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x = origian salary

1.02 x  =  £37638

x = £37638/1.02 =  £ _________

I graphed it for you, can you take it from here now?

Because the order doesn't matter, 4! (which is 4x3x2x1) would be your final answer.

4!=24

This question has already been answered.

https://web2.0calc.com/questions/help-stuck-on-this

It is actually not very hard.

Get a common denominator on the RHS and equate coefficients.

Give it a go and if you get stuck post what you have attempted.

\(\frac{(2x^2 + 3x - 5)}{x(x^2 - 1)} = \frac{A}{x} + \frac{B}{(x - 1)} + \frac{C}{(x + 1).}\)

A please would have helped, but look at it like this

\(\frac{T-45}{P}=\frac{1}{3}\qquad and \qquad \frac{P-45}{T}=\frac{3}{5}\)

Now solve them simultaneously.

If n is a positive integer, and \(0 \le x \le 1\) then \(\lfloor nx \rfloor\) can take take the values 0, 1, 2, ... n   i.e it can take n+1 values.

This should help you to answer the question.

And thanks very much for the compliment.  

I enjoy using GeoGebra. (which is a free download or you can use it online)

It is capable of much more than I have so far learnt. 

The only downside is that I have found very few good instruction tools. 

So it is harder than it should be to learn.  

Still, I find it a lot of fun to use and it is great when I learn to do new things with it.  :)

https://www.jiskha.com/questions/1870248/there-were-76-strawberries-and-rambutans-in-a-basket-john-gave-away-2-5-of-the

Considering the fact that this line is parallel to the slope represented by this equation, we know that the y-intercept is different, but the slope remains the same.

We change this equation into y = ax+b form:

y = 4x + 13

and substitute the y- intercept for b

y = 4x + b

we then substitute the values of the given coordinate into the equation:

23 = 4(4)+b

then simplify

23 = 16 + b

7 = b

substitute 7 for b, and we get:

\(y = 4x + 7\)

I believe the answer to this question is:

\(24\)

Simplify via distribution:

45<9x+27<153

subtract:

18<9x<126

divide by 9

2

When the digits in the number 2005 are reversed we obtain the number 5002 and 5002=a*b*c such that a, b and c are three distinct primes. What are a, b, and c?

2 x 41 x 61 = 5002 but I don't know what reversing the order of the numbers has to do with anything.  

_.

Let x be the amount of money Henry had

at first then

he spent 1/6 of x and additional $10 on food

     spent on food :      \( {1 \over 6}x +10\)
   now remaining money is :   \(x- {1 \over 6}x-10\)
                                        =     \( {5 \over 6}x-10\)
    He spent 1/2 of remaining money and additional  

    $  on books

   spent on books : \({1\over 2}({5\over 6}x-10)+7={5\over 12}x+2\)
  
   he was at the end left with $13

  =>        \(({5 \over 6}x-10)-({5 \over 12}x+2) = 13\)
   =>                 \( {5 \over 12}x-12=13\)
   =>          \({5 \over 12}x = 25 => x = 25 * {12 \over 5} = 60\)
 

so Henry had $60 at first

x/40  +   28 / 60   =   x/32                  28/60 is the fraction of an hour represented by 28 minutes

x/32 - x/40 = 28 / 60      solve for x  = the number of miles

Thanks Catmg.

I actually did not realize that the units were different  

Hello :))

To start, the x intercept is found when y = 0, and the x intercept is found when x = 0. 

x intercept

0 = -3/2x + 6

y intercept

y = -3/4(0) + 6

Any idea how to go from here?

=^._.^=

Hi Melody,

I love your diagrams, they are always so helpful for visualizing the problem. 

One small note, since one length is in cm and the other is in mm, I think it would be helpful to convert one of them so that the units are the same. 

550mm = 55cm

:))

=^._.^=

You are welcome :)

Hi Juriemagic.

Here is the pic. Now use Pythagoras's theorem to find r.   

If I have misunderstood then let me know.  

Triangle ABC has side lengths c = 29, a = 40, and b = 40. Find the inradius of triangle ABC. Find the circumradius of triangle ABC.

Hello Guest!

\(sin( \dfrac{\gamma}{2} )=\dfrac{c}{2a}=\dfrac{29}{2\cdot40}\\ \dfrac{\gamma}{2}=21,2538°\\ \color{blue}\gamma =42.5076°\\ \color{blue}\alpha =\beta =68.4762°\)

\(f(x)=tan(\frac{\alpha}{2})x=tan(34.2381°)\cdot x\\ x=\dfrac{c}{2}=14.5\\ r_i=tan(34.2381°)\cdot 14.5\\ \color{blue}r_i=9.918\\ \)

\(m\ of\ \overline{AC}=tan(68.4762)\\ m\ of\ g(x)= -\dfrac{1}{tan(68.4762)}\\ g(x)=-\dfrac{1}{tan(68.4762)}\cdot (x-29)\\ x=14.5\\ g(x)=5.640\)

\(h=\sqrt{a^2-\dfrac{c^2}{4}}=\sqrt{40^2-\frac{29^2}{4}}\\ \color{blue}h=37.279\)

\(r_c=h-g(x)=37.279-5.640\\ \color{blue}r_c=31.639\)

The inradius of triangle ABC is 9.918.

The circumradius of triangle ABC is 31.639.

  !

g(x) = (3x + 1)/(2x + g(x))       Huh?