All Answers 352701 Answers

Hi Melody,

yep, I realised my error...thanx for your help!!

Hi guest,

sorry for replying only now, thanx a lot,you have helped me see my error..thanx again..

Thank you very much for solving it! And yes, after i did some googling, turns out there is a difference between how the english use of notation and our county use of log notation.

If the centre values of the histogram bars are x_i and the heights of the histogram are h_i, then assuming the widths are all the same:

\(x_{ave}=\Sigma_ix_ih_i/\Sigma_ih_i\)

Further to my reply #1, I should have said that the construction lines from the three vertices of the triangle should be perpendicular to the mirror and the same length behind the mirror as in front.

The median is the middle number in the list. 

We have the numbers:

3, 5, 5, 7, 8, 9.

The middle number will be bigger if we add numbers larger than the largest number in the list, which is 9.

So let’s just add 10, 11, and 12

Now we have the new set:

3, 5, 5, 7, 8, 9, 10, 11, 12 

Now the new middle number is 8

See if the following helps. The dotted lines are construction lines. Three are needed to create triangle image. Then draw dotted line from LL to P. Then draw line from L to K and from K to P.

Which of the coordinates presented in the list of options are the vertices of a right isosceles triangle?

Which of the coordinates presented in the list of options are the vertices of a right isosceles triangle?

2*4*2=16

Well the 5 does not make sense but lets look at a possible meaning.

Note that  when an English speaking person sees    \(log_25\)

They would SAY it as                                        log of 5 base 2     or   log 5 base 2

\(m=\frac{log_25}{log_35}\\ m=\frac{log5}{log2}\div \frac{log5}{log3}\\ m=\frac{log5}{log2}\times \frac{log3}{log5}\\ m=\frac{log3}{log2}\\ mlog2=log3\\ log2^m=log3\\ 2^m=3\\~\\ \)

\(2^{2m}+2^{m+2}\\ =(2^m)^2+2^m*2^2\\ =3^2+3*4\\ =9+12\\ =21 \)

If the pic looks a little different perhaps you should post that  

Sorry guest, I have only just seen your post.  I could easily have missed it.

If you were a member you could have sent me a private message with the address of this thread and that way i could not have missed it. 

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GOOD EXAMINATION GUEST!  You are right. :)     

Let m and n be positive integers such that m = 24n + 51.

What is the largest possible value of the greatest common divisor of 2m and 3n?

m=3(8n+17)

Ltt's consider where  n is a multiple of 17 

let n = 17k where k is a positive integer.

n=17k

m=3(8*17k+17)

m=3(9*17k)       error   m=3*17(8k+1)

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3n=3*17   *  k

2m=3*17   * 2(8k+1)        

If k is even then 2 is another factor.

Assume k is even and let k=2c

3n=3*17 *2  *  c

2m=3*17*2  (16c+1)        

I do not think that c and 16c+1 can have any common factors.

Which means that the highest possible common factor is 3*17*2 = 102

So if n is a multiple of 34 the highest common factor is 102.

If n is a multiple of 17 but NOT of 2 then the highest common factor is 51

if n is not a multiple of 17 and is odd the HCF is 3

if n is not a multiple of 17even the HCF is 6

I think this is right.....

Hi Juriemagic,

Your y is equal to x.

The length and bredth are     x and  x+16

Let the width of the rectangle = W

Then the length of the rectangle = W + 16

[W + 16] / W = 4 / 3, solve for W                 cross multiply

[W + 16] = 4 / 3W                                        Subtract W frm both sides

16 = 4 / 3W - W

16 = 1 / 3W                                                  divide both sides by 1/3

W = 16 / (1/3)

W = 16 x 3

W = 48 cm - the width of the rectangle

48 + 16 = 64 cm - the length of the rectangle. So that:

64:48 = 4:3

1)   tan(x) = opposite/adjacent   so  x = tan^-1(opposite/adjacent)  

      Here we have:  x = tan^-1(5/20)

      You can use the calculator on this site to evaluate this  (note that atan is the same as tan^-1).

2)   sin(angle) = opposite/hypotenuse   so   sin(45°) = 4sqrt(2)/x  or  x = 4sqrt(2)/sin(45°)

3)  Take the "base" to be the 11cm side.  The "height" is then given by 9*sin(63°) cm  The area is obtained from (1/2)base*height.

If 'm' and 'n' are holding the single digits place (and it is not 2002 TIMES 'm')  and 'm' and 'n' cannot be negative, then n= 0 and m=0   would result in 20020 + 444440

If you meant to ask   (2002)*m  + (44444)*n     there is a different answer......     What did you mean?

IF the two smaller sides squared and added together equal the third (longest side) squared then it IS a right triangle

First one:

2^2 + 15^2  = 17^2 ??????   If yes, it is a right trangle according to the Pythagorean Theorem...

4 + 225 = 289

229   does NOT equal 289    so the first one is NOT a right triangle....

can you do the rest of them?    The third example seems like you may have too many numbers...or not enough spaces

Oh okay

I got it like 10 minutes after i asked for help. Thanks anyways! 

What do you mean    'I cant type n '      You did...

5^n = 5^14    n=14

i cant type n, what do i do?

Sure! Hope you understand....keep at it !

thx;