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The golden ratio is used in architecture and art because it is believed to produce aesthetically pleasing divisions and proportions. ... It is widely believed that the design of the Parthenon in Athens is based on the golden ratio

yes i would 

What do you want to do....graph this ???

log ₂ 16  + log ₂ 16   =   4 + 4  =  8

So

A. log ₂ 256  =  8

B.  8

C  . log  ₂ 2^8  =     8 log ₂ 2  = 8 * (1)  =  8

Parallel lines have the same slope

The slope of  r  is     [ -4 -1 ]   / [ -4 -6] = [ -5 ] / [-10] = 5/10  = 1/2

A (0,2) and (6, 5)

slope =   [ 5 - 2] / [ 6 - 0]  =  3/6  =  1/2     parallel

B(8,2) and (6, 5)

slope = [ 5 - 2] / [ 6 - 8 ] =   3/-2     =  -3/2   not parallel

C(2, 0) and (5,6)

slope  = [ 6 - 0 ] / [ 5 - 2]  =  6 / 3  =  2   not parallel

D(5,2) and (3, 0)

slope  = [ 0 - 2 ] / [ 3 - 5] = -2/-2  =  1   not parallel

1/6+3/4=11/12

Suppose ABC is a scalene right triangle, and P is the point on hypotenuse AC  such that angle ABP = 45° . Given that AP=1 and CP=2, compute the area of ABC.

Because angle ABP = 45, then the right angle ABC is bisected....this sets up the following relationship in the triangle

AP/CP = AB/BC

1/2  = AB/BC

Let AB = x

So BC = 2x

And AC = 5

So....by the Pythagorean Theorem, 

AB^2 + BC^2  = AC^2

x^2 + (2x)^2  =  5^2

x^2 + 4x^2  = 25

5x^2  =  25

x^2  =  5

x =  sqrt (5)  = AB

2x  = 2sqrt(5)  = BC

So.....the area of ABC =  (1/2)AB * BC  = (1/2)sqrt(5) * 2sqrt (5)  =  5 units^2

I'll do the first.....the second should be easy based on this

3(1) - 1  = 2

3(2) - 1  = 5

3(3) - 1  = 8

3(4) - 1 = 11

3(5) - 1  = 14

Let A = Probability of selecting a black chip with an even number = (1/2)

Let B = Probabilty of selecting a black chip = (3/5)

P ( A  l B )  =   P (A) * P(B)         (1/2) * (3/5)

                      ___________  =  __________ =             1 / 2

                          P(B)                    (3/5)

This makes sense....we already have a black chip in hand.....there is a (1/2) probability that it has an even number

Triangle ABC has AB=BC=5 and AC=6. Let E be the foot of the altitude from B to AC  and let D be the foot of the altitude from A to BC. Compute the area of triangle DEC.

Here's an image :

Let A = (0,0)   C = (6,0)

The triangle is isoceles.....so E will bisect AC....so  ....EC = 3

And....triangle AEB is a 3-4-5  right triangle with AE = 3, EB = 4  and AB = 5

So....B = (3,4)

Sine angle BCE = 4/5 = sin DCA = sin DCE

And we can find AD  using the Law of Sines

AD/sin DCA = AC/sin ADC

AD/ (4/5) = 6/sin90

AD = (4/5)6  =  24/5 =  4.8

And...using the Pythagorean Theorem, 

DC =  sqrt (6^2 - 4.8^2 )   = 3.6

And  EC = 3

So....the area of triangle DEC  =

(1/2) (EC) (DC) sin DCE   =

(1/2)(3)(3.6) (4/5)  =

4.32 units^2

Just add these and divide by 2.......that will be your answer

We can use something known as "Pick'sTheorem" to  answer this...

When the vertices of a figure have integer coordinates [ like this one]....the area is given by

(Number of  integer coordinates on  the boundary / 2 ) +( number of interior  points with integer coordinates) - 1 

Number of integer coordinates on the boundary   =  5

Number  of integer coordinates  in the interior = 21

So....the area is

(5/2)  + 21 - 1   =

2.5 + 20  =

22.5 units^2

I figured it out it was C

It equals 3x−y.  

g=1 or g=−3

no like terms but if its 

2x+3=0 

then

x=-3/2

^{I blame the insanity on Melody, she’s always saying degrading stuff to people on here. -Synth}

I’ve not noticed any insanity, but I suppose your already stressed brain is now overheating, compelling this desperate observation.  Get a life!

^{I detect plagiarism... -PartialMathematician} 

I detect arrogant stupidity at the genetic-molecular level and dumbness at the quantum level.

^{Actually, Grammarly detects plagiarism -PartialMathematician} 

No. It doesn’t. You just think it does.  Detecting plagiarism requires educated human-level intelligence. That requirement probably leaves you out. 

^{I just say, Gah Ga! -PartialMathematician} 

No surprise! These are stupidity marker identifications: 

GA

^{a little overboard dont you think you could still get your point across without cursing them out –Dark calculus}

A little moronically stupid, don’t you think? You could get your point across better by using punctuation.  Sign up at Learn-me-how-to-wrighte-gooder.com.  Use DarkEnglish as your user name. 

I scarcely cursed him-out, DC. I used shitball, to maintain the adjective continuity started by another (sometimes very funny) troll.  My post needs at least one vulgarity/curse word else the intended recipient would not understand it –he probably doesn’t anyway.

 It’s important to understand your audience and to compose at or near their level of understanding. Sometimes it has to be dumbed-down. Most understand vulgarities and curses; they are called base words for a reason. A string of obscenities will not make for a balanced, coherent commentary, but a few of them can add catalytic seasoning of understanding.  

Reread the edited post. Is it better? I think it is, but I doubt it will change the melt rate of delicate snowflakes. 

What do you think? Or do you think? Probably not. 

GA

the positive integers are arranged in the pattern illustrated below if this pattern continues indefinitely, what is the number immediately above 39863?

1  2 5 10 17 26

3  4 7 12 19 28

6  8 9 14 21 30

11 13 15 16 23 32

18 20 22 24 25 34

27 29 31 33 35 36

As follows:

Actually, there is no need for my equation (1).  Equation (2) shows that u_n is strictly less than 2 - √n for all n greater than or equal to zero. 

Thanks Rom   

That's some keen insight there Melody!