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x - 5y  =  7                                                 -->      x -   5y  =  7  

15y = 3x - 9    (subtract 3x from both sides)  -->  -3x + 15y  =  -9

To cancel out the y-term, get both coefficients to by 15 by multiplying the top equation by 3:

                   x -    5y  = 7         (times 3)      -->    3x  -  15y  =  21

           (leave the second equation alone)      -->   -3x + 15y  = -9 

                   (add down the comumns)          -->     0x + 0y  =  12

This problem is impossible to solve because all the x's and y's disappear.

The first equation is:  3x - 15y  =  21; the second equation (after you multiply it by -1) is:  3x - 15y  =  9;

there is no way that 3x - 15y can be both 21 and 9; therefore, impossible.

When you divide by a fraction, you multiply by the reciprocal.

√5 / (1/13)  =  √5 · (13/1)  =  √5 · 13  =  13√5

on this calc it will become atan

arc tan is the same as inverse tan

[2nd function]   [atan]         

6x + 5y  =  3              (multiply this equation by 2)  -->     12x + 10y  =  6

9x - 10y  =  -48          (leave this equation alone)    -->       9x - 10y  =  -48

                                                                                       -------------------

                                      add down the columns:                21x         = -42     --->   x  =  -2

Substitute -2 back in for x in the first equation:

6(-2) + 5y  =  3                                       Since x = -2  and  y = 3, the solution is (-2, 3).

  -12 + 5y  =  3                                        Thus, a = -2  and  b = 3, and a + b = 1

           5y  =  15

             y  =  3

baysour,

1*1=1  NOT 2

could you fix this on yours please.

I'll still give you points though for you good effort.  :)

Let  L =  larger number    and   S = smaller number

L + S  =  17        The sum of the two numbers is 17.

L  =  2 + 2S        The larger number is two more than twice the smaller.

Substitute the value of L from the second equation into the first equation:

(2 + 2S) + S  =  17

2 + 3S  =  17

      3S  =  15

        S  =  5   

        L  =  12

√12  =  √4 · √3  =  2√3 

-1/3 x 21/1               Multiply the numerator times the numerator and the denominator times the denominator.

=  -21/3                    Now, simplify.   -21 ÷ 3  =  7

=  -7

You'll need to complete the problem.

Call the lenght L.  Since the length is 5 more than the width, the width is L - 5.

Perimeter = (L) + (L - 5) + (L) + (L - 5)  =  26

Simplifying:  4L - 10  =  26

                         4L  =  36

                           L  =  9                          W  =  L - 5  =  9 - 5  =  4

What are the choices?

Use the onsite calc on the home page.

pi/(42^9)=

$$5(6+2x)=6x+10$$

now solve it

Thanks Alan

Alan, this is my interpret for Q3.3 why at point c the direction doesn't change . 

At C the object moving along a straight line so its acceleration is tangent to the path and parallel to the velocity 

 I don't know if it is correct or no 

Also I want your own interpret to learn from you 

Hi Braksess,

I really like your dogged determination to understand this!

I think you are having problems with this

$$xy-x=x(y-1)$$

so that is the bit I am going to look at.

Look at the rectangle below.     

The area of the whole rectangle is      $$x\times y \quad units^2$$

I have cut a little rectangle off the end.  The area of the cut off bit is   $$1\times x=x \quad units^2$$

so the area that is left when you take away the litle bit at the end is  

 $$\\x\times y - x\\
or\; just\\ xy-x$$

The area that is left after you take away the bit at the end is displayed in yellow below.

The length of the top is y-1  (because 1 unit was cut off)

The side is still x  units

The area is   x(y-1)

SO          $$xy-x=x(y-1)$$

LETS look at it the other way around

you probably know that     3(x-1)=3*x-3*1 = 3x-3

It works with letters too

$$x(y-1)=x\times y - x\times 1 = xy-x$$

NOW lets look at how to factorise it going in the other direction.

$$\\xy-x=x\times y - x\times 1\\
$x is a common factor so we can factor it out and we will be left with $y-1$ in the bracket.$\\
=x(y-1)$$

h² + 14h + 3  =  5

The form that you must have:

-- the squared term must have a coefficient of 1

-- the left side must have the squared term and the linear term; the number must be on the right side.

First, move the 3 to the other side (by subtracting 3 from both sides):

h² + 14h        = 2

There are three steps in completeing the square:

--  divide the coefficient of the linear term by 2       14 ÷ 2  =  7

-- square that result                                                    7²  =  49

-- add this number to both sides.

h² + 14h + 49  =  2 + 49

(h + 7)(h + 7)  =  51                                        Factor:

       (h + 7)²  =  51                                          Find the square root:

         h + 7  =  ±√51                                        Removd the 7 from the left side:

               h  =  -7 ±√51

6 / (6b + 4)  =  2 / (b - 4)

Cross multiply:  6(b - 4)  =  2(6b + 4)

Distribute:        6b - 24  =  12b + 8

Subtract 6b:         - 24  =  6b + 8

Subtract 8:           - 32  =  6b

Divide by 6:          -16/3  =  b

(60x - 48000) · .7  =  .7 · (60x - 48000)

Use the Distributive Law:     =  (.7)·(60x) - (.7)·(48000)

                                          =  42x - 33600

[36x^(1/4)]^1.5

=  [36]^1.5 · [x^(1/4)]^1.5

If you have an exponent to an exponent, multiply the exponents together:  (1/4) x 1.5  =  3/8

=  [36]^1.5 · [x]^(3/8)

An exponent of 1.5 is an exponent of 3/2 which means cube it and find the square root (either order);:

=  216 · x^(3/8)

First.....the true mathematician would have to set up a rigorous proof to determine whether or not such a thing could actually be accomplished. 

Then, even after a proof was posited, it would have to undergo peer review scrutiny - and possible revision.

This whole process would probably take 3pi years - or so - to arrive at a successful resoution of the problem.

Until then, everyone would be lefti in the dark.........so to speak.......

OK, rosala...now that I know what the "book answer"  is .......the compounding was for 1.5 years!!

Here's the proof

A = 4096(1 + .0625)^(1.5*2) =

A = 4096(1 + .0625)^(3) = Rs 4913

So....there you go.......

You have 9 sets and you have 10 sets. If you join the 10 to the 9 and count them all... you will have a total of 19. So 9+10 equals 19