All Answers 358149 Answers

arctan (1/2)  =  theta   =  26.565°

Area  =   (1/2)(60)(40) sin (26.565°)  ≈   536.66  units^2 

We know that the three angles of a triangle sum up to 180, so angle Z = 75. We know that X = 60, so the angle bisector must split YXZ into 30 and 30. Now we can see that the angle bisector has split triangle XYZ into two smaller triangles, one being XWZ. Again, we can use our knowledge of the sum of triangle angles, so X + W + Z = 180 = 30 + 75 + W

So angle XWZ = \(\boxed{95}\)

A =  (3/5)B     

A + 12  :  B + 12   =   3 : 4

(3/5)B + 12  :  B + 12  =  3 :  4

[(3/5)B + 12 ]           3

___________  =    ___               cross-multiply

    [ B + 12 ]              4

4  [  (3/5)B + 12 ] =  3 [ B + 12 ]

(12/5)B + 48  =  3B + 36

48 - 36  =  3B  - (12/5)B

12   =  (3/5)B

12 (5/3)  = B  =  $20  =  what  Brent had at first

The answer is (0,-11/3).

Any x  that makes the denominator =  0    is not in the domain

sqrt (x^2 - 3x)

But     x^2  - 3x       must  be > 0

So

x^2 - 3x  > 0

x ( x - 3)  >  0

This is true  if    x < 0  or  x > 3

So.....the domain is

(-inf , 0)  U  (3 , inf)

a/3  + 1  = a + 3

1 - 3  =   a - a/3

1 - 3  =  (2/3)a

-2  =  (2/3) a

(3/2)(-2) = a

-3  =  a    {  just as figlavaplanet  found  !!!  }

The one and only vaule for a is -3

(100 + N)  / (60+N)      =  (180 + N) / (100 + N)

(100 + N)^2  =  (180 + N) (60 + N)

10000 + 200N  + N^2  =  10800 + 240N + N^2

200N - 240N =  10800  - 10000

-40N  =  800

N =  800 / -40  =   -20 

Common Ratio   =  (100 -20) / (60 - 20)  =  80 / 40   =   2

sin A  / CB  =   sin B / AC

sin (45)  / (4sqrt 3)  =  sin B  / (4 sqrt2)

(1/sqrt 2)  / sqrt 3  =  sin B / (sqrt 2)

1 /sqrt (3)  = sin B

arcsin (1/sqrt 3)  = B  ≈  35.26°

Sum of first ten terms  -  Sum of first nine terms =   tenth term  ......so....

(10)(10+1)(10-2)  -  (9) (9 + 1) (9 - 2)   =

880  -    630   =  

250  = tenth term

 N=2; D=12;a=(listfor(S,S=17, S=24, (sumfor(k, 0, ((S - N)/D), ((-1)^k * (N nCr k) * (S - D*k - 1) nCr (N - 1));printa, ">>Total =",sum(a)

(8, 7, 6, 5, 4, 3, 2, 1) >>Total = 36

The probability is: 36 / 144 ==1 / 4

Rearrange as

-11x + y =   14

  ax + y  =   - 4   

This system will have no solutions if  a  =  -11

yea, Hes like an epic troll if i remember correctly

1/x  + 1/y =  3

1/x -  1/y =   7                   add these equations

2/x  = 10           

2/10  = x   =  1/5

So

1 / (1/5)  + 1/y  =  3

5   +  1/y   =  3

1/y  =  3 - 5

1/y  =  -2

-1/2  =  y

So

x +  y  =  

1/5    -  1/2   = 

2/10  -  5/10  =

-3 / 10

Simplify the left-hand side with a common denominator: \(\large{{(x^2-4x)g + (x+5)h \over x^3 + x^2 - 20x } = {x^2 - 3x + 5 \over x^3 + x^2 - 20x}}\)

Now, recall that the denominators of the fractions are equal, we can ignore them, giving us: \((x^2 - 4x)g + (x+5)h = x^2 - 3x + 5\)

The only way to get an \(x^2\) term on the left-hand side is if it comes from the term \((x^2 - 4x)g\), meaning \(gx^2= x^2\)

Thus, we know that \(g = 1\). 

Likewise, doing the same thing with the \((x+5)h\) term, we notice that the coefficient of 5 can only come form the term 5h, meaning \(h = 1\)

Thus, the ratio \({ h \over g} = \color{brown}\boxed{1}\)

Lancelot Link???

Isn't that the thing with the monkey ????

I will assume that all the cups are different and all the balls are the same.

There are 10C3 ways to choose three cups = 120

There are 10C2 ways to choose 2 cups = 45  

    but either one could have the 2 balls so that is realy 90 ways

there are 10 ways they can all be in the same cup

so that makes a total of 220 ways and 90 of those have exactly 2 balls in one cup

so     90/220  = 9/22

I am not 100% sure it is correct.  I think it is though.

When you are given the answer that your teacher/site says is correct please share it with us.

Start by sorting them into bigger than 1 and smaller than 1.

then come back again if you need too.

The first quadratic simplifies to 20x^2 + 30x + 26, and the second one expands to m^2x^2 + 2mnx + n^2. As the constant terms are the only terms that are different between these two, we know that 2mnx = 30x. Simplifying, we get \(mn=\boxed{15}\)

If we need a binomial, then that means we need only 2 terms. One being \(36x^2\), and the other being an integer. This means we have to cancel out the terms with a variable of x. 

Lets let the missing integer be y:

\((3x+1)(12x-y)=36x^2-3xy+12x-y\)

We just need to find an integer y such that \(-3xy+12x=0\) We can divide both sides by -3 and we see that y has to equal \(\boxed4\)

If there are 10 cups then the chance of a ping pong ball landing in any cup is\(\frac1{10}\)

The first ball can go in any cup, but one of the next balls has to land in that same cup, and one has to land in a different cup. So the probability of this is \({\frac1{10}\cdot\frac9{10}=\boxed{\dfrac9{100}}}\)

-x + 3 =  0                          2x  + 1  =  0

3 = x                                   2x  = -1

                                            x = -1/2

3 +  -1/2 =    5/2

13, 28, 520, 133, 55

For problems like these, we only have 5 terms to calculate. Therefore, brute forcing would be a convenient method

Third term =  2^3 + 8^3 =  520

Fourth term =  5^3 + 2^3 + 0^3   =  133

Fifth term =  1^3 + 3^3 + 3^3 =  55

Note an interesting thing

Sixth term  =  5^3 + 5^3    =  250

Seventh term =  2^3 + 5^3 + 0^3  =  133

So.....starting with the fourth term , the series repeats in a  cycle of three terms