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navik [9.2K]
3 years ago
13

Is the difference between two rational numbers always rational number

Mathematics
2 answers:
vladimir1956 [14]3 years ago
7 0
Not always. It depends on the teacher and the school. Depends on the rules and how your being tought.
Alenkinab [10]3 years ago
6 0
Hello,

An integer is a rational number (ex 5=5/1=10/2...)
The sum of 2 rationals is a rational.
Substract a rational is adding its opposite.
The difference of 2 rationals is always a rational (substraction is a intern law)
You might be interested in
Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.
grandymaker [24]

Answer:

Lines a and b are parallel

Lines a and c are perpendicular

Lines d and c are perpendicular

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

Part 1) Find the slope of Line a

we have the points

(-3,4) and (3,6)

substitute in the formula

m=\frac{6-4}{3+3}

m=\frac{2}{6}

simplify

m_a=\frac{1}{3}

Part 2) Find the slope of Line b

we have the points

(-10,-3) and (-8,3)

substitute in the formula

m=\frac{3+3}{-8+10}

m=\frac{6}{2}

m_b=3

Part 3) Find the slope of Line c

we have the points

(0,5) and (3,-4)

substitute in the formula

m=\frac{-4-5}{3-0}

m=\frac{-9}{3}

m_c=-3

Part 4) Find the slope of Line d

we have the points

(4,-7) and (13,-4)

substitute in the formula

m=\frac{-4+7}{13-4}

m=\frac{3}{9}

simplify

m_d=\frac{1}{3}

Part 5) Compare the slopes

Remember that

If two lines are parallel then their slopes are the same

If two lines are perpendicular then their slopes are opposite reciprocal

we have

m_a=\frac{1}{3}

m_b=3

m_c=-3

m_d=\frac{1}{3}

therefore

Lines a and b are parallel (slopes are equal)

Lines a and c are perpendicular (slopes are opposite reciprocal)

Lines d and c are perpendicular (slopes are opposite reciprocal)

6 0
3 years ago
If you need 2 liters of soda for every 12 students at the school dance, and you sold 360 student tickets to the dance. About how
GalinKa [24]

Answer:

60 liters

Step-by-step explanation:

360/12=30

30x2=60 liters

Hope this helps! :)

4 0
2 years ago
Read 2 more answers
For <img src="https://tex.z-dn.net/?f=e%5E%7B-x%5E2%2F2%7D" id="TexFormula1" title="e^{-x^2/2}" alt="e^{-x^2/2}" align="absmiddl
nevsk [136]
I'm assuming you're talking about the indefinite integral

\displaystyle\int e^{-x^2/2}\,\mathrm dx

and that your question is whether the substitution u=\dfrac x{\sqrt2} would work. Well, let's check it out:

u=\dfrac x{\sqrt2}\implies\mathrm du=\dfrac{\mathrm dx}{\sqrt2}
\implies\displaystyle\int e^{-x^2/2}\,\mathrm dx=\sqrt2\int e^{-(\sqrt2\,u)^2/2}\,\mathrm du
=\displaystyle\sqrt2\int e^{-u^2}\,\mathrm du

which essentially brings us to back to where we started. (The substitution only served to remove the scale factor in the exponent.)

What if we tried u=\sqrt t next? Then \mathrm du=\dfrac{\mathrm dt}{2\sqrt t}, giving

=\displaystyle\frac1{\sqrt2}\int \frac{e^{-(\sqrt t)^2}}{\sqrt t}\,\mathrm dt=\frac1{\sqrt2}\int\frac{e^{-t}}{\sqrt t}\,\mathrm dt

Next you may be tempted to try to integrate this by parts, but that will get you nowhere.

So how to deal with this integral? The answer lies in what's called the "error function" defined as

\mathrm{erf}(x)=\displaystyle\frac2{\sqrt\pi}\int_0^xe^{-t^2}\,\mathrm dt

By the fundamental theorem of calculus, taking the derivative of both sides yields

\dfrac{\mathrm d}{\mathrm dx}\mathrm{erf}(x)=\dfrac2{\sqrt\pi}e^{-x^2}

and so the antiderivative would be

\displaystyle\int e^{-x^2/2}\,\mathrm dx=\sqrt{\frac\pi2}\mathrm{erf}\left(\frac x{\sqrt2}\right)

The takeaway here is that a new function (i.e. not some combination of simpler functions like regular exponential, logarithmic, periodic, or polynomial functions) is needed to capture the antiderivative.
3 0
3 years ago
What is this simplified?
miv72 [106K]

Answer: -8 square root of 3 (choice a)

Step-by-step explanation:

You have to find 2 numbers that multiply to 48 and in the same time, 1 of these numbers is a perfect square. In this case, the numbers are 16 and 3. So -2√16*3

Then since 16 is. A perfect square, and the square root is 4, you take out the 4 and multiply it by -2 so that is -8 and now you are left with -8√3. Hopefully that helped.

7 0
2 years ago
Read 2 more answers
Is negative 5 a rational number or an irrational number<br><br><br> (Pleasee help me)
solong [7]

Answer:

Negative five is in fact a rational number.

Step-by-step explanation:

Rational numbers can either be negative or positive. An irrational number would be pi (3.14159 etc.)

8 0
3 years ago
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