All Answers 358098 Answers

answer of 9+10 = 19

Start by subtracting 12 from both sides :)

Hi Funkygal,

Welcome to the forum  

ALWAYS give help in preference to giving answers.  

Answers without explanations are usually worse than useless.

Whereas, explanations without answers are to be encouraged :)

No need to use your units in the equation, until you're finshed calculating.

$${\mathtt{3\,215.52}}{\mathtt{\,\times\,}}{\mathtt{50}} = {\mathtt{160\,776}}$$

$${\frac{{\mathtt{160\,776}}}{{\mathtt{1\,400}}}} = {\frac{{\mathtt{2\,871}}}{{\mathtt{25}}}} = {\mathtt{114.84}}$$

= 144,84 m3

No I do not know.     

The question does not really make sense but

80%=0.80=0.8

and

0.8% =0.8/100 = 0.008

The external angle of a triangle (120) is equal to the sum of the 2 opposite internal angles (58+?)

$$x^2\times x = x\times x\times x = x^3$$

.

Thanks Alan, that is a really neat feature in Desmos that I have only just started to make proper use of.  

Your answer is neat though Melody!  I didn't realise you could click on the circular icons in Desmos to switch the curves on and off. 

.

You beat me Alan.  :(

Two answers are always better than one!  :))

I have graphed this in 3 steps to try and show you pictorially how it is done.

4{[4(x-1)+3]-[2(2x-1)+3]} = ?

$$\small{\text{$ 4 \cdot\{\,[\,4(x-1)+3\,]-[\,2(2x-1)+3\,]\,\} $}} \\
\small{\text{$ = 4 \cdot[\,(4x-4+3)-(4x-2+3)\,]$}} \\
\small{\text{$ =4 \cdot(\, 4x-4+3-4x+2-3\,)$}} \\
\small{\text{$ =4 \cdot(\,-4+2\,)$}} \\
\small{\text{$ =4 \cdot(-2)$}} \\
\small{\text{$ =-8 $}}$$

It's taken a while, but, 6789 = 5.

Given the geometric sequence:   9,  3,  1,  ...  .      Find S6

ratio r =  $$\small{\text{$
\frac{3}{9}=\frac{1}{3} $}}$$ and $$\small{\text{$a=9$}}$$ so

$$\small{\text{$
\boxed{a_n=a\cdot
\left(
\frac{1}{3}\right)^{n-1}}
$}}$$

$$s_6=9+3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}\\ \\
s_6=13+0.\overline{481}\\\\
s_6=13.\overline{481}$$

how would i turn 1/2^-3 into a positive exponent ?

$$\dfrac{1}{ 2^{-3} } = \left( \dfrac{1}{ 2 } \right)^{-3}\\\\
\small{\text{
Formula:
$\boxed{
\left( \dfrac{a}{b} \right)^{-3}
= \left( \dfrac{b}{a} \right)^{3}
}$}}\\\\
\left( \dfrac{1}{ 2 } \right)^{-3}
=\left( \dfrac{2}{ 1 } \right)^{3} = 2^3$$

How many numbers are in the list 2008,2003,1998,...8,3

arithmetic sequence: 

$$\small{\text{
$
a_1,\,
a_2,\,
a_3,\,
a_4,\,
a_5,\,
a_6,\,
\cdots
,\, a_n
$}}
\qquad
\small{\text{
$\boxed{
a_n=a_1+(n-1)\cdot d
}
\qquad
$ or
$\qquad \boxed{
n=1+\dfrac{a_n-a_1}{d}
}
$
}}$$

If the distance between the numbers  $$\small{\text{$d = -5$}}$$ and $$\small{\text{$a_1=2008$}}$$ and $$\small{\text{$a_n=3$}}$$ then we find n:

$$\small{\text{$
\begin{array}{rcl}
n &=& 1+\dfrac{a_n-a_1}{d} \\\\
n &=& 1 + \dfrac{3-2008}{(-5)}\\\\
n &=& 1 + \dfrac{-2005}{(-5)}\\\\
n &=& 1 + \dfrac{2005}{5}\\\\
n &=& 1 + 401\\\\
n &=& 402
\end{array}
$}}$$

There are 402 numbers in the list.

Hi Civonamzuk,

What you have done may well be correct but I don't follow your logic.

Could you please add in some more working ?

Hi MathsGod1

Watch and learn :))

What is   $$0.\bar 4 $ as a fraction$$

Let  X=0.444444444

so

10X=4.44444444.....

   X =0.44444444

subtract

10X-X = 4      All the other 4's subtract away

9X=4

X=4/9

Find the coefficient of x^6 in the expansion of (2x+1)^12 

$$\\\small{\text{$(2x+1)^{12} $}}\\\\
\small{\text{
$
= \binom{12}{0}\cdot(2x)^{12}\cdot 1^0
+ \binom{12}{1}\cdot(2x)^{11}\cdot 1^1
+ \binom{12}{2}\cdot(2x)^{10}\cdot 1^2
+ \binom{12}{3}\cdot(2x)^{9}\cdot 1^3
+ \binom{12}{4}\cdot(2x)^{8}\cdot 1^4+
$}}\\\\
\small{\text{
$
+ \binom{12}{5}\cdot(2x)^{7}\cdot 1^5
+ \textcolor[rgb]{1,0,0}{
\binom{12}{6}\cdot(2x)^{6}\cdot 1^6
}
+ \binom{12}{7}\cdot(2x)^{5}\cdot 1^7
+ \binom{12}{8}\cdot(2x)^{4}\cdot 1^8+
$}}\\\\
\small{\text{
$
+ \binom{12}{9}\cdot(2x)^{3}\cdot 1^9
+ \binom{12}{10}\cdot(2x)^{2}\cdot 1^{10}
+ \binom{12}{11}\cdot(2x)^{1}\cdot 1^{11}
+ \binom{12}{12}\cdot(2x)^{0}\cdot 1^{12}
$}}$$

Coefficient of $$\small{\text{$x^6$}}$$ :

$$\small{\text{
$
\begin{array}{rl}
&\textcolor[rgb]{1,0,0}{\binom{12}{6}\cdot(2x)^{6}\cdot 1^6} \\\\
=&\binom{12}{6}\cdot(2x)^{6}\\\\
=&\binom{12}{6}\cdot2^6\cdot x^6\\\\
=&\binom{12}{6}\cdot 64 \cdot x^6\\\\
=&924\cdot 64 \cdot x^6\\\\
=&59136\cdot x^6\\\\
\end{array}
$
}}$$

The coefficient of $$\small{\text{$x^6$}}$$ is 59136

I don't understand this question

$$sinxcos30-cosxsin30=\frac{sinx-\sqrt3cosx}{2}$$