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\((a+2)(a+2)\\ = a(a+2) + 2(a+2)\\ = (a)(a) + (2)(a) + (2)(a) + (2)(2)\\ = a^2 + 2a + 2a + 4\\ = a^2 +4a + 4\)

Btw the way you type is super cool. The Guest who asked the question.

In Maths, (I assume you mean 'e')

\(e=\displaystyle\sum^{\infty}_{0}\dfrac{1}{n!}\)

In Physics, E usually means energy like in the famous formula E = mc²

Btw the c in E = mc² means the speed of light using the unit ms^-1.

:)

I think a²+4a+4.

So easy@!@

-7.5=y/2.22-1.5

<=> -6 = y/2.22

<=> y = -6*2.22

<=> y = -13.32

Hello Electric Pavlov,

\(4mol\times6.022{\color{red}1}\times 10^{23}atoms/mol\)

\(=24.0884\times10^{23}atoms\)      !

A bridge hand is made up of 13 cards from a deck of 52. Find the probability that a hand chosen at random contains 6 of one suit, 4 of another, and 3 of another

6 hearts, 4 diamonds, 3 clubs and no spades

Number of favourable hands  13C6*13C4*13C3 * 4!   becasue it can by 6 clubs or whatever

nCr(13,6)*nCr(13,4)*nCr(13,3) * 4! = 8421716160

Number of possible hands = 52C13

8421716160/nCr(52,13) = 0.0132622619354851

So the probablility will be  0.0132622619354851

arctan   that is atan is the same thing. :)

atan(1)=45         that is if you are in degrees :)

Latent heat of melting of ice = 334 J/g so energy required for 384 g is 384*334 J → 128.256 kJ

.

2.3 feet of water = 1 psi

See http://www.kylesconverter.com/Pressure/Feet-of-Water-to-Pounds-per-Square-Inch 

The function is homogeneous if f(tx,ty) = f(x,y) where t is any number.

Do you think  tan(tx + ty) = tan(x + y) or not?

the sum of the squares of 3 positive, consecutive numbers is 149. Find the answer

Yes I suppose it is a bit silly but some of us find questions like this fun :)

let the integers be

x-1, x and x+1

so their squares will be

\((x-1)^2,\;\; x^2\;\; and\;\; (x+1)^2\\ (x-1)^2+x^2+ (x+1)^2=149\\ x^2-2x+1\quad +x^2\quad +x^2+2x+1=149\\ x^2+1\quad +x^2\quad +x^2+1=149\\ 3x^2+2=149\\ 3x^2=147\\ x^2=49\\ x=7\)

So the numbers are 6,7 and 8

best represents a triangle with the lengths 10in., 12in., 15in.,

Sorry YaraYugi you had the right idea but you got a bit confused. :)

In any triangle the longest side is opposit the biggest angle.

And we want to know if the biggest angle is greater or less than 90 degrees

so I will call the short sides a and b and the long side c

a=10, b=12 and    c=15

If

\(a^2+b^2>c^2 \qquad \text{Then angle C is acute}\\ a^2+b^2=c^2 \qquad \text{Then angle C is a right angled}\\ a^2+b^2<c^2 \qquad \text{Then angle C is obtuse}\\ \)

 10^2+12^2 = 244

15^2=225

244>225 so Angle C is acute

This is an acute angled triangle.

Here is the triangle drawn to scale

Hi Metallica22   :)

How to simplify (-1+ sqrt 5)/(4) divided by 2

\(\frac{ (-1+ \sqrt 5)}{4} \div 2\\ =\frac{ (-1+ \sqrt 5)}{4} \times \frac{1}{ 2}\\ =\frac{ -1+ \sqrt 5}{8} \\ or\\ =\frac{ \sqrt 5-1}{8} \\\)

Sorry HSC I have no idea.  This is probably one for Heuraka or Alan ....

I just watch a Khan Academy  youtube clip on homogenous equations but it didn't help with your question :(

2) In a meeting, everyone shakes hands with another person.

If the total number of shaking hands is 2016 times,

how many people was in the meeting?

Let n = people in the meeting

\(\begin{array}{|rcll|} \hline \frac{ n\cdot (n-1) } {2} &=& 2016\ \text{handshakes }\\ n\cdot (n-1) &=& 4032 \\ n^2-n &=& 4032 \\ n^2-n -4032 &=& 0 \\\\ n &=& \frac{1+\sqrt{1-4\cdot(-4032) } }{2} \\ n &=& \frac{1+\sqrt{ 16129 } }{2} \\ n &=& \frac{1+127 } {2} \\ n &=& \frac{ 128 } {2} \\ n &=& 64 \\ \hline \end{array}\)

7x-3>6x-6

\(\begin{align}\\7x-3&>6x-6\\ 7x-3+3&>6x-6+3\\ 7x&>6x-3\\ 7x-6x&>6x-3-6x\\ x&>-3\\ \end{align}\)

1000(3) ^t/4 . ¼ In 3

\(\frac{1000.(3) ^t}{4} \times \frac{1}{4}ln 3\\ =\frac{1000\times ln3\times (3) ^t}{16} \)

Ok, what about it - there is no question. :/

how do you convert from Celcius to Fahrenheit ?

Formula:

\(\begin{array}{|rcll|} \hline T(°F) = T(°C) × 1.8 + 32 \\ \hline \end{array} \)

Example:
Convert 20 degrees Celsius to degrees Fahrenheit:

\(\begin{array}{|rcll|} \hline T(°F) = 20°C × 1.8 + 32 = 68 °F \\ \hline \end{array}\)

how do I write 285 millionths in sceintific notation?

Each mole has Avagadro's number of atoms in it:  6.022 x 10^23     you have 4 moles

 4x 6.0223 =24.088 x 10^23  atoms

cos25 = x / 1,027.483

1,027.483*cos25 = x

1027.483*cos(25) = 931.215843948137871

x= 931.215843948137871

To factor this polynomial you must first be comfortable with the idea of the difference or squares. 

Eg.   a^2 - b^2 =  (a+b) (a-b)

*This will help you solve the problem*

Now for the problem:

\(16x^4 - 81\)

\((4x^2)^2 - 9^2\)

\(a^2 - b^2 = (a+b)(a-b)\)

Set: a to \(4x^2 \)

       b to \(9\)

\((4x^2 + 9) (4x^2-9) \)

Notice that the term on the right side is another difference of squares hence you can factor it even more. The term on the left side can not be factored because it is a sum of squares.

For the term on the right set  a to 2x and b to 3

\((4x^2 + 9) (4x^2-9)\)

\((4x^2 + 9) (2x+3)(2x-3)\)

This is your final answer: \((4x^2 + 9) (2x+3)(2x-3)\)

sin A = 0.42 

A = arcsin 0.42

arcsin(0.42) = 24.834587489702

A = 24.8 degrees