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this was all that was given and that's what I thought as well but I figured anyone on here had more experience and might be able to figure it out differently.

Kinda' hard to answer without a pic, SS.....

Thank you...it's my fault, could have been logged in ...!

Sorry, tertre....didn't know that was you answering....good job!!!!

If we draw a diagonal....this will divide the parallelogram into two equal areas

So....one of these areas forms a triangle with an area of 4√2  and sides of s and 2s   and an included angle between these sides of 45 degrees

So

Area of triangle  =   (1/2 (s) (2s)sin (45)

4√2  = (1/2)(2s^2) * (1/√2)

4√2  = s^2/ √2       multiply both sides by √2

4√2 *√2  =  s^2

4 * 2      =   s^2

2 √2   =  s

Draw a parallelogram.

Break the parallelogram into two 45-45-90 triangles.

Take one of the triangles, and fill in all the missing lengths.

Opposite to the 45 angles should be \(\frac{s\sqrt{2}}{2}\).

Now, the area of a a parallelogram is base * height, and \(\frac{s\sqrt{2}}{2}*2s=8\sqrt{2}, 2s^2=16, s^2=8, s=2\sqrt2.\) 

Not too much to sweat, here

We have a 30-60-90 right triangle

The side opposite the 30 degree angle  =  (1/2) the hypotenuse  = 13  =  this is one leg

The side opposite the 60 degree angle  =  13√3  = this is the other leg

Area  =  product of the legs  / 2    =    (13) (13)√3   / 2    =   169√3 / 2 ≈   146.4 cm^2

BTW....the "height" is optional....it's either one leg length or the other.....depending upon your favorite orientation  !!!!

log₄(11) + log₈(11) + log₆₄(11)

Note that we can use the change-of-base theorem to write

log11/ log4  + log 11/ log 8   +  log 11 / 64  =

log 11/ log2^2    + log 11 / log 2^3  +  log 11 / log  2^6   =

log 11/ [2 log 2]  +  log 11 / [ 3 log 2 ] + log 11 /  6 log(2)  =

[ 1/2 + 1/3 + 1/6]  log 11 / log 2   =

[ 3/6 + 2/6 + 1/6 ]  log 11 / log 2  =

[ 1 ]   log 11 / log 2  =

Write back as

log ₂ 11

So  b + n  =   13

https://web2.0calc.com/questions/for-each-problem-below-solve-algebraically-then-use_2#r1

(x+4)(x-3) = 0    expand

x^2 +x -12 = 0

Second one....the idea here is to find the x and y intercepts  of the line

x intercept....let y = 0

2x + 0 = 6

2x = 6

x = 3

y intercept......let x = 0

2(0) + y = 6

y = 6

Triangle area  =    (x int) (y int) /2    =     (3) (6) / 2   =   9  units^2

x = 3y

2x + 5y  = 11          sub the first equation into the second  for x

2(3y) + 5y = 11

6y + 5y = 11

11y = 11

y = 1

An d  x  = 3(1)  = 3

So  A  = (3, 1)   .....sum of coordinates  =  4

We can use the cosine inverse to find the angle

cos (theta)  = 5 / 25   = 1 / 5

So

arccos (1/5 ) = theta  ≈  78.5°......this is unsafe 

To find the safe distance, D.....we can solve this

cos 75  =  D  / 25          multiply both sides by  25

25 * cos 75  ≈  6.47 ft ≈  6.5 ft = D

We are looking for two integers that multiply to -24  and sum to -5

-8  and +3  seem to fit the bill....so....we have.....

(x - 8) ( x + 3)

The diagonal  length  =  40√2  ft

And we need to double this since we have two diagonals  = 80√2 ft

And the perimeter of the room is  4 * 40  =  160 ft

So     80√2 + 160  ≈  273 ft  of lights needed

So....the number of strands neede  = ceiling [ 273 / 30 ]  =    10 strands

sumfor(n, 2, 100, (log(n) / log(100!)) = 157.97 / 157.97 = 1

Thanks, CU!!!

Using CU's diagram.....

BF = 6    and angle FPC = 75°

tan FPC  = FC /PF

tan 75 = FC / 6

6tan 75 = FC

6 tan (45 + 30) = FC

FC  = 6 [ tan 45 + tan 30 ] / [ 1 - tan45*tan30]

FC = 6[ 1 + √3/3] / [ 1 - 1*√3/3]   

FC = 6 [ 3 +  √3] / [ 3 - √3]

FC = 6[9 + 6√3 + 3 ]  / [ 9 - 3]

FC = 6 [ 12 + 6√3 ] / [ 6]

FC = [ 12 + 6√3 ]

So....BF + FC  =  6 + [ 12 + 6√3]   =  18 + 6√3  =  BC

So   AB   =   (2/√3)BC   = (2/√3) [ 18 + 6√3]  =  36/√3  + 12 =  12√3 + 12

10% =100% * (0.5)^(d/73.83), solve for d
0.1 =0.5^(d/73.83)     Take the log of both sides
log(0.1) =d/73.83 * log(0.5)
d/73.83 =log(0.1) / log(0.5)
d/73.83 =3.3219281.....
d =73.83 * 3.3219281...
d =~245 - days for given amount to decay to 10%.

Ok so can you explain more about how you would find the square then because you don't know any of the sides except the rules 

2014 - 2006 = 8 years

8,600 - 3,800 =$4,800 - Growth over 8 years

$4,800 / 8 = $600 - Linear growth per year.

2014 - 2002 = 12 years since the initial deposit.

12 x $600 = $7,200 - growth over 12-year period.

$8,600 - $7,200 = $1,400 - initial deposit in 2002.

So that the linear function would look like this:

$8,600 =$1,400 + $600n, where n is number of years since 2002.

Use your knowledge on special triangles (especially 30, 60, 90)

Also use this diagram to help:

Try to find the side length of the square then use special triangle rule to find the bottom side of the triangle, this will lead you to the length of BC.

shut up noah ur jsut salty and i am not lying cause u verified what i said lol dumb

im using it as both unlike you who jsut makes salty comments about me and iamjeff