x=≥-1

4*-1+12(=8)≥5*-1+13(=8)

$$\\4^3=2^x\\\\
(2^2)^3=2^x\\\\
2^6=2^x\\\\so\;\; x=6$$

this was an easy one - if the question is harder then you will need to use logarithms. 

inverse what?

do you mean [2nd] function?

We can not get to every question - there are too many. 

When questions 'fall off' the first page we give them lower priority because we figure you may have already found your answer somewhere else.  If this is not the case we encourage you to draw our attention to your question.  This will almost always work.

Here are instrictions on how it should be done.

cube root of 8

equals 2 because    2*2*2=8

cube root of  343 =    $$\sqrt[3]{343}=7$$

because 7*7*7=343

I hope that helps   

Does anyone want to answer one of 315's physics questions?

Same as atan.

Press shift and click on tan, sin or cos

$$272.74 * 108.25\% \\\\
=272.74*108.25/1000\quad dollars$$

How many feet are in a mile ?

$${\mathtt{1}}{mile}\,\, {\rightarrow}\,\, {feet}$$     = 5280 feet

$$300\div 5.5 \qquad $miles per hour$$$

if x = 25 results in y = 200, x = 100 so y = 50, x = 200 so y = 25 etc, what mathmatical formula does this represent ?

$$x\cdot y = 5000$$

hyperbola:  $$y = \frac{5000}{x}$$

What is 2.5 cm if 1cm equals 0.1 km ?

$$\small{\text{
$
\begin{array}{rcl}
1\ \mathrm{cm} & \widehat{=} & 0.1 \ \mathrm{km} \\
2.5\ \mathrm{cm} & \widehat{=} & x \ \mathrm{km}
\end{array}
$
}}\\\\
\small{\text{
$\dfrac{1}{2.5} = \dfrac{0.1}{x} $}} \\\\
\small{\text{
$\dfrac{2.5}{1} = \dfrac{x}{0.1} $}} \\\\
\small{\text{
$ x=0.1\cdot \dfrac{2.5}{1} $}} \\\\
\small{\text{
$ x=0.25\ \mathrm{km} $}} \\\\$$

Oops! Seems I got the sign wrong.

2x + 3 = 2(x + 1.5)  

8 times 

M=log₉E means that 9^M = E

N = log₂₇E means that 27^N = 2E   or   27^N/2 = E

This means 9^M = 27^N/2

Take logs of both sides (I'll use log to the base e, or ln):  ln(9^M) = ln(27^N/2)

Using a property of logarithms this can be written as: ln(9^M) = ln(27^N) - ln(2)

Using another property of logarithms: M*ln(9) = N*ln(27) - ln(2) or:   M = N*ln(27)/ln(9) - ln(2)/ln(9)

This is in the form y = m*x + c, which is the general form of a linear equation (here y = M, x = N, m = ln(27)/ln(9),

c = -ln(2)/ln(9)), so the answer is yes.

.

1.  You can type in the number and then press the following button:

or

2.  You can type sqrt(4791) and press "=" 

.

We could take Chris's development a little further as follows:

Given 2^2x - 2^x - 2 = 0 we can rewrite it as (2^x)² - 2^x - 2 = 0

Let y = 2^x, so the last equation can be written as:  y² - y - 2 = 0 or (y + 1)(y - 2) = 0

so y = -1 and y = 2

However, replacing y by 2^x we see that there is no solution to 2^x = -1, so we must have just 2^x = 2, or 2^x = 2¹ giving x = 1 as the only real solution.

.

I assume you want to graph this......???

How do I find the x-intercepts of  ?

$$\boxed{x^4-7x^2-3=0}\qquad
\small{\text{
we set $ z= x^2 $ with $\boxed{x=\sqrt{z}}
$}}\\\\
\small{\text{we have $ z^2-7z-3= 0 $}}\\\\
\small{\text{$
z_{1,2}=\dfrac{7\pm\sqrt{49-4\cdot (-3)} } {2}
$}}\\\\
\small{\text{$
z_{1,2}=\dfrac{7\pm\sqrt{ 49+12 } } {2} = \dfrac{7\pm\sqrt{ 61 } } {2}
$}}\\\\
\small{\text{$
z_1 = \dfrac{7+\sqrt{ 61 } } {2} \qquad z_2 = \dfrac{7-\sqrt{ 61 } } {2}
$}}\\\\
\small{\text{$x = \pm \sqrt{z_{1,2}} $ }}\\\\
\small{\text{$x_1 = + \sqrt{z_{1}} = \sqrt{ \dfrac{7+\sqrt{ 61 } } {2} } $ }}\\\\
\small{\text{$x_2 = - \sqrt{z_{1}} = -\sqrt{ \dfrac{7+\sqrt{ 61 } } {2} } $ }}\\\\
\small{\text{$x_3 = + \sqrt{z_{2}} = \sqrt{ \dfrac{7-\sqrt{ 61 } } {2} } \qquad 7 - \sqrt{61} < 0 \quad ! \quad (non-real)
$ }}\\\\
\small{\text{$x_4 = - \sqrt{z_{2}} = -\sqrt{ \dfrac{7-\sqrt{ 61 } } {2} } \qquad 7 - \sqrt{61} < 0 \quad ! \quad (non-real)
$ }}\\\\$$

3.2 times N equals 0.96......so we have....

3.2 * N  = .96   divide both sides by 3.2

N = .3

The length of the ski run is the hypoteneuse of a right triangle......we know an angle and the opposite side....so we have

sin 24.4 = 1100 / hypoteneuse  .....  rearrange

hypoteneuse = 1000 / sin 24.4  = 2662.76 ft. long

I think you mean a "dodecagon"......which is a 12-sided figure.....{a "dodecahedron" is a 3-dimensional figure}

Assuming the dodecgon is regular......

Since the circle's area is 36pi, we have that the circle's radius must be = 6

So....the area is given by  12 equal triangles with apex angles = 30 degrees and whose sides = 6

12*(1/2)(6)(6)sin30 =

6^3 (1/2) = 108 sq. units

You sometimes see an expression like: 21 + -7 you can write it as 21 - 7 and evaluate it that way.