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So we'd simplify this like

First we will multiply 3 by 4x and 2 and also open the brackets aswell!

3(4x+2)-6x

=12x + 6 - 6x                (And now we will place the like terms together along with their signs)

=12x - 6x + 6       (and now out here we will simply subtract 12x and 6x and so this will give us our answer)

=6x + 6     ANSWER

wow Alan that was so easy!Thank u so much!i would give u a point for a clearer answer!Thank you!

Multiply both sides by 4

2.5x +1.5(x - 4) = -4x

Multiply the bracketed term by 1.5

2.5x + 1.5x - 1.5*4 = -4x

Simplify the left-hand side

4x - 6 = -4x

Add 4x to both sides

8x - 6 = 0

Add 6 to both sides

8x = 6

Divide both sides by 8

x = 6/8

Simplify

x = 3/4  (or x = 0.75)

A thousand times five means 1000 x 5 so this gives us 5000  ANSWER!

Melody not only in Australia , Teacher's Day isnt in many countries!i think other countries should as well celebrat such days ! If u had read the wikipedia then u might have also read that it was introduced by a special person in India!And u know out here we celebrate many such kind of days like Friendship Day, Teacher's Day , Children's Day etc!So these are celebrated to honour different people and all!And its also fun !

Its some thing like colors of happiness in the whole country!

Thanks Rosala.

We don't have teachers day in Australia.  I think it should be introduced.  

-7+s = 29

s = 29+7

  = 36

Change the sign behind the number because you are moving the number 7 from the left to the right.

E.g. the '=' is the magic bridge. Whenever the numbers or alphabets move from one side to another, the magic bridge will change the sign.

The story should help you to remember it. 

Hope I've helped you! :)

can anyone answer

Ok.  You can use whatever symbols you like for both son's age and father's age.  Let me use x for son's age and y for father's age then.

father (y) is now 4 times as old as son (x) is now.   y = 4x   ...(1)

5 years ago father was y-5 years old, and son was x-5 years old.  At that time father was 7 times as old as his son.

 y - 5 = 7*(x - 5)    ...(2)

Replace the y in (2) by using (1)

4x - 5 = 7*(x - 5)

4x - 5 = 7x - 35

4x - 5 + 35 = 7x 

4x +30 = 7x

4x + 30 - 4x = 7x - 4x

30 = 3x

x = 10  ...(3)

Put (3) into (1)

y = 4*10

y = 40

Is this any clearer?

Alan this question is still confusing me . Can you please put x in place of sons age and then try and solve this maybe that way I can understand this much easily!

Area of Beijing: A ≈ 16400km²

Take standard marble diameter: d = 5/8"

Number of marbles of 1 marble depth required to cover Beijing: N ≈ A/d² ≈ 6.5*10¹³

One mole of marbles = Avogadro's number worth of marbles; Av ≈ 6*10²³

Depth of Avogadro's number of marbles on Beijing ≈ d*Av/N ≈ 1.5*10⁵ km  

They would reach about half way to the moon!

1+1=0 and $${{\mathtt{x}}}^{{\mathtt{0}}}$$=1

Let f = father's age and s = son's age

f = 4*s                                 father is 4 times older than son

f - 5 = 7*(s - 5)                   5 years ago father was f -5 and son was s-5  and father was 7 times older

Replace f in 2nd equation above with 4s from first equation,

4*s - 5 = 7*s - 7*5  so that:

30 = 3*s

s = 10

f = 4*10 = 40

Find an equation of the tangent line to the circle x2+y2=9 at the point (2, √5)

The radius r of the circle is 3, because $$x^2+y^2=r^2$$ and $$r^2 = 9$$

The distance of the point of the co-ordinate origin amounts   $$\sqrt{2^2+\sqrt{5}^2}=\sqrt{4+5}=\sqrt{9}=3 = r$$

so the point lies on the circle: The equation is: $$y=-\dfrac{x_p}{y_p}\left( x-x_p \right) +y_p$$ or $$y=-\dfrac{x_p}{y_p}x +\dfrac{r^2}{y_p}$$

so  $$x_p = 2 \quad y_p=\sqrt{5}\\
y=-\dfrac{2}{\sqrt{5}}x +\dfrac{r^2}{\sqrt{5}}$$finally  $$y=-\dfrac{2}{\sqrt{5}}x +\dfrac{9}{\sqrt{5}}$$

Rewrite as y = (9 - x²)^1/2

The slope at any point x is then given by slope = -x/(9 - x²)^1/2

When x = 2 the slope is -2/(9 - 2²)^1/2 = -2/√5

The equation of a straight line is y = m*x + c where m is the slope and c is a constant (the y-intercept).  We know the slope and can find c because we know that when x = 2, y = √5, so

√5 = (-2/√5)*2 + c

c = √5+4/√5 or c = √5*(1+4/5) 0r c = 1.8*√5

So  y = (-2/√5)*x + 1.8*√5

or y = √5*(-2/5)x + 1.8*√5

or y = -0.4*√5*x + 1.8*√5

a+9-9=14-9

a=5

A simple check to determine if a number is divisible by 3 is to keep adding up the digits of the number and see if the result is divisible by 3.

So:  1+7+8+6 = 22

        2 + 2 = 4

4 isn't divisible by 3, so neither is 1786.

$${\frac{{\mathtt{4}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{3\,008}} = {\frac{{\mathtt{3\,008}}}{{\mathtt{25}}}} = {\mathtt{120.32}}$$

Rearrange as 

√(x + 14) = 8 - 2x

Square both sides

x + 14 = (8 - 2x)²

x + 14 = 64 - 32x + 4x²

Collect like terms

4x² - 33x + 50 = 0

$${\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{33}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{50}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\frac{{\mathtt{25}}}{{\mathtt{4}}}}\\
{\mathtt{x}} = {\mathtt{2}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{6.25}}\\
{\mathtt{x}} = {\mathtt{2}}\\
\end{array} \right\}$$

Check in the original equation:

$${\mathtt{LHS}} = {\sqrt{{\mathtt{6.25}}{\mathtt{\,\small\textbf+\,}}{\mathtt{14}}}} \Rightarrow {\mathtt{LHS}} = {\mathtt{4.5}}$$

$${\mathtt{RHS}} = {\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{6.25}} \Rightarrow {\mathtt{RHS}} = -{\mathtt{4.5}}$$

So x ≠ 6.25

Check the other solution

$${\mathtt{LHS}} = {\sqrt{{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{14}}}} \Rightarrow {\mathtt{LHS}} = {\mathtt{4}}$$

$${\mathtt{RHS}} = {\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}} \Rightarrow {\mathtt{RHS}} = {\mathtt{4}}$$

So x = 2 is the solution to the original equation.

$$cube root of 125 = $\sqrt[3]{125}=125^{1/3}$$

on the calc this could be entered as  125^(1/3)

I think Aziz means 

asin(0.01)

The general equation for a sphere, centred at (0,0,0) is  x² + y² + z² = r²

Rearrange this as  z = (r² - x² - y²)^1/2    

The slope of z with respect to x is given by

∂z/∂x = -x/ (r² - x² - y²)^1/2

The slope of z with respect to y is given by

∂z/∂y = -y/ (r² - x² - y²)^1/2

You have the values of x, y and r, so I'll leave you to plug them into these formulae.

$$\\12.0\times 10^{-19} - 4.8\times 10^{-19 }\\\\
=(12.0- 4.8)\times 10^{-19 }\qquad \mbox{Here I have 'factorised'}\\\\
=7.2\times 10^{-19 }\\\\$$