be written in the form of fraction with denominator equal to 1.

This means that a natural number can always be a rational number.

Hope this helps :)

Paraphin [41]4 years ago

5 0

The Rational numbers ( Q ) include the Natural numbers ( N ):
A natural number is always a rational number.

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Ignore everything I wrote but I’m supposed to be writing two-column proofs and I need help with these

zavuch27 [327]

What you have so far is perfect. You started with the given statements and then use the definition of midpoint to show that each piece is equal to one another.

From here, use the transitive property

We combine these two statements

WX = XY
XY = YZ

into the following

WX = YZ

So we can effectively say WX = XY = YZ meaning the segments WX, XY and YZ are all the same length.

Through similar logic, we can chain together

VW = WX
WX = XY

to get VW = XY

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Consequently this means VW, WX, XY, and YZ are all the same length

Let's call that length m.

m = length of segment VW = length of WX = etc etc

This means,

VY = VW+WX+XY = m+m+m = 3m

and

WZ = WX+XY+YZ = m+m+m = 3m

Both VY and WZ are exactly 3m units long, therefore, VY = WZ

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3 years ago

The length of a rectangle is 3 ft more than twice the width, and the area of the rectangle is 54 ft2. find the dimensions of the

andrew-mc [135]

A = L * W
A = 54
L = 2W + 3

54 = W(2W + 3)
54 = 2W^2 + 3W
2W^2 + 3W - 54 = 0
(2W - 9)(W + 6) = 0

2W - 9 = 0
2W = 9
W = 9/2
W = 4.5 <== width

W + 6 = 0
W = -6....it wont be this one because it is negative

L = 2W + 3
L = 2(4.5) + 3
L = 9 + 3
L = 12 <==length

4 0

4 years ago

Can someone please help me factor this

Dmitry_Shevchenko [17]

Answer:

$\huge\boxed{\bf\:1}$

Step-by-step explanation:

$\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }$

Take $\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 }$ & factorise it at first.

$\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \\= \frac{\left(x-3\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}\\= \frac{x-1}{x-4}$

Now factorise the next set : $\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }$ .

$\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\= \frac{x-4}{x-1}$

Now, multiply the two simplified results.

$\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}$

$\rule{150pt}{2pt}$

7 0

3 years ago

-3/4 / (-8/5) write in simplest form

Shkiper50 [21]

Answer:

Ans = 15/32

Step-by-step explanation:

-3/4 / (-8/5)

= -3/4 ÷ (-8/5)

= -3/4 * -5/8

= 15/32 (- * - = +)

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4 years ago

In your own words, explain what it means to dilate a triangle.

mrs_skeptik [129]

Answer:

It means that you take a triangle and make another one but this time it is not the same size of the first one but the same shape. In other words make it bigger or smaller than the first one.

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3 years ago