geno3141

Angle(FHG) = 180 - 135 = 45

Angle(FGH) = 180 - 105 = 75

Angle(HFG) = 180 - (45 + 75) = 60

Angle(DFC) = angle(HFG) = 60

Angle(FDC) = 180 - 119 = 61

Angle(DCF) = 180 - (60 + 61) = 59

Angle(BCA) = 180 - 59 = 121

Angle(CBA) = 180 - (40 + 121) = 19

Let's finish labelling the vertices of the triangle:  let C be the vertex at angle(x) and let D be the upper vertex.

Arc(BC) = 160^o because it is double the angle.

Arc(CD) = arc(BC) because their chords are congruent. Therefore, arc(CD) = 160^o.

This means arc(BD) = 360^o - 160^o - 160^o = 40^o.

Angle(x) is one-half the arc it intercepts, so it is 20^o.

Since  WX || YZ   --->   angle(WXY) + angle(XYZ)  =  180^o  

                            --->             (3x - 5) + (90) + (2x)  =  180^o

                            --->                                 5x + 85  =  180^o

                            --->                                         5x  =  95^o

                            --->                                           x  =  19^o 

Just at the end.

For instance:  add these numbers together:  0.545, 0.545, 0.545, 0.545, 0.545:

Unrounded, you get 2.725.

If you round at the end (to the nearest hundredth), you'll get 2.73.

If you round at every step, you would have  0.55, 0.55, 0.55, 0.55, 0.55  for a total of 2.75, which is too large.

Sometimes, it will make no difference; but, to be save, only round the last answer.

Since  2 + sqrt(5)  is a root  2 - sqrt(5)  is also a root.

This means that  [ x - (2 + sqrt(5)) ]  and  [ x - (2 - sqrt(5)) ]  are factors.

Multiplying these factors together gives you  x² - 4x - 1.

Since  1 - sqrt(2)  is a root  1 + sqrt(2)  is also a root.

This means that  [ x - (1 - sqrt(2)) ]  and  [ x - (1 + sqrt(2)) ]  are factors.

Multiplying these factors together gives you  x² - 2x - 1.

Multiplying  x² - 4x - 1  and  x² - 2x - 1  together gives you  x⁴ - 6x³ + 6x² + 6x + 1.

Complete the square of  4x² + 5x + 2

Step 1:  Separate the  4x² + 5x  part from the  2:     [ 4x² + 5x ] + 2

Step 2:  Factor out the 4 from the first part:              [ 4(x² + 5/4x) ] + 2

Step 3:  Complete the square of  x² + 5/4x

              --  Divide  5/4  by 2   --->   5/8

              --  Square this result   --->   25/64

Step 4:  Be careful when putting this into the parentheses, because this value will be multiplied by 4, so you'll

              have to subtract out  4 · 25/64  =  25/16  to keep the expression balanced:

                                                                               [ 4(x² + 5/4x + 25/64) ] + 2 - 25/16

Step 5:  Simplify:  4(x + 5/8)² + 7/16

Usng the formula  Area  =  pi · radius²

1)  Find the area of the inner-most circle (radius = 1)

2)  Find the area of the target, which is outer-most circle (radius = 3)

3)  Divide the answer of step 1 by the answer of step 2.

The proportion is:  MP : PN  =  PN : PO

So, you need to solve:  10 : x  =  x : 2

AC²  =  AB² + BC²     --->     AC²  =  12² + 5²     --->   AC  =  13

AD / AB  =  AB / AC     --->     AD / 12  =  12 / 13     --->     AD  =  144/13

DC  =  AC - AD     --->   DC  =  13 - 144/13     --->     DC  =  25/13

AD / DB  =  DB / DC     --->   DB²  =  AD · DC     --->     DB²  =  (144/13) · (25/13)

                  --->     DB  =  60/13

DB is the geometric mean of AD and DC.