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we make them have a LCM denominator which is 30 so the equation beomes 4 9/30 + 3 12/30+ 10/30 + 15/30 but then we change the 4 9/30 into 129/30 and 3 12/30 becomes 102/30 so the equation becomes  (129 + 102 + 10 + 15)/30=256/30=128/15=8 16/30=8 8/15 so our final answer is 128/15 or 8 8/15

so we get that 1/2=0.5 and so the equation becomes 0.75-0.25+0.5=1 so our final answer is 1.

so we have that 1/2=0.5 and 3/8=0.375 so when we plug them in we have 9.25-0.5+0.375=9.125=9 1/8 so our final answer is 9.125 or 9 1/8.

If p = sin(arccot(x)), q = cot(arcsin(x)), and p^2 = f(q)/(1 + f(q)), then find f(5).

thank you somuch

We have \(k(x) = 3 - \sqrt{x-3}\)

Obtain by solving the quadratic \(x=k^2-6k+12\) for k and choosing the branch that is a reflection of \(x^2-6x+12\) in the line y = x.

First, find the equation of the dashed line :  y =  1/2  x-1/2

    the shaded area is GREATER than this line, but does not include the line

y > 1/2 x - 1/2

You are quite right.  I simply calculated the total distance travelled, without thinking carefully about the paint!

The graphs below show the various stages:

Find the radius of the circle passing through the points (0,0), (2,0), and (-1,3).

Circumcenter is located at  (1, 2)

yeaaa i'm an army too lol

.25 is the same as   25 / 100   = 1/4

so you have    9  1/4   - 1/2   + 3/8      to add/subtrat fractions , you need to have a common denominator ....8  will work in this case (you could use 12 or 16   etc)

9 1/4   =  37 / 4   =   74/8

1/2 = 4/8

so you have     74/8 - 4/8 + 3/8   =  (74-4+3) / 8 = 73/8 =  9  1/8

4 + 2i    would be the other root.

Simplify:        [ a(a + 1) / 2 ]²  -  [ a(a - 1) / 2 ]² 

  =                  [ (a² + a) / 2 ]²  -  [ (a² - a) / 2 ]²​ 

  =            (a⁴ + 2a³ + a²) / 4  -  (a⁴ - 2a³ + a²​) / 4 

   =              [ (a⁴ + 2a³ + a²)  -  (a⁴ - 2a³ + a²​) ]  /  4

   =              [ a⁴ + 2a³ + a² - a⁴ + 2a³ - a² ] / 4

   =                                     4a³ / 4

   =                                         a³ 

His cost is:  26 kg x $20.00 / kg  +  30 kg x $36.00 / kg  =  $1600.00

He creates:  26 kg  +  30 kg  =  56 kg.

His income:  56 kg x $30.00 / kg  =  $1680.00

His profit:  $1680.00 - $1600.00  =  $80.00

His percentage profit:  $80.00 / $1600.00  =  0.05  =  5%

-5*-2 = +10 

That is the largest possible value.

There are 360^o around each point.

There are 60^o in each vertex angle of an equilateral triangle.

There are 90^o in each vertex angle of a square.

To find the number of degrees in each vertex angle of a regular pentagon, use this formula:

    degrees  =  (n - 2)·180^o / n  (where n = number of sides)  =  (5 - 2)·180^o​ / 5  =  108^o.

360^o - 60^o - 90^o - 108^o  =  ..... 

( x + 1/x ) / ( x - 1/x )  =  5 / 4

Cross-multiply:       4( x + 1/x )  =  5(x - 1/x )

                                  4x + 4 / x  =  5x - 5/x

Multiply by x:                4x² + 4  =  5x² - 5

Add 5:                           4x² + 9  =  5x² 

Subtract 4x²:                          9  =  x²

Two possible answers:  3  and  -3

If you place these numbers back into the original equation, you will find that 3 works and that -3 doesn't work.

Hi fellow ARMY~

1/2 in decimal form is 0.5. We replace 1/2 with its decimal value. So we have 0.75-0.25+0.5=0.5+0.5=1.

What is the actual problem? Is it a loan of 2060 to be paid back in monthly payments of $31 per month over a period of 92 months? Just state your question in plain English and we will give you the formula and show you how to solve it.

Parallel line ==> coefficients of x are equal

3a + 2 = a - 4 ==> 2a = -6 ==> a = -3.

1)  A square, a regular pentagon, and a regular n-gon surround a point.

     The number of degrees in each vertex angle of a regular n-gon is:  (n - 2) · 180^o / n

     We know that each vertex angle of a square has 90^o.

     Each vertex angle of a regular pentagon has  (5 - 2) · 180^o / 5  =  108^o.

     There are 360^o around each point.

     Subtracting the vertex angle of a square and the vertex angle of a regular pentagon,

     we are left with:  360^o - 90^o - 108^o  =  162^o.

     Now we use the formula:   (n - 2) · 180^o / n  =  162^o  to find the value of n.

                  (n - 2) · 180^o  =  162^o · n

               180^o · n - 360^o  =  162^o · n

          180^o · n - 162^o · n  =  360^o 

                            18^o · n  =  360^o 

                                     n  =  20

The areas of similar polygons have the same ratio as the squares of the corresponding sides.

[Perimeters count as lengths.]

Since Area ( polygon A )  +  Area( p0lygon B )  =  65     --->     Area( polygon B )  =  65  -  Area( polygon A )

Area( polygon A) : Area( polygon B )  =  Perimeter( polygon A )² : Perimeter( polygon B )² 

Area( polygon A) : [ 65 - Area( polygon A ) ]  =  12 : 18

To make the algebra easier, call Area( polygon A ) = x

--->   x : ( 65 - x )  =  12 : 18     

Cross-multiply:  12( 65 - x )  =  18x

                            780 - 12x  =  18x

                                     780  =  30x

                                          x  =  26

--->   65 - x  =  65 - 26  =  39

Team A will win the tournament if the games go like this:

A and A:                              (0.60) · (0.60)  =  .....

A and B and A:       (0.60) · (0.40) · (0.60)  =  .....

B and A and A:       (0.40) · (0.60) · (0.60)  =  ..... 

Find each of the individual probabilities and add those values together  .....