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If you just want to factor this expression then look for two numbers that multiply to make 12 and add to make 8:

1      12    product 12 sum 13

2      6      product 12 sum 8

3      4      product 12 sum 7

So it looks like 2 and 6 are the numbers we want.

x² + 8x + 12 can be written as (x + 2)(x + 6)

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Septillion = 1 000 000 000 000 000 000 000 000

This one is pretty tricky, because it is not an equation. 

But...

Say x=3

x^2 + 8x + 12 = 45

Hope I helped.

Type in your numerator and your denominator next to each other separated by a slash/.

E.G.: 87/89

If you want to have an operation between two fractions do this:

(87/89) * (17/90) = X

$$\\sin30 = \frac{57.74}{d}\\\\
dsin30 = 57.74\\\\
d = \frac{57.74}{sin30}\\\\$$

$${\frac{{\mathtt{57.74}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{30}}^\circ\right)}}} = {\frac{{\mathtt{2\,887}}}{{\mathtt{25}}}} = {\mathtt{115.48}}$$

$$\\f(x)=2x + 2\\
y=2x+4\\
$swap the x and the y over$\\
x=2y+4\\
x-4=2y\\
y=\frac{x-4}{2}\\\\
f'(x)=\frac{x-4}{2}\\$$

9 + 10 = 19 Because 10 = 5 + 5, 9 = 4+5, thus 5+5+4+5=19!

Here is the pic  

thank you Alan.  I think you have made a small error, the sides of the triangle are in the ratio 3:4:5

but their lengths are 6,8 and 10 cm

so the radius of the circle is 5cm

Thank you Alan:)

A Taylor series expansion of f(x) about point x=a can be written as:

$$f(x)=f(a)+f'(a)(x-a)+\frac{1}{2!}f''(a)(x-a)^2+...$$

If we set a = 0 here:

f(x) = (2-x)^1/2                f(0) = 2^1/2

f'(x) = -(1/2)(2-x)^-1/2      f'(0) = -(1/2)2^-1/2

f''(x) = -(1/4)(2-x)^-3/2     f''(0) = -(1/4)2^-3/2

... etc.

so

f(x) = √2 - x/(2√2) - x²/(8*2^3/2) ...  

(this could be tidied up by shifting all the √2s in the denominators to the numerators - by multiplying by √2/√2)

Similarly for the other one, which is best written as  f(x) = (1 - x²)^-1/2 to start with.

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y is inversely proportional to x just means: y = k/x where k can be positive or negative.

"Proportional to" just refers to the magnitude unless otherwise specified.

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Google translate from Czech:

A right triangle has a perimeter of 24 cm. Its sides are in the ratio 3: 4: 5. What is the radius of the circle circumscribing the triangle?

First find where the perpendicular bisectors of two of the sides intersect.  This is the centre of the circumscribing circle.  A 3:4:5 circle is a well-known right-angled triangle, so the perpendicular bisectors of the two shorter sides meet at x = 3/2, y = 2  (where the triangle has vertices at (0, 0), (3, 0) and (3, 4)).

The radius is then given by r = √[(3/2 - 0)² + (2 - 0)²]  = 5/2

This answer should be doubled - see Melody's reply.

Google translate to Czech:

První zjistit, kde se kolmé bisectors na dvou stran protínají. To je centrem obalové kružnice.A3: 4: 5 kruh jea dobře známý pravoúhlého trojúhelníku, takže kolmé bisectors na obou kratších stranách setkat při x = 3/2, y = 2 (kdethe trojúhelník má vrcholy na (0, 0), (3, 0) a (3, 4)).

Poloměr je pak dána r = √ [(3/2 - 0) 2 + (2-0) 2] = 5/2

Tato odpověď by měla být dvojnásobná - viz odpověď Melody.

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Alan or Chris, could you please comment on my question here.

two things are directly proportional if as one gets bigger the other also gets proportionally bigger but the constant can be negative, cant it? So how does that work?

Thanks you

Yes P and Q are directly proportion.

1kg=2.20462pounds

so

P=2.20462Q

2.20462 is the constant of proportionality.  :)

Alan, if you are in the mood I thing that this one is for you. :)

Please use the calc on the home page.

Google translate from Czech:

Foreign tour was attended by 42 women, 36 men and 62 children. What percentage of the total number of participants were women?

Total number of people = 42 + 36 + 62 = 140

The fraction that are women = 42/140 = 0.3

To get the percentage multiply this by 100:

Percentage of women = 100*0.3 = 30%

Google translate into Czech: 

Celkový počet osob = 42 + 36 + 62 = 140

Frakce, že jsou ženy = 42/140 = 0,3

Chcete-li získat procento vynásobte to o 100:

Procento žen = 100 * 0,3 = 30%

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I already answered this one!

f(a)=3a-4

0=3a-4

solve for a

That's just the way the cookie crumbles sometimes 

the sine value is given by the y value on the unit circle.  When th angle is 0, the y value is 0 so sin0=0

They haven't converted the time of 560 years to 22.5 grams!

The meaning of a half-life is that if you start with N grams now, then in a half-life's time you will have half of what you started with, namely half of N grams, or N/2 grams.  

So if you start with 45 grams now, then in 560 years you will have 45/2 grams (22.5 grams).

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Thanks Alan.  

Use the x^y button.  eg  3 x^y 4  or 3 x^y (4²)

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