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Each interior angle of the decagon is ((n-2) * 180)/n= 144 degrees. So if D is shifted over to J which is 6 or 4 angles over, x= 144 * 6 or 144 * 4= 864 or 576 degrees. Neither angle is less than 180 degrees, so I'm not sure if the problem is correct.

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Unroll the glass cylinder to make a rectangle .....then reflect the image(to make for the fact the fly must cross over the lip of the glass to the inside) to make a double rectangle ....then use the measurements to calculate the distance

sqrt (12^2 + 9^2)  = 15

An area of a prism is the area of the base time the height. Box A's area is just 4 * 10 * 3= 120in^3. Box B's area is the area of the base triangle (8/2) * 3= 12 times the height 6, so 12 * 6= 72in^3. Since 120>72, Box B is made of less cardboard.

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I don't know if that will work.....the honey is INside the glass....the fly is on the OUTside.

I wrote a computer program, and it said that the minimum value was 3/4.

Start with the type of picture drawn by EP  -- respresenting the unrolled cylinder as a rectangle.

Place this rectangle upon a coordinate grid with the

-- bottom-left corner at (0,0)

-- bottom-right corner at (24,0)

-- top-left corner at (0,10)

-- top-right corner at (24,10)

-- fly at (24,4)

-- drop of honey at (12,7)

Moving from fly to honey will be the distance sqrt(12² + 3²)  =  sqrt(153)

[you can draw a right triangle and use the Pythagorean Theorem or use the distance formula]

OK....I think there is a shorter way anyway.....I think it is 15 cm.....diagram to follow.

\(\sqrt{x}-9=8\)

Add 9 to both sides

\(\sqrt{x}=17\)

Square both sides

\(x=289\)

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A cube with a volume of 1000 cm is a 10cm x 10cm x 10cm cube. This means that the largest cylinder that can fit in that cube is 10cm tall and has a diameter of 10cm. With that, the area of the cylinder is 25pi * 10= 250pi.

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Solve:  (3x + 1) / (3x + 2)  =  (x + 2) / (x - 5)

                  (3x + 1)(x - 5)  =  (x + 2)(3x + 2)                        (cross multiply)

              3x² + x - 15x - 5  =  3x² + 6x + 2x + 4                    (multiply out)

                           -14x - 5  =  8x + 4                                     (simplify)

                                 -22x  =  9

                                      x  =  -9/22

Given:  PQ : QR : RP  =  FG : GH : HF

              3  : x + 3 : 2   =   6 : 6x + 2 : 4

So:  (x + 3) : (6x + 2)  =  2 : 4                                                      (you could use 3 : 6; it doesn't matter)

       (x + 3) / (6x + 2)  =  2 / 4

                    4(x + 3)  =  2(6x + 2)                                                (cross multiply)

                     4x + 12  =  12x + 4

                               8  =  8x

                                1  =  x

Find  QR  =  x + 3  =  1 + 3  =  4

If C is the center of the circle, then angle(P₁CP₂)  =  360^o / 12  =  30^o.

To find the length of chord P₁P₂, we can use Heron's formula:  c²  =  a² + b² - 2·a·b·cos(C)

--->   c²  =  1² + 1² - 2·1·1·cos(30^o)

              =  1 + 1 - 2·sqrt(3)/2

              =  2 - sqrt(3)

Since all chords equal each other, the sum is:  12( 2 - sqrt(3) )  =  24 - 12·sqrt(3)

n(A union B)  =  n(A) + n(B) - n(A intersect B)

                      =    57  +   24  -  17  =  64

|x+1|+|x-2|=3

x+1+x-2=3   or     -(x+1)+x-2=3     or   x+1-(x-2)=3     or  -(x+1)-(x-2)=3

2x-1=3         or     -x-1+x-2=3        or   x+1-x+2=3       or  -x-1-x+2=3

2x=2            or            -3=3           or         3=3             or      -2x+1=3

x=1              or                      rubbish                            or        -2x=2

x=1 or x=-1

I have checked by substituting.  (in my head)

Idenity the graphed linear equation.

Hello Guest!

\(D:\ y=-5x-2\)

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Just to be clear.

I am not necessarily recommending the use of discord.

I really do not understand it but I do think Asad means well.

I have vaguely wanted to learn to use discord for a while now.

All I recommended to Asad is that he posted publicly rather than just privately to me. 

People can make up their own minds if this has any benefit to them.

If anyone has anything constructive to say that would be good.

The difference of measures between the arcs subtended by chord AB is 160°. Line l is tangent to the circle at point A. Find the measure of the angle between the tangent l and secant AB.

Hello Guest!

Die Differenz der Maße zwischen den durch den Akkord AB eingeschlossenen Bögen beträgt 160 °. Die Linie l tangiert den Kreis am Punkt A. Ermitteln Sie das Maß für den Winkel zwischen der Tangente l und der Sekante AB.

The angle between the radius vector and the secant is
(180°-160°) / 2 = 10°.
The angle between the radius vector and the tangent is 90°.
The angle between the tangent and the secant is
90° + 10° = 100°.

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If  a = b - 1/5b, then:

a =4/5b  and b =5/4a or:

b = a + 1/4a

You answered correctly  

(b c - b - c - 1) (b c + b + c - 1) 

a (x-h)^2 + k

3 (x+2)^2 -8

a = 3    h = -2       k = -8

I think the following will you the maximum numbers of coins:

1 - 13 quarters  x  0.25 = $3.25

$5.00  -  $ 3.25 = $1.75 left 

2 - 12 dimes  x  0.10 = $1.20

$1.75  -  $1.20 =$ 0.55 left

3 - 11 nickels x  0.05 =$ 0.55

$0.55 - $0.55 = 0 left.

4 - So, you can have a maximum of: 13 quarters  +  12 dimes  +  11 nickels = $5

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