Can someone help me with this problem? 
I nned to solve this literal equation for the indicated variable: 
D = C - s/n (for s) The indicated variable is Depreciation 

If you mean:

                     s  
            D = C - ---
                     n

Clear of fractions by multiplying every term by LCD = n

           Dn = Cn - s

Add s to both sides

       s + Dn = Cn

Add -Dn to both sides

            s = Cn - Dn

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

If you mean:

                 C - s  
            D = -------
                   n

Clear of fractions by multiplying both sides by LCD = n

           Dn = C - s

Add s to both sides

       s + Dn = C

Add -Dn to both sides

            s = C - Dn

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

Edwin

Please...I need help solving the following 
system by graphing

 x - 2y =  8
3x - 2y = 12

1.  Find the x-intercept of the first equation,
    by substituting y = 0 and solving for x

      x - 2y = 8
    x - 2(0) = 8
           x = 8
         
    So the x-intercept is the point (8,0) on 
    the x-axis


2.  Find the y-intercept of the first equation, 
    by substituting
    x = 0 and solving for y

    x - 2y = 8
    0 - 2y = 8
       -2y = 8
         y = -4

    So the y-intercept is the point (0, -4) on 
    the y-axis.

Plot these two points and draw a line through them.



3.  Find the x-intercept of the second equation, 
    by substituting y = 0 and solving for x

        3x - 2y = 12
      3x - 2(0) = 12
             3x = 12
              x = 4 
         
    So the x-intercept is the point (4,0) on the 
    x-axis

4.  Find the y-intercept of the second equation, 
    by substituting x = 0 and solving for x

      3x - 2y = 12
    3(0) - 2y = 12
          -2y = 12
            y = -6

    So the y-intercept is the point (0, -6) on the 
    y-axis.

Plot these two points and draw a line through them 
on the same set of axes.



Now look and see what the coordinates are of the point
where the two lines cross:

You will notice that point is directly under 2 on the 
x-axis, and it's directly to the right of -3 on the
y-axis.  So the solution of the system is

(x,y) = (2,-3)  

We can check that to see if it is correct. Substitute
x=2 and y=-3 into both of the original equations and
see if you end up with the same number on both sides.

     x - 2y = 8                 3x - 2y = 12
(2) - 2(-3) = 8            3(2) - 2(-3) = 12
      2 + 6 = 8                   6 + 6 = 12 
          8 = 8                      12 = 12

It checks in both. 

Edwin

  (4t - 2) + (3t + 8) = -15

Put 1's before each parentheses

1(4t - 2) + 1(3t + 8) = -15

Use the distributive law to remove the parentheses:

      4t - 2 + 3t + 8 = -15

               7t + 6 = -15

                   7t = -15 - 6

                   7t = -21

                    t = -3

Edwin

Name an example that shows that three points are 
always coplanar, but four points are not always coplanar.

Any three points are the vertices of a triangle, which is 
a plane figure.  However it's each to find a fourth point 
that is not in the plane of that triangle.

Edwin

A ball is thrown upward from the roof of a 
building 100m tall with an initial 
velocity of 20m/s when will the ball reach 
a height of 80m

The formula is

s = sO + vOt + at²/2

where
s = h = the height of the ball off the ground in meters
sO = hO = the initial height = 100 m
vO = the initial velocity = 20 m/s
t = the number of seconds
a = g = -9.8 m/s² (the acceleration of gravity)

------------------------
Substituting:

h = (100) + (20)t + (-9.8)t²/2

h = 100 + 20t - 4.9t²

That's the formula for the height h in meters 
at any time t seconds.

Plug in h = 80m and solve for t

80 = 100 + 20t - 4.9t² 

4.9t² - 20t - 20 = 0

If you like, clear of decimals by multiplying 
thru by 10

49t² - 200t - 200 = 0

Use the quadratic formula and you'll get

t = -.83 and 4.92, approximately

Discard the negative answer.  The legitimate answer is
4.92 seconds.

Analysis:

at 0 seconds, the height is 100 m
at 1 second, the height is 115.1 m
at 2 seconds the height is 120.4 m

then it starts falling

at 3 seconds, its height is 115.9 m
at 4 seconds its height is 101.6 m
at 4.92 seconds its height is 80m
at 5 seconds its height is 77.5 m
at 6 seconds its height is 43.6 m
at 7 seconds its height is 0, i.e., it hits the ground.

Edwin

solve for x  

9(5x - 3) + 5(2x + 4) = 2(3x + 3)

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

Multiply the 9 by the 5x, getting 45x.  So far we have:

45x

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

9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Multiply the 9 also by the -3.  So far we have:

45x - 27

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

9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Multiply the +5 by the 2x.  So far we have:

45x - 27 + 10x

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

9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Multiply the +5 also by the +4.  So far we have:

45x - 27 + 10x + 20

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

9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Copy the equal sign:

So far we have:

45x - 27 + 10x + 20 =

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

9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Multiply the 2 by the 3x.  So far we have:

45x - 27 + 10x + 20 = 6x

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

9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Multiply the 2 also by the +3.  So far we have:

45x - 27 + 10x + 20 = 6x + 6

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

45x - 27 + 10x + 20 = 6x + 6

Now combine the 45x and the +10x. So far we have

      55x - 27 + 20 = 6x + 6

Now combine the -27 and the +20:

            55x - 7 = 6x + 6

Now get rid of the -7 on the left by adding 
its opposite +7 to both sides of the equation:

            55x - 7 = 6x + 6
                + 7      + 7
          --------------------
            55x     = 6x + 13

Close up the gap:

                55x = 6x + 13

Now get rid of the 6x on the right by adding 
its opposite -6x to both sides of the equation:

                55x = 6x + 13
               - 6x  -6x 
             ------------------
                49x =      13

Close up the gap

                49x = 13

Get rid of the 49 coefficient by dividing both sides
by 49

                49x     13
               ----- = ----
                 49     49

Cancel the 49's on the left

                 1  
                49x     13
               ----- = ----
                 49     49
                  1

                        13
                   x = ----
                        49

That's the answer: x = 13/49, thirteen forty-ninths.

Edwin

What is the equation to represent the relationship among the integers for: 

The greater of two consecutive even integers is six less than twice the smaller.

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

The idea is to get all the words out and mathematical symbols in

Let S = the smaller (of two consecutivs integers)

Since the greater is one more than the smaller

we let S + 1 = the greater.

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

The greater of two consecutive even integers is six less than twice the smaller.

So replace the red words by S + 1 and the blue words by S.

S + 1 is six less than twice S. 

Now replace " twice S " by " 2S ", and we have

S + 1 is six less than 2S

Replace the word " is " by an equal sign " = ".

S+1 = six less than 2S

The only thing left is to decide how to get rid of the words
"six less than".

Let's think about what, say, "six less than 10" means. It means to start with
10 and then subtract 6, or 10 - 6.  This, of course, would be 4.

Let's also think about what, say,  "six less than 73" means. It means to start
with 73 and the subtract 6, or 73 - 6. This, or course would be 67.

Now let's think about what "six less than 2S" means. It means to start with
2S and subtract 6, or 2S - 6.  We don't know what this would be, so all we can
do is just leave it as 2S - 6.  

So the final equation is

S + 1 = 2S - 6

Edwin

Find the sum for the following set of numbers:
-3.5, -1.4, -0.5, 3, 5, 1, 2

Find the sum of first two

(-3.5) + (-1.4)

The rule is: They have like signs, so add their absolute values
and attach their common sign.

They are both negative, which means they have the same sign,
so we add 3.5 and 1.4, getting 4.9, and we attach their common
sign, which is "-". So we have -4.9:

Sum of first two = -4.9

-------

Now let's find the sum of that and the 3rd one:


(-4.9) + (-0.5)

The rule is: They have like signs, so add their absolute values
and attach their common sign.

They are both negative, which means they have the same sign,
so we add 4.9 and 0.5, getting 5.4, and we attach their common
sign, which is "-". So we have -5.4:

Sum of first three = -5.4



-------

Now let's find the sum of that and the 4th one:


(-5.4) + (3)

The rule is: They have opposite signs, so subtract their 
absolute values (larger minus smaller) and attach the sign 
with the larger absolute value.

They have opposite signs, so we subtract 3 from 5.4, getting 
2.4, and we attach the sign of -5.4 because its absolute 
value is larger than 3's absolute value, which is "-". 
So we have -2.4:

Sum of first four = -2.4

-------

Now let's find the sum of that and the 5th one:

(-2.4) + (5)

They have opposite signs, so we subtract 2.4 from 5, getting 2.6, and we attach
the sign of 5 because its absolute value is larger than 3's absolute value.
sign, which is "+". So we have +2.6, but we can drop the +:

Sum of first five =  2.6

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

Now let's find the sum of that and the 6th one:

(2.6) + (1)

The rule is: They have like signs, so add their absolute values
and attach their common sign.

They are both positive, which means they have the same sign,
so we add 2.6 and 1, getting 3.6, and we attach their common
sign, which is "+". So we have +3.6, but we can drop the +:

Sum of first six = 3.6

------

Find the sum of that and the 7th or last one

(3.6) + (2)

The rule is: They have like signs, so add their absolute values
and attach their common sign.

They are both positive, which means they have the same sign,
so we add 3.6 and 2, getting 5.6, and we attach their common
sign, which is "+". So we have +5.6, but we can drop the +:

Sum of them all  = 5.6

Edwin

Factor completely: 6x^2-5y-3xy+10x using 
SEVERAL methods please. Thanks! 

6x² - 5y - 3xy + 10x

1. Rearrange the terms like this

6x² - 3xy + 10x - 5y

Factor 3x out of the first two terms

3x(2x - y) + 10x - 5y 

Factor +5 out of the last two terms

3x(2x - y) + 5(2x - y)

Factor (2x - y) out of each term

(2x - y)(3x + 5)

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

2. Rearrange the terms like this

6x² + 10x - 3xy - 5y

Factor 2x out of the first two terms

2x(3x + 5) - 3xy - 5y 

Factor -y out of the last two terms

2x(3x + 5) - y(3x + 5)

Factor (3x + 5) out of each term

(3x + 5)(2x - y)

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

See if you can rearrange them a third way.

Edwin

Gsmani's solution is OK, but he changed the inequality to
an equal sign.  I think you should keep the inequality
symbol < all the way to the end: 

  Let Reger's age now = x
  
  So Melanie's age 8 yrs. ago = 2x   .......  (given)
  
  Melanie's present age =  2x+8
  
  the sum of their present age = x+2x+8 < 41
 
  3x+8 < 41.   so 
    3x < 41-8 
    3x < 33
     x < 11. 
  
  So Roger's present age is no more than ll.

Edwin

Dearest tutors, can you help me regarding my problem? thank you for that..
3. How much pure alcohol must be added to 8 quarts of a 20% solution of alcohol
produce a 40% solution?
-----------------------------------------
Let the answer be x.

First we figure the amount of LIQUID we'll have. Then we figure the amount of
ALCOHOL we'll have.

We have 8 quarts of LIQUID to start with and we add x quarts of LIQUID, so we
end up with 8+x quarts of LIQUID.  

Now we figure the amount of ALCOHOL.

Only 20% of the 8 quarts we start with is ALCOHOL. 20% of 8 quarts is 1.6
quarts.  So we have 1.6 quarts of ALCOHOL to start with, and we add x quarts
of ALCOHOL, so we end up with 1.6+x quarts of ALCOHOL.

Now we reason that the 1.6+x quarts of ALCOHOL we end up with must be 40%
of the 8+x quarts of LIQUID we end up with, so we put that into an equation:

   1.6+x quarts of ALCOHOL EQUALS 40% of 8+x quarts of LIQUID, or

               1.6+x = .40(8+x)

solve that and you'll get x = 8/3 or 2 2/3 quarts.  If you can't solve that,
post again and we'll help you solve it.

Edwin

solve for x. 
-6x/5=-7/6 
Negative 6x over 5 (as a fraction) = Negative 7 over 6 (as a fraction)

The LCD is 30 because the smallest integer both 5 and 6 will divide
evenly into is 30.  So start with the original equation

        -6x      -7
       ----- = -----
         5        6

Now multiply both sides by 30, written as 30/1:

 30     -6x     30     -7
---- · ----- = ---- · ----
  1      5       1      6

Now on the left cancel the 5 in the bottom into the 30 in the top.
Similarly on the right cancel the 6 in the bottom into the 30 in the top,
Upon cancelling, you get 6 on the left, and 5 on the right:

 6              5 
 30     -6x     30     -7
---- · ----- = ---- · ----
  1      5       1      6
         1              1

Now you have the 6 times the -6x on the left, which gives -36x
Similarly, you have the 5 times the -7 of the right, which gives -35,
so you have:

        -36x = -35   

Now divide both sides by -36. On the left you will have just x, and
on the right side if you divide -35 by -36 you get +35/36

          x = 35/36

Edwin

SOLVE 3X + Y = 6 FOR Y

      3X + Y = 6

We want to leave just Y on the left, so we
get rid of the 3X by adding its opposite,
-3X, to both sides

      3X + Y = 6
     -3X         - 3X
   --------------------
           Y = 6 - 3X

Edwin

SOLVE THE EQUATION M-2N=9 IF THE DOMAIN IS {-1,0,5}

"Domain" comes before "Range" in the dictionary, and
M comes before N in the alphabet, so I will assume
the values in the domain are for M, and so the values
in the range will be for N.

Post again if your teacher reverses the roles of M and N.

Plug in -1, 0 and 5 for M, then solve for N:

 M - 2N = 9         M - 2N = 9         M - 2N = 9
-1 - 2N = 9         0 - 2N = 9         5 - 2N = 9
    -2N = 9+1          -2N = 9            -2N = 9-5
    -2N = 10             N = -9/2         -2N = 4
      N = -5                                N = -2

So the range is {-5, -9/2, -2}

Edwin

Rewrite the equation 2x – 8y = 48 
as a function of x.

1. Solve for y
2. Replace y by f(x)

2x – 8y = 48
    -8y = 48 - 2x

Divide thru by -8 

      y = -6 + 1/4x

Replace y by f(x)

   f(x) = -6 + 1/4x

Edwin

Graph the inequality.
	x > 1
please help

Draw a number line

--------------------------------
-5 -4 -3 -2 -1  0  1  2  3  4  5

x > 1 says that we want to shade all the
values that are greater than 1.  These
will be all the numbers to the right of 1,
but not including 1.  So we put this "("
at 1 and shade the line to the right and
put an arrow on the right end of the
shaded line, which indicates that the
numbers greater than 1 extend all the
way to the right:

-------------------(============>
-5 -4 -3 -2 -1  0  1  2  3  4  5

That's all there is to the graph of x > 1

Some teachers and textbooks want you to
use an open circle instead of "(". If so,
the answer would be:

-------------------o============>
-5 -4 -3 -2 -1  0  1  2  3  4  5


Edwin

Can you please solve.

x  1  2  3  4 
a 18 16 14 12

a=????
Thanks Brad

something like x + 8 -6!!!!!!!!!!

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


The successive values of "a" differ by -2
But the successive values of "x" differ by only 1
However the successive values of "2x" will differ by 2

So let's put in a list between them for 2x

 x  1  2  3  4  
2x  2  4  6  8
 a 18 16 14 12

Now we can observe that 2+18=20, 4+16=20, 6+14=20, 8+12=20

So it must be that 2x + a must equal 20, or

2x + a = 20, or solving for a

     a = 20 - 2x.

So the answer is 20 - 2x

Edwin

Give f(x)=5x^2-3x+1, find f(-2).

 f(x) = 5x² - 3x + 1

Replace all the x's on both sides with empty 
parentheses:

f(  ) = 5(  )² - 3(  ) + 1

Now fill in all the empty parentheses with -2

f(-2) = 5(-2)² - 3(-2) + 1

Leave the left side as it is but simplify the
right side:

f(-2) = 5(-2)² - 3(-2) + 1
f(-2) = 5(4) + 6 + 1
f(-2) = 20 + 7
f(-2) = 27
 
So you see, functional notation merely amounts
to "plugging in" for x what's in the parentheses
after the "f".

Edwin

Find the slope of any line perpendicular to 
the line through point (6,3)and (7,7).

You need two things:

1. The slope formula
2. The fact that perpendicular lines have slopes
   which are reciprocals but with the opposite sign.



1. 
     y2 - y1     (7) - (3)     4
m = --------- = ----------- = --- = 4
     x2 - x1     (7) - (6)     1

2.

The slope of a line perpendicular to a line with 
slope 4/1 is the reciprocal of 4/1 with the sign
changed.  That is, it's

        m = -1/4

Edwin

Find the slope and y intercept

x = -8

This is an unusual type of line.

A line whose equation is of the form x = a
is a vertical line "a" units right of the y-axis
if "a" is positive, and |a| units left of the
y-axis if "a" is negative.

Such a line has neither a slope nor a y-intercept.
All other lines have both, but this kind doesn't.



Edwin

WRITE AN EQUATION IN SLOPE INTERCEPT FORM OF THE 
LINE SATISFYING THE GIVEN CONDITIONS. PASSES 
THROUGH(5,4) AND (6,-1)

We need two things:  the slope formula and the 
point-slope form of a line:

Slope formula for the line thru (x1,y1) and (x2,y2):

     y2 - y1
m = ---------
     x2 - x1

Point-slope form for the equation of the line with 
slope = m passing thru (x1,y1)

y - y1 = m(x - x1)

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

(x1,y1) = (5,4) and (x2,y2) = (6,-1)

     y2 - y1     (-1) - (4)      -5
m = --------- = ------------ =  ----- = -5 
     x2 - x1      (6) - (5)       1


y - y1 = m(x - x1)

y - 4 = -5(x - 5)

Now when you simplify this, you will have 
the slope-intercept form y = mx + b

y - 4 = -5(x - 5)

y - 4 = -5x + 25

    y = -5x + 29

The slope is the coefficient of x, which is 5
and the y-intercept is (0,29)

Edwin

Simplify. 
    ____
3[³Öx5y5]

Prime factor what's under the cube root radical:
    ___________________
3[³Öx·x·x·x·x·y·y·y·y·y]

Since it's cube root (index 3), group like factors 
into groups of 3 each:

    _______________________
3[³Ö(x·x·x)·x·x·(y·y·y)·y·y]

Each group of three is a perfect cube, and so each
comes out in front of the radical as a single factor
That is the (x·x·x) is x3 and so it comes out in front
of the radical as a single x.  Same for (y·y·y).  The
factors that didn't get grouped stay under the radical:

        _______
3·x·y·³Öx·x·y·y
 
Simplify
      ____
3xy·³Öx2y2

Edwin

  __ _
3Öa5Öa

Multiply under the radicals
  __
3Öa6
  _____
3Ö(a3)2

3a3

Edwin

find the square root of 50/32 completely broken down:
      _____            _____       __
_    / 50        _    / 25        Ö25     5
 \  / ----    =   \  / ----   =  ----- = ---
  \/   32          \/   16        Ö16     4

Edwin

solve this equation y=-1/2x if the domain is {-2, -1, 0, 1, 2}
What i get is that you have to plug in the numbers, but how do
i present the answer?? Please help!

Yes, plug in the numbers, and give the range:

The domain is {-2, -1, 0, 1, 2}

The range is gotten by plugging those in:

The range is {1, 1/2, 0, -1/2, -1}

That's my guess as to how to present the answer,
i.e., give the domain.

Edwin

1/3(s - 2) = s + 4

Clear of fractions by multiplying both 
sides by LCD = 3


3[1/3(s - 2)] = 3(s + 4)

Cancel the 3 and the 1/3

1
3[1/3(s - 2)] = 3(s + 4)
    1

       s - 2 = 3(s + 4)

Distribute the right side:

       s - 2 = 3s + 12

Add 2 to both sides

           s = 3s + 14

Add -3s to both sides

         -2s = 14

Divide both sides by -2

           s = -7

Edwin

    z*8 = z

     8z = z

Add -z to both sides

 8z - z = z - z

     7z = 0

Divide both sides by 7

    7z     0
   ---- = ---
     7     7

      z = 0

Edwin

4x + 2 = 10

There are two terms on the left, +4x and +2, 
and 1 term on the right, +10.

The 4x term contains a variable and is on the left

The +2 term does not contain a variable and is 
on the left

The 10 term does not contain a variable and is 
on the right.

The idea is to 

1. Get rid of any term on the left that DOES NOT contain
a variable.

2. Get rid of any term on the right that DOES contain
a variable.

To get rid of a term, add its oppose to both sides:

We only need to get rid of the +2 term of

4x + 2 = 10

We do that by adding -2 to both sides

4x + 2 = 10
    -2   -2
-----------
4x + 0 =  8
    4x =  8

Now we must get rid of the coefficient 4. To
get rid of a coefficient, divide both sides
by it:

    4x     8
   ---- = ---
     4     4


Cancel the 4's on the left and the 4 into the
8 on the right:

    1      2
    4x     8
   ---- = ---
     4     4
     1     1

      x = 2

To check:

  4x + 2 = 10

substitute (2) for x:

4(2) + 2 = 10
   8 + 2 = 10
      10 = 10

That has the same number on both sides, so the
answer, x = 2, is right.

Edwin

The Proprietor of a managerie was asked how many 
parrots and how many elephants it included. He replied, 
" well, the lot have 32 heads and 100 feet." How many 
of each kind were there?

You don't need algebra to figure it out, but I will show 
you the algebra way. However first let's reason it out 
without using algebra.

Since there are 100 feet, that means there are fifty pairs 
of feet. Therefore there are 50 - 32 or 18 more pairs of 
feet than heads.  These 18 extra pairs of feet must belong
to the elephants.  So there are 18 elephants, which
accounts for 18 heads, thus the remaining 32 - 18 or 14 
heads must belong to the parrots.  

Answer: 18 elephants, 14 parrots

Check:

The 18 elephants have 18 heads and 18×4 or 72 feet
The 14 parrots have 14 heads and 14×2 or 28 feet.
That's 18+14=32 heads and 72+28=100 feet.

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

Now, by algebra:

Let P = the number of parrots.
Let E = the number of elephants.

Parrots have one head, so there are P parrot heads.
Elephants have one head, so there are E elephant heads.
Since there are 32 heads in all,

P + E = 32

Parrots have 2 feet so there are 2P parrot feet.
Elephants have 4 feet so there are 4E elephant feet. 
Since there are 100 feet in all,

2P + 4E = 100

So you have the system of equations:

 P +  E =  32
2P + 4E = 100

Solve that system and get P = 14 and E = 18   

Edwin