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The cosine rule?!?

BD = sqrt(12² + 4² - 2*12*4 * cos(BCD))       and then what?!?

(n - 1)³  =  n³ - 3n² + 3n - 1

n³  =  (n - 1)³ + 37     --->     n³  =  ( n³ - 3n² + 3n - 1 ) + 37

                                             n³  =  n³ - 3n² + 3n - 1 + 37

                            3n² - 3n - 36  =  0

                          3( n² - 3n 12 )  =  0

                                n² - n + 12  =  0

                            (n - 4)(n + 3)  =  0

    Either  n = 4  or  n = -3

Everyone, please do not answer this, it is an AoPS Algebra B writing problem. Ask on your message board. However if they are busy a helpful hint is that the sum of all coefficients is f(1) and the sum of the even coefficients minus the sum of odd coefficients is f(-1).

5x(6x+7y)(6x-7y)

https://math.stackexchange.com/questions/340890/how-many-ways-are-there-to-distribute-5-balls-into-3-boxes-under-additional-con/340957#:~:text=Thus%20the%20total%20number%20of,balls%20in%203%20distinguishable%20boxes.

Multiply the numerator and denominator by   1 + 2i

to get

(-5 + 10i)/5  =   -1 + 2i

1111  has 4 ones     divide by   11   =   101     two ones ...half as many

1003

5.88 x 10¹²     miles is a light year (given)

    multiply this by 8.5

= 49.98 x 10¹²

~~ 5.0 x10¹³  miles (rounded)

37.5 x 10⁶   + 7.1 x 10⁶  =   44.6 x 10⁶ = 4.46 x 10⁷

Ude this and plug-in your numbers:

https://www.algebra.com/algebra/homework/Average/Average.faq.question.1139001.html

https://brainly.com/question/10674061

I live in Australia though.  

That is why my icon is a kangaroo road sign.  It is a photo of a real road sign    

No it is not :)

Thanks for your input but I think something you should include if you are giving out advice or suggestions is cost. 

Not exact cost, you may not even know that, but just an idea of cost. 

In particular, is a resource free, relatively inexpensive or pricey.

It is of key importance to almost everyone.

Yesssss, I love AoPS. 

I've never done Kumon tho. 

I shall look into the classes and books.

Right now, I'm only doing alcumus, ftw, and mathcounts trainer. 

For alcumus, I'm kinda stuck on the int alg part, so I might just enroll in that course. 

Hopefully I improve. :))

Thanks,

=^._.^=

8! / ( 3!3!2!)

I have shown it but I am sure I have not done it by the intended method

My method is far from elegant.

Find BD in terms of  angle BCD using the cosine rule  and also

Find BD in terms of  angle BAD using the cosine rule  

not that angle BCD and angle BAD are supplementary which means  cos

Solve for angle

Then use to find distance  BD

Do the same for AC

Then you can just substitute to show that they are the same. 

I am sure this is not quite the intended solution.

Ask questions if you want to :)

\(RHS = (cos^2x-sin^2x)*\frac{1}{cos^2x}\\\)

I am sure you can finish it.

Thank you!! :)

Values of  x  that make the denominator 0 must be excluded from the domain.

Values of  x  that make the expression inside the square root negative must be excluded from the domain.

So.... any values of  x  that make  x² - 5x  less than or equal to zero must be excluded from the domain.

x² - 5x  ≤  0

To find which values of  x  make this negative, first let's find which values make it equal zero.

x² - 5x  =  0

x(x - 5)  =  0

x  =  0     or     x  =  5

The graph of   y = x² - 5x  is a parabola that intersects the  x-axis when  x = 0  and  x = 5.

So to find which values of  x  make the expression negative, we can test a point in each of the following intervals:

(-∞, 0)  or  (0, 5)  or  (5, ∞)

(-1)² - 5(-1)   =   1 + 5   =   6   >   0    So the values of  x  in (-∞, 0)  make the expression positive

(1)² - 5(1)   =   1 - 5   =   -4   <   0   So the values of  x  in  (0, 5)  make the expression negative

(6)² - 5(6)   =   36 - 30   =   6   >   0  So the values of  x  in  (5, ∞)  make the expression positive

And so the values of  x  that fall in the range [0, 5]  must be excluded from the domain.

So the domain is:

(-∞, 0)  U  (5, ∞)

A quick Venn diagram sketch:

https://web2.0calc.com/questions/on-18-of-her-calls-there-is-no-answer-or-the-line#r1

1)   Pentagon has interior angles that sum to   (n-2)*180 = 540      take it from here

2)    area of a square = l * w    but l and w are equal

     so area =   l^2

         18 = l^2      then you can find 'l' 

                                  diagonal is Pythag theorem     diagonal = l^2 + l^2         Take it from here

3.) Opposite angles in an inscribed quad are supplementary (add to 180 )    Take it from here