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Simply use the equations $x=r\cos\theta, y=r\sin\theta$ upon dividing both sides by $r$.

Not sure, on my end it seems like "Guest".

The other answer isn't insightful whatsoever.

Note RHS = $\frac{8}{15}$ and LHS = $\frac{j+k}{jk}$. So $15j+15k=8jk$. Now use simons favorite factoring trick.

By distance formula, $(2a-4)^2+(a-5)^2=(2\sqrt{30})^2$. Solve for $a$ via quadratic methods.

For obvious reasons, $(0,0)\to (m,n)$ can be done in $\binom{m+n}{m}=\binom{m+n}{n}$ ways. We let $f(m,n):=(0,0)\to (m,n)$.

So we just want $f(5,7)-f(4,3)f(5-4, 7-3)$, which is trivial to compute using the expression for $f(m,n)$.

Note that by synthetic division $-3 x^2 + 12 x + 22 = (-3 x - 3)(x - 5) + 7 = -3(x+1)(x-5)+7$. Divide both sides by $x-5$.

I suspect that the is more coding written into the isbn number.  

I was just looking at a book and the isbn number is split into 5 sections

3-1-3-5-1    (digits each)

One of those probably represents the publisher, one would be where it is published etc.

So not all number combinations could ever be used because you would run out of numbers in one section before another section would reach its limit.  

It is good to be curious about the things we see and obviously, math-minded people are going to be curious about numbers.   

For x , the midpoint will be   exactly between 1 and -10   at   - 4.5

  for y   the midpoint is exacly between 4 and -17   at  - 6.5      You can finish ....

I know this is from 2012 but I really need the answer can someone please help?

if all 0's count as one of the numbers there will be 10¹³  possibles :   10 000 000 000 000     (ten trillion)

We need to move from point Q the same distance as from P to Q

  for 'x'  moving from P to Q we go from 5 to 3     or  -2      go  -2 MORE from Q ....from    3 to 1     

    for 'y' moving from 3  to  8    is  + 5     move + 5 more from Q   to 13

Point T is then   1,13

Thanks for your efforts Notguest but please next time answer on the original thread.

It would be nice if you went back to the original and put another post linking your answer here with the others.

I mean a post with a link to your answer here.

I have answered on the original post.   

It would have been easier for me to answer if you had just typed it in.

I cannot just copy it and I like the question to be in my answer as sometimes kids change the original question.

Each of the digits 6,7,8,9,  is used no more than once to form an integer N.

  How many possible N's are multiples of 3 ?

To be a multiple of 3 the digits have to add to a multiple of 3

6+7+8+9=31     that is no good, not all digits can be used.

31-1 =30 but there is no 1s

31-1-6 = 31-7=24=3*8    so a three digit number could contain   6,8 and 9     there are 3!=6 of those

31-1-9 = 31-10  but there are no 10s

So there are 6   3-digit possibilities.

If I add pairs I get

13, 14, 15, 15, 16, 17

Only 15 is a multiple of 3

so the number could be   69, 96, 78, 87    there are 4 of them

There are 2 one digit ones ,   6 and 9

so we have    6+4+2 = 12

Yea beacause it got answered and I posted this question when there was no answer there

First ....graph the lines ..then when you find thepoint of intersection, you can calculate the area of the rectangle (below) and subtract the area of triangle 1 and 2 :

Thanks for your effort but both are wrong.

Vertex (-4,0)

Vertex form     y = a ( x+4)^2 + 0

                      sub in the point (1,75) to calculate 'a'

                           75 = a ( 1 +4)^2      so a = 3

AH = 2.589578409

HD = 1.084656205

 (x-a)(x-b)=0

x^2-(a+b) +ab=0

a=-a-b. So b=-2a. and ab=b So a=1

Thus b=-2 one solution as follows

x^2+x-2 =0 = (x‐1)(x+2) thus x=1 or -2

3x + y + xy  =  115     --->     y + xy  =  15 - 3x     --->     y(1 + x)  =  15 - 3x     --->     y  =  (15 - 3x) / (1 + x)

Graphing this, I get the point  (1, 56).

From this, we can get the value of  x + y.

Pretty sure there's only one, where a=b=0. 

For a and b to be solutions you would have to have (x-a)(x-b)=0 which means x^2-(a+b)x+ab=0 which does not match the required form of equation.

I assume you're asking what the magnitude/norm of the vector is? In which case it's \(\sqrt{7^2+16^2}=17.46\)