All Answers 356462 Answers

I get the general solution and when testing it, like n=1 , n=2 , n=99 etc.. it works when substituiting in the equation. However, the general solution is not equal to what is required. 
e.g. i got \(x=\frac{(8n+5)\pi}{8}\) this satisfies \(tan(3x-\frac{\pi}{4})=tan(x)\) for all n, but the question says \(x=\frac{(4n+1)\pi}{8}\) is the answer which is not equal to what I got (although both satisfies the equation). Does anyone have an explanation please?

EACH of the spikers could be paired with any of the 5 setters

  5 x 5 = 25 combos of teams possible

How about you give the addresses of the previous questions/answers.

there is no point in me giving the same/similar answer as before if you did not understand the first time.

If you do not understand an answer you should quiz the answerer on the original thread.

You can make a new post directing people to the original and you can ask for it to be unlocked if it is locked.

The diagonal of a rectangle is 15 cm, and the perimeter is 38 cm. What is the area? 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Shorter side = a            Longer side = 19 - a

a² + (19 - a)² = 15²

a = 1/2(19 - √89)

19 - a = 1/2(19 + √89)

Rectangle area = 68 cm²

9 and 3 o'clock     n = 3 , 9

Find the 3 intersection points and then find the point that is equidistance from all 3 points. 

To find the point, set it as (x, y) and use the distance formula d = sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2). 

=^._.^=

(x(x - 1)(x - 2))       If the value makes the denominator = 0 then that value is not in the domain of x values

 0    + 1    + 2    = 3

Find CB via pythag theorem

3^2 + CB^2 = 14

CB = sqrt(5)

Tan B = opp/adj = 3 / sqrt(5)    or  3/5  * sqrt5

These numbers do not work.....if there are 48 spanish only students, there will have to be 53 chinese only students....which totals 101 students even without counting students who take both languages......   bad question.....

First clean up both of the equations :

2.2x -3.1y = - 3.2

.9x +y = 8.8                <===== multiply by 3.1   then add to the top equation to get

2.79x + 3.1y = 27.28    <====Add to top equation

4.99 x = 24.08

x = 4.826                        <====== use this value of 'x' in either of the equations to calculate 'y'      You can finish.....

The slopes between any of the two lines must be equal

(7- -5) / (-1-3)    =   (y-7) / (-6 - -1)          now....simply solve for 'y'  

    12 / -4           =    (y-7) / (-5)

-5 * 12/ -4         = y - 7

      15 = y-7

y = 22

That's interesting, but it isn't what the problem was asking for. 

I'm not sure what the problem wants but I think it's  (n + 1)³ – (n)³  =  x²  

In the diagram below, EU = 8, UF = 7,GV = 5, VH = 15, and UV= 8. Find XY.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

UX = n           VY = m

n(8+m) = 56

n = 56 / (8+m)

m(8+n) = 75

m = 75 / (8+n)

m = 75 / [8+56 / (8+m)]

m = 6.293001428

n = 56 / (8 + 6.293001428) = 3.91800143

XY = 18.21100286

Point slope form :

y-1 = 6/5 ( x-5)       

Assuming that bags need to be completely full, we get $\dfrac{\frac{11}{2}}{\frac{1}{3}} = \frac{11}{2} \cdot 3 = 16.5$, meaning that $\boxed{16}$ bags will be filled and $\boxed{\frac{1}{6}}$ pounds will be left for the packer to eat. 

$BYX$ ~ $ABC$ by $AAA$ similarity. Because $ABC$ has $45-45-90$ angles it follows that $BYX$ has $45-45-90$ angles (and is isosceles).

The diagram below explains $45-45-90$ triangles. 

Thus, we can see that $BY = \frac{12}{\sqrt{2}} = 6\sqrt{2}$. 

Similarly, we can see that $BA = 18\sqrt{2}$ by triangle $ABC$. 

Subtracting $BC - BY = 12\sqrt{2} = AY$. 

Thus the ratio is $\frac{BY}{AY} = \frac{6\sqrt{2}}{12\sqrt{2}} = \boxed{\frac{1}{2}}$, which is our answer. 

Sorry to interrupt but this is a Singapore math question type

x x 1       x x 3     x x 5     would be the odd numbers

5 * 4    x 3    = 60 odd three digit numbers

I know what you said....but 132 is incorrect.....your answer book has a mistake

Let $f(x)=3x+2$ and $g(x)=ax+b$, for some constants $a$ and $b$. If $ab=20$ and $f(g(x))=g(f(x))$ for $x=0,1,2...9$ find the sum of all possible values of $a$.

For nested functions, we take the interior function and substitute it into $x$ of the outer function. 

$f(g(x)) = 3ax + 3b + 2$

$g(f(x)) = 3ax + 2a + b$

$3ax + 3b + 2 = 3ax + 2a + b \rightarrow 2a = 2b+2$

Thus, we need to solve the system of equations 

$ab = 20$

$2a = 2b + 2$

We can either solve for a variable and substitute into the other equation, or we can guess and check to see that our solutions are 

$a = 5, b = 4$

$a = -4, b= -5$

Thus the sum of all possible values of $a$ is $5 - 4 = \boxed{1}$. 

I said the answer is 132