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wow, nauseated, you really have been acting more like a vicious timberwolf than a adorable puppy lately. well, anonymous, if you want a war, I would be more than happy to give you one. All you have to do is: join the true side (my side). oh wait, it's 8:24 pm, time to send one of my men: Christopher

Parallelograms have the propery that consecutive angles are supplementary.

The length of the smaller diagonal - SD -  is given by the Law of Cosines, thusly :

SD^2 = 4^2 + 5^2 - (2)(4)(5)cos(41) =

SD^2  = about 3.288 units

The length of the longer diagonal - LD - is given by

LD^2 = 4^2 + 5^2 - (2)(4)(5)cos(180-41) =

LD = about 8.44 units

2 sin x = 1         add 1 to both sides

sin x = 1/2        divide both sides by 2

x = 150            use a calculator to solve 

2x-3(x-1)=-1     simplify

2x - 3x + 1  = -1

-x + 1  = -1      subtract 1 from both sides

-x  = - 2          multuply both sides by -1

x = 2

The 8th term is given by

4 + (4/5)(8 -1)  =

4 + (4/5)(7) =

9.6

"Between" 6AM  and 6PM  it occurs 11 times

1 time between  6AM and 7AM              1 time between   1PM and 2 PM

1 time between  7AM and 8AM              1 time between   2PM and 3 PM

1 time between  8AM and 9AM              1 time between    3PM and 4PM 

1 time between  9AM and 10AM            1 time between    4PM and 5 PM 

1 time between  10AM and 11AM          1 time between    5PM and 6PM 

1 time  {at  noon}

(1 - 2x^2)^5        

The x^4 term will be

C(5,2)[1]^3 [2x^2]^2  = 10 [1] [ 2x^2]^2  =  [10*4]x^4

So...the coefficient is 40

I'm assuming simple interest here

The interest we earn  is 1440 - 1200  =$240

So

I = Prt        Where P = 1200 and r = .04    {4%}

240  = 1200(.04)t   simplify

240 = 48t     divide both sides by 48

240/48 = t = 5 years 

2.5 cups makes 24 cookies   {2 dozen}

72 is three times as many.

So  3 x 2.5  = 7.5 cups to make 72.

Mathematically, we have

2.5 / 24 = x / 72     cross-multiply

180 = 24x       divide both sides by 24

x = 7.5

The boat that is traveling 34 mi/h will travel 68 miles in 2 hours.

The boat that is travelind 22 mi/h will travel 44 miles in 2 hours.

The angle between is 100°.

The distance between them is the third side of a triangle. Use the law of cosines:

c²  =  a² + b² - 2·a·b·cos(C)

c²  =  68² + 44² - 2·68·44·cos(100)

Can you finish it from here?

Yes? No?

8 x 26 cm  =  208 cm

Multiplying by 1/2 is the same as dividing by 2 ...

28 x (1/2)  =  28 ÷ 2  =  14

guys just stop fighting. it will make my early birthday present if you guys stop fighting

Beside the obvious way of multiplying this, factor by factor, you can use this expansion:

(a + b)⁵  =  ₅C₀ · a⁵ · b⁰ + ₅C₁ · a⁴ · b¹ + ₅C₂ · a³ · b² + ₅C₃ · a² · b³ + ₅C₄ · a¹ · b⁴ + ₅C₅ · a⁰ · b⁵ 

In this problem:  a = 2x     b = -1:

(2x - 1)⁵  =  ₅C₀(2x)⁵(-1)⁰ + ₅C₁(2x)⁴(-1)¹ + ₅C₂(2x)³(-1)² + ₅C₃(2x)²(-1)³ + ₅C₄(2x)¹(-1)⁴ + ₅C₅(2x)⁰(-1)⁵ 

   =  (1)(32x⁵)(1) + (5)(16x⁴)(-1) + (10)(8x³)(1) + (10)(4x²)(-1) + (5)(2x)(1) + (1)(1)(-1)

   =   32x⁵ - 80x⁴ + 80x³ - 40x + 10x - 1

. . . Paint ;)

Thanks :)

Do not even address me as young lady. Your not my father! Also, I just don't want you to fight, come on just listen to me. It will make my day and my birthday next week if you don't fight Alan. I'm trying to make peace here.

what you saying about me, baka? you calling me "underranked?" if you are, you and I have lots of talking to do, young lady!