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Hint:  Use Pick's Theorem.

Since there are 5 factors and the product is 1/32, find the fiftth root of 1/32, which is 1/2.

Solve:  cos( pi / n )  =  0.50

--->   pi / n  =  cos^-1(0.50)

--->        pi  =  n · cos^-1(0.50)

--->        n  =  pi / cos^-1(0.50)

--->        n  =  3

Each of the other factors have a value of -0.50.

It's very simple...

Let's find the angle using the tree height and the length of the shadow.

Tree height   H_t = 30 ft

Length of the shadow is 65 ft

Length of the tree shadow is  65 ft - 25 ft = 40 ft

Angle   A = ?                tan(A) = 30/40 ≈ 36.87°

Pole height    H_p = tan(A) * 65 = 48.75 ft   

- sqrt( -29 )  =  -i·sqrt(29)

The volume of a cube can be found by:  V  =  s³   --->   512  =  s³   --->   s  =  8

The surface area of one side is  8 x 8  =  64 square inches.

If you want to know the surface area of three sides, you will need to multiply this answer by 3.

There are two asymptotes, one at x = 1 and the other at x = 5.

Therefore, the denominator must include these two factors:  (x - 1)(x - 5).

Since only one choice has this, it must be the one that you choose.

In parallelogram the adjacent angles are supplementary.

Angle  A = 62°         

Angle  ADC = 180° - 62° = 118°   

Ok, after getting some help for number 2, I can't trust that number 1 is right because first, you didnt really show much work, and second, i got a different answer that was correct for number 2.

isnt the question asking for what a+b+c is?

you can create a ratio. the answer is 150 paperclips.

o wait its 150

They probably meant this  ( see diagram )  

The floor:  9 feet by 12 feet is the same as 108 inches by 144 inches.

The area will be 108 inches x 144 inches  =  15,552 square inches.

Each tile is 4 inches by 6 inches which is an area of 4 inches x 6 inches  =  24 square inches.

Dividing 15,552 square inches by 24 square inches gives an answer of 648 tiles.

h  =    x

b₁ =   x

b₂ = 2x

Area  =  ½·h·(b₁ + b₂)   --->   Area  =  ½·x·(x + 2x)    --->   Area  =  ½·x·(3x) 

                                     --->   Area  =  (3/2)·x²

Let             x  =  liters of the 10% solution.

Then  30 - x  =  liters of the 30% solution

(percentage) · (amount)  +  (percentage) · (amount)  =  (final percentage) · (final amount)

             0.10 · x               +               0.30 · (30 - x)     =                        0.25 · 30 

                                                  0.10x + 9.00 - 0.30x  =  7.50         

                                                               9.00 - 0.20x  =  7.50

                                                                       - 0.20x  =  -1.50

                                                                                x  =  7.5     liters of the 10% solution

                                                                        30 - x  =  22.5    liters of the 30% solution

Try this:  (x - 1) / [ (x + 1)·(x - 2) ]  <= 0

There are 2! = 2 ways to arrange the 2 refuseniks.

There are 4! = 24 ways to arrange the other 4.

Multiplying these together, we get 48 ways.

There are 10 different places to put the refuseniks:  (X = refusenik; - = other)

          X-X---          -X-X--          --X-X-          ---X-X

          X--X--          -X--X-          --X--X

          X---X-          -X---X

          X----X

10 x 48  =  480 ways.

Thank you so much!

Here are the additional answers: 1 bag will seed 80 sq m. Thus 26708 sq m will need 26708/80 = 333.85 = 334 bags. Cost of every bag = $12.64 => Cost to seed entire plot = 334 * 12.64 = 4221.76$

it's 7:11 because surface area of a cylinder is 2\(\pi\)rh+2\(\pi \)r^2, so you have to take the square roots of 49 and 121 and you get 7:11

Thank you! Do you know how to do #2?

A graphing form for a parabola is:  y - k  =  a(x - h)² where (h, k) is the vertex.

The vertex is midway between the focus and the directrix.

Since the focus is (4, 3) and the directrix is  y = 1, the vertex is at (4, 2).

Therefore, the graphing form is:  y - 2  =  a(x - 4)².

To find a, let's put the value of (8, 6) into this formula:  6 - 2  =  a(8 - 4)² 

                                                                                            4  =  a(4)²   

                                                                                            4  =  a·16

                                                                                            a  =  4/16   --->   a = ¼

So, the equation is:  y - 2  =  ¼(x - 4)² 

Multiplying out:         y - 2  =  ¼(x² - 8x + 16)

                                 y - 2  =  ¼x² - 2x + 4

                                       y  =  ¼x² - 2x + 6

a = ¼   b = -2  c = 6