geno3141

The outside circle has a radius of 10 cm; therefore, the area of the whole logo is:  pi·10²  or  100pi

The outside of the blue region is a circle of radius 7 cm; therefore its area is:  pi·7²  or  49pi

The inside of the blue region is a circle of radius 4 cm; therefore its area is:  pi·4²  or  16pi

The blue area is the outside region minus the inside region:  49pi - 16pi   =  33pi

The percentage of the logo that is blue is:  33pi / 100pi  =  33/100  =  0.33  =  33%

angle(VPL)  =   ½·arc(VKP)  =  ½·148^o  =  74^o

angle(JPV) + angle(VPL)  =  180^o     --->     angle(JPV) + 74^o  =  180^o​     --->     angle(JPV  =  106^o

Setting the denominator to zero will break up the domain into 5 parts.

2x² + x - 6  =  0     --->     (2x - 3)(x + 2)  =  0     --->     x = 1.5  and  x = -2.

The five parts are:  1)  the region below x = -2

                                2)  x = -2                                                              <--- at this point there is a break in the graph

                                3)  the region between x = -2 and x = 1.5

                                4)  x = 1.5                                                            <--- at this point there is a break in the graph

                                5)  the region above x = 1.5

Choose a number in the region below x = -2  ---   any number, I chose -5.  Place this number into the problem to see

if the answer is above 0 or below 0. It's above 0, so this region "works".

Choose a number in the region between x = -2 and x = 1.5  ---   any number, I chose 0. Place this number into the

problem to see if the answer is above 0 or below 0. It's below 0, so this region "doesn't work".

Choose a number in the region above x = 1.5  ---   any number, I chose 5.  Place this number into the problem to see

if the answer is above 0 or below 0. It's above 0, so this region "works".

So, the answer is:  (-infinity, -2)  union  (1.5, infinity)

Angle(A)  =  ½( arc(BC) - arc(BE) )

      50      =  ½( (4x + 20) - (2x - 10) )

      50      =  ½( 4x + 20 - 2x + 10 )

      50      =  ½( 2x + 30 )

      50      =  x + 15

            x  =  35

Can you finish this problem? ...

I think that it is the sqrt(39) ...

"Simplest radical form" means to take an answer like  sqrt(40)  and rewrite is as  2·sqrt(10).

7.21111....  is the common fraction  649 / 90 ...

What was the problem?

The median of an isosceles triangle is perpendicular to the opposite side and goes to the middle of the opposite side.

For this problem, call the midpoint of the side opposite angle(A) "M".

BM = 5 and AB = 8 and triangle ABM is a right triangle   --->   AM² + 5²  =  8²

Can you take it from here?

Since the triangle is an equilateral triangle, the incenter will be the center of the sphere (label this point C).

The incenter is two-thirds of the distance from a vertex to the midpoint of the opposite side; therefore LO  =  (3/2)·LC.

Since LC = 2m; LO  =  3m

Triangle LOK is a 30-60-90 right triangle, making  KO  =  sqrt(3)·m  and  LK  =  2·sqrt(3)·m.

Formula for the volume of a cone:  V  =  (1/3)·pi·r²·h   =   (1/3)·pi·[sqrt(3)·m]²​·3m

Formula for the surface area of a cone:  SA  =  pi·r·L + 2·pi·r²  =  pi·sqrt(3)·m·2·sqrt(3)·m + 2·pi·[sqrt(3)·m]²  

There are 20 cards.

How many are multiples of 3?    3, 6, 9, 12, 15, 18     =     6

How many are greater than 10?  11, 12, 13, 14, 15, 16, 17, 18, 19, 20     =     10

Without counting repeats there are 13 that work.

Probability:  13/20

sin(85^o) x 13  =  12.95

Therefore, an opposite side must be at least this long to porduce a triange.

10 is too short  -- there is no triangle.