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The LCM  is sinx*cos^3x....so we have

cos(x) cos^3 (x) / [ sin (x) * cos^3 (x)] +

[2 sinx * sin x * cos^2 (x)] / [sin (x)cos^3 (x)] +

[ sin (x) sin^3(x)] / [ sin(x) cos^3 (x) ]  =

[cos^4 (x) + 2 sin (x) cos^3(x) + sin^4 (x)] / [ sin (x)cos^3(x) ] =

[cos^4 (x) + 2 sin (x) cos(x) * cos^2(x) + sin^4 (x)] / [ sin (x)cos^3(x) ]  =

[ cos^4 (x) + sin(2x)*cos^2(x) + sin^4(x) ]  / [ sin(x)cos^3(x) ]

An official Census is a comprehensive survey of the whole nation. It is estimated that in 1985, there were 90 million households in the U.S. A poll of 2,500 households cannot compare, in accuracy, to the official Census of some 90 million households. Therefore, I would say that the discrepancy is due to "The sample size was too small".

f(x)  =  x / (x - 1)^2

This will have a horizontal asymptote at y = 0    the graph will approach this as it increases without bound both in a positive and negative direction

And it will will have a vertical asymptote at x  = 1

As x approaches 1 from both sides, y → infinity

To see this....pick some x values on either side of x = 1 that are increasingly closer and closer to 1 and evaluate them in the function.....here are some test values :

 https://www.wolframalpha.com/input/?i=x+%2F+(x+-+1)%5E2++++for+x+%3D+.9,.99,+.999,.9999,+1.0001,+1.001,+1.01

Look  at the graph here : https://www.desmos.com/calculator/8yxvmnqor7

Thanks! ily 'guest' xoxo

D/85 =[D-30]/70, solve for D

D=170km - outgoing distance to the beach

170-30 =140 km-return distance

170/85 =2 hours - time taken to get to the beach.

[170 - 30] / 70 =2 hours - return time.

idk... would the formula be

   85x=70(x-30)?

Statement 2 and 3

Is this the full question? Theres something fishy about it...

You said:

G(-3) < G(2)

and

G(-3) = G(2)

Those can't both be true.

3000 / 15   = 200 truckloads full

f(x)  = [ 3x - 7 ] / [ x + 1 ]

For rational functions like this that have the same power poynomials in the numerator and denominator.......we can find the horizontal asymptote by dividing the term with the greatest power in the numerator by the term with the greatest power in the denominator.....so

3x / [ (1)x ]  =  3

So.....we will have a horizontal asymptote at  y = 3

And as x approaches -1 from the left, y →  infinity

And as x approaches -1 from the right, y → -infinity

So....the range is  (-infinity, 3) U (3, + infinity )

Here's a graph showing this : https://www.desmos.com/calculator/dq3shmjv9x

Hi Melody!

\(If \ p \in \Re \ and \ c ^ 3 = p, there \ is \ only \ one \ solution \ for \ c. \)

Greeting, asinus :- )

nuts

Note....144 = 12^2  and  256  =  16^2

So

144 * 256  = c^2

(12^2)(16^2)  = c^2

( 12 * 16 ) ^2  = c^2

(192)^2   = c^2

192  =  c

( sqrt (2)   + sqrt (3) ) ^2  =

( sqrt (2) + sqrt (3) ) * ( sqrt (2)  + sqrt (3) )  =

( 2 + 2sqrt(2)sqrt(3)  + 3 )  =

5 + 2sqrt(6)

nothing to see here

If 20 players had an average age of 20, then the sum of their ages = 20 *20 = 400

When two quit, 18 players had an average age of 19......the sum of their ages = 18 * 19  = 342

So......the sum of the ages of the two players who quit must have been 400 - 342  = 58

So......theoretically, any combination of ages that add to 58 are possible !!!!!

To square root something, in a way is to find the one number when multiplied by it self is equal to your starting number, for example the square root of 64 would be 8 since 8x8 is 64.

So if you are squaring the square root, the equation "simplified" would end up being 2+3. 

(sqrt of 2  +  sqrt of 3)2

the ^2 negates the square roots of 2 and three leaving you with 2+3 in the brackets.

So your answer would be 5

25 and 25

u r the greatest! Thanks!

The perimeter  is given by 2W + 2L     where W and L are the width and length

And we are told that  L = 2W - 6  .... so we have

84   = 2W + 2 ( 2W - 6)   simplify  

84 =  2w + 4W - 12

84 = 6W - 12    add 12 to both sides

96  = 6W    divide both sides by 4

96 / 6 = Width   =  16 cm

And the Length is   2(16) - 6  =   32 - 6   =   26 cm

5! ways  = 120 ways

A triangle is 180 degrees no matter what (all of the angles will add to make 180)

so

       180-130=50

and 50/2=25

 so the angles are 25 degrees, 25 degrees and 130 degrees 

if u add them all up again u get 180 degrees 

hope that helps!!!

factorials man. i dont know what group u got

Look at the graph, here :  https://www.desmos.com/calculator/wsr4thr9vo

Note that the function is defined for all values of x.

2 sqrt (5) / [ 2 sqrt (7) + 3 sqrt (3) ]

Note that 2 sqrt (7) = sqrt (28)  and 3 sqrt (3)  = sqrt (27)

So we have

2 sqrt(5) / [ sqrt (28) + sqrt (27) ]

Multiply top/bottom by the conjugate of the denominator → [sqrt (28) - sqrt (27) ]] 

And we have

[2 srqt (5)] [ sqrt (28) - sqrt (27)] / [  28 - 27 ]  =

[2 srqt (5)] [ sqrt (28) - sqrt (27)] / 1 =

[2 srqt (5)] [ sqrt (28) - sqrt (27)]   =

[2 sqrt (5)] [ 2 sqrt (7)  - 3 sqrt (3) ]=

4 sqrt (35)  - 6 sqrt (15)