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angle AHB = 120 degrees

If I'm not mistaken...  A_(MTG) = 20.833 u²

CP = 2/3 * [sqrt(3² + 4²)] = 10/3 

\(\frac{ \sqrt{1500}}{4π}=\frac{38.7298334621}{π}=\frac{38.7298334621}{3,14...}\)~3.08202222031

By stars-and-bars, the number of ways is C(9,4)*C(8,4) = 8820.

2 moles of Fe result in 2 moles of FeCl3

so 5.5 moles of Fe will result in 5.5 moles of FeCl3

                            5.5 * ( mol wt of Fe    +  3*mol wt of Cl )   gms    ( you'll need periodic table of elements)

Circle circumference   is  

   pi * d   

        or      pi * 2 * r            since d = 2r              (don't forget units :   meters,  inches,    cm   etc in your answer !)

circumference/pi = d

 The length of the shortest leg = [sqrt(16² - 8²)] / 2

Important: If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant.

PY² = PB * PA

Thanks!

By Power of A Point, \(PB \cdot PA = PY^2\).

Therefore, \( PB = \frac{PY^2}{PA} = \frac{10^2}{15} = \frac{20}{3}. \)

And as a result \(AB = PA - PB\), meaning that \(AB\) is \(15 - \frac{20}{3} = \frac{25}{3}\)

there is no picture guest

the anwser is -13

Here's a link:    https://web2.0calc.com/questions/help_54234

Need more context -- what does the diagram look like? 

9 - 2x = 35.....

+2x        +2x

9 = 35 + 2x

-35    -35

-26 = 2x

*1/2     *1/2

x = -13. 

30-60-90 triangles have a property where the shortest side is \(\frac{1}{2}\) of the longest side. It also has a property where the other leg is \(\frac{\sqrt3}{2}\) of the longest side in a triangle. 

Because the triangles are 30 - 60 - 90 triangles we know that the length of the hypotenuse of the smaller triangle is \(16 \cdot \frac{\sqrt3}{2} = 8\sqrt3\).

And to find the shortest side of this triangle we refer to what is above showing us that the shorter leg of the smallest triangle is \(8\sqrt3 \), which is your final answer. 

30.978

From the equation   2 moles of Fe will result in 3 moles copper

   so .325 moles Fe will result in  .4875 moles Cu

Cu weights 63.546  gm per mole

.4875 moles  * 63.546  gm / mole = ..........  gm of Cu

An ant is walking on a hexagon. At each step, he moves from the vertex on which he is standing to an adjacent vertex. After 6 steps, what is the probability that he is standing on the same vertex on which he began?  

If the ant is allowed to backtrack any time he wants to, my guess is the odds are 50-50.  In other words, he might or he might not. 

Close, but how many edges does a hexagon have?

Deleted - brain malfunction!!

We have a 30 60 90 triangle.

Let $BC = x.$ $AC = x \sqrt{3},$ and $AB = 2x.$

We also have $AC * CB = \sqrt{3} * AB.$

Let $DB = y.$ Then $$y^2+3=x^2,$$ and $$3+(2x-y)^2 = (x \sqrt {3})^2.$$ (by the pythagorean theorem.)

Expanding, we have $$y^2+3=x^2,$$ and $$4 x^2 - 4 x y + y^2 + 3 = 3 x^2.$$

If we solve this equation, we get $x=2$ and $y=1,$ for integer solutions. Thus $BD = y = 1.$

Simple. put them all in 1 lunch box and put the 4th one in the backpack.

Let this sum be $S.$

$S = 1/2 + 2/4 + 3/8 + n/2^n$

Multiplying by two:

$2S = 1 + 1 + 3/4 + ... 2n/2^n$

We subtract these, we can shift the infinite series over one term:

$S = 1 + 1/2 + 1/4 + ... + 1/2^n$

Using the geometric series formula, $\frac{1}{1-1/2} = \boxed{2}$