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x+37>51   subtract 37 from both sides

x > 51 - 37

x > 14

Here's the first one

Anchor the British Diplomat in any position

The Germans can then be arranged in 4! ways = 24 ways  and the French can be seated in 3! ways = 6 ways

And the Germans and French themselves can each be seated in 2! ways  = 2 ways  on either side of the British  diplomat....so the total arrangements  =  2! * 3! * 4!  =  2 * 6 * 24  =  288 arrangements

1/3 x 300 = 100m - The length of the last 3rd of the drop.

Your question is not clear!.

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what is 2d^8 / 4d^3

2d^8 / 4d^3  divide both sides by 2

d^8/2d^3      subtract the exponents

d^(8 - 3) =d^5 /2

d^5/2

I have taken 7a under the square root sign. I also don't know what you mean by "extraneous solutions!"

Solve for a:
a = sqrt(7) sqrt(a) - 6

Subtract sqrt(7) sqrt(a) + a from both sides:
-sqrt(7) sqrt(a) = -a - 6

Raise both sides to the power of two:
7 a = (-a - 6)^2

Expand out terms of the right hand side:
7 a = a^2 + 12 a + 36

Subtract a^2 + 12 a + 36 from both sides:
-a^2 - 5 a - 36 = 0

Multiply both sides by -1:
a^2 + 5 a + 36 = 0

Subtract 36 from both sides:
a^2 + 5 a = -36

Add 25/4 to both sides:
a^2 + 5 a + 25/4 = -119/4

Write the left hand side as a square:
(a + 5/2)^2 = -119/4

Take the square root of both sides:
a + 5/2 = (i sqrt(119))/2 or a + 5/2 = -(i sqrt(119))/2

Subtract 5/2 from both sides:
a = (i sqrt(119))/2 - 5/2 or a + 5/2 = -(i sqrt(119))/2

Subtract 5/2 from both sides:
Answer: | a = (i sqrt(119))/2 - 5/2      or        a = -(i sqrt(119))/2 - 5/2

After the box turtle and the map turtle escape, there are 18 turtles left, with an average age of 21. Therefore, the sum of those 18 turtles ages is 18*21=378. This is 62 less than 440, so the sum of the escaped turtles' ages is 62.

The only two ages in the original table that add up to 62 are 26 and 36, so the box turtle (being the older of the two) must be 36.
 

Each of these animals has 4 legs. 

Do 10+40+20 and get 70

That is the total amount of animals

Now, multiply 70 by 4 to get 280

70*4=280

There are 280 legs, assuming none of these animals has lost a leg.

(e^pi)-pi = 19.9990999791894698

hmmm idk about this one. It's close and if you round its perfectly even at 20. 

7*=-28

*=-28/4

*=-7

Take 5.50 and multiply it by 250% or 2.5

5.50*2.5 = 13.75

The price of the toy is $13.75

6x³-y²-3xy 

x=-2

y=4

6(-2)³-(4)²-3(-2)(4)

6(-8)-16-(-24)

-48-16+24

-48+8

-40

The answer to the equation with the given values for x and y is -40.

x=-28/7

x=-4

Cheko has been saving part of his allowance in a bag every month. The bag containing $2 and $10 notes had a total value of $1116. 6 pieces of $10 notes were exchanged for $2 notes of the same value. In the end, the number of $10 notes was the same as the $2 notes. How many $2 notes were there at first?

Call the number of $2 and $10 notes at the end, N

So

2N  +  10N  =  1116    simplify

12N  = 1116     divide both sides by 12

N =  93

And 6 $10 bills  =  $60

So.....this = 30  $2  bills

So....there must have been  93 - 30  =  63  $2 bills initially  and 99 $10 bills

Check

2(63)  + 10(99)  =  $1116

i luv despacito..only beliebers would think the same way..luv yall guys

1/2*1/3=1/6

l 3x + 1 l  +  2  =  0

Notice that the result of the absolute value will be ≥ 0.....so  adding 2 to this will be positive......thus.....the left side can never  = 0

Taylor series expansion can be used here as follows:
Series expansion at x = 0:
Sin^-1(x) =x + x^3/3! + 3^2.x^5/5! + 3^2.5^2.x^7/7! + 3^2.5^2.7^2.x^9/9! + 3^2.5^2.7^2.9^2.x^11/11!.......and so on.
This is the same as:
Sin^-1(x) = x + [1/2.3]x^3 + [1.3/2.4.5]x^5 + [1.3.5/2.4.6.7]x^7 + [1.3.5.7/2.4.6.8.9]x^9....etc.
The steps here are self-explanatory.

Taylor Series  around x = 0

x + x^3/6 + (3 x^5)/40 + (5 x^7)/112 + (35 x^9)/1152 + (63 x^11)/2816 

if i received a check for $520,662 and my contract took out 8%, what was the original price?

Let the original amount = M, then we have:

M x [100% - 8%] = $520,662

M x 0.92 = $520,662 divide both sides by 0.92

M = $520,662 / 0.92

M = $565,936.96 - This is the original amount before 8% deduction.

There is no solution! See above. Are you sure you've written the equation correctly?

y=2.6x

y=0.5558x^2-2.482x+4.4573

Set the y's equal.....and we have

2.6x  =  0.5558x^2-2.482x+4.4573     subtract  2.6x from borh sides

 0.5558x^2 - 5.082x +4.4573  =  0

And the solutions are  

x ≈  0.982689      and   x  ≈   8.16089

We can see right away that there is no solution....it's impossible to subtract a non-zero quantity from something - in this case, 4m - and have the result equal to 4m