You can put this solution on YOUR website!
36 = 6×6 = (2×3)×(2×3) = 2×2×3×3 = 2²3²
Edwin

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(27y^{9)-1/3
`
Write 27 as 33
`
(33y9)-1/3
`
Multiply the outer exponent -1/3 by each inner exponent:
`
3-1y-3
`
To get rid of the negative exponents move base and exponent from
numerator to denominator and chaneg the sign of the exponent to +
`
` 1
-----
31y3
`
Erase the 1 exponent
`
` 1
-----
`3y3
`
Edwin
AnlytcPhil@aol.com}

You can put this solution on YOUR website!

solve the problem and describe the steps you used
7 - 4c = 10c
`
`
7 - 4c = 10c
`
There are two terms on the left. They are 7 and -4c. There is one
term on the right, 10c.
`
We want to get rid of all terms on the left which DON'T contain c, and
get rid of all terms on the right that DO contain c.
`
The term 7 is on the left and does not contain c. So we get rid of it
on the left by adding the opposite of 7, namely -7, to both sides of
the equation:
`
` ` ` ` ` ` ` ` `7 - 4c = 10c
`
` ` ` ` ` ` `7 - 4c - 7 = 10c - 7
`
That gives ` ` ` ` `-4c = 10c - 7
`
The term 10c on the right contains c. So we get rid of it on the right
by adding the opposite of 10c, namely -10c, to both sides of
the equation:
`
` ` ` ` ` ` ` -4c - 10c = 10c - 7 - 10c
`
That gives ` ` ` ` -14c = -7
`
Now we divide both sides of the equation by the coefficient of c on the left, which is -14:
`
` ` ` ` ` ` ` ` ` `-14c` ` `-7
` ` ` ` ` ` ` ` ` ------ = -----
` ` ` ` ` ` ` ` ` ` -14 ` ` -14
`
Now cancel the -14's on the left, and cancel the negative signs on the right, and get
` ` ` ` ` ` ` ` ` ` ` ` ` ` `7
` ` ` ` ` ` ` ` ` ` ` `c = -----
` ` ` ` ` ` ` ` ` ` ` ` ` ` 14
`
Now reduce 7/14 to 1/2
`
` ` ` ` ` ` ` ` ` ` ` ` ` ` 1
` ` ` ` ` ` ` ` ` ` ` `c = ---
` ` ` ` ` ` ` ` ` ` ` ` ` ` 2
`
Edwin
AnlytcPhil@aol.com

You can put this solution on YOUR website!
can you show me how to do this problem
the rule: evaluate the function f(x)=3x-10 for
the given value of the variable.
x=-2
can you show me how to do it please!!!
`
f(x) = 3x - 10
`
Since x = -2, just replace x everywhere by -2 and simplify the right side
`
f(-2) = 3(-2) - 10
`
f(-2) = -6 - 10
`
f(-2) = -16
`
That's all there is to it!
`
Edwin
AnlytcPhil@aol.com

You can put this solution on YOUR website!
"PLEASE HELP ME W/ THIS PROBLEM. THANK YOU.
REDUCE 45/75 TO LOWEST TERMS.
`
Think of a whole number smaller than the numerator 45 that
will divide evenly into 45.
`
I thought of 5. So write
`
45 = 5×9
`
There is no integer smaller than 5 that will divide evenly
into 5. So think of a number smaller than 9 that will divide
evenly into 9.
`
I thought of 3. So write
`
45 = 5×9 = 5×3×3
`
Now there are no whole numbers smaller than 3 that will divide
evenly into 3, so we have prime factored 45 as 5×3×3
`
Now lets do the same thing with the denominator 75.
`
Think of a whole number smaller than 75 that will divide evenly
into 75.
`
I thought of 5. So write
`
75 = 5×15
`
There is no integer smaller than 5 that will divide evenly
into 5. So think of a number smaller than 15 that will divide
evenly into 15.
`
I thought of 5. So write
`
75 = 5×5×3
`
Now there are no whole numbers smaller than 3 that will divide
evenly into 3, so we have prime factored 75 as 5×5×3
`
So we have
`
`45 ` ` 5×3×3
---- = --------
`75 ` ` 5×5×3
`
Now we cancel the 5's
`
` ` ` ` 1
`45 ` ` 5×3×3
---- = --------
`75 ` ` 5×5×3
` ` ` ` 1
`
That leaves
`
`45 ` ` 3×3
---- = -----
`75 ` ` 5×3
`
Now cancel the 3's
`
` ` ` ` 1
`45 ` ` 3×3
---- = -----
`75 ` ` 5×3
` ` ` ` ` 1
`
That leaves
`
`45 ` ` 3
---- = ---
`75 ` ` 5
`
So that's the answer, 3/5.
`
Edwin

You can put this solution on YOUR website!
What is the answer to the equation: 10 to the zero power.
Is it zero or n/a??
'
1⁰ = 1, 2⁰ = 1, 3⁰ = 1, 2.7⁰ = 1, 8.47⁰ = 1, (-7)⁰ = 1
`
Every number raised to the zero power is 1 with one exception.
`
That one exception is that 0⁰ is not defined".
`
10 is not 0, so therefore 10<sup>0</sup> = 1
`
Edwin

You can put this solution on YOUR website!

` X +` Y - Z =` 3
-3X ` ` `+ Z = -5
` X + 2Y - Z =` 3
`
Here are the seven steps.
1. Pick a letter. (If one of the equations has only two letters, choose the
` `letter that is missing)
2. Pick an equation that contains that letter
3. Solve for that letter in that equation.
4. Substitute what you get into any other equations that contains that letter,
` `and simplify.
5. Now you have only two equations in one unknown
6. Solve that system for the two letters they contain
7. Substitute the values of those two letters in the result of step 3.
`
1. Pick a letter. (If one of the equations has only two letters, choose the
letter that is missing)
`
Since the second equation, -3X +Z=-5, has no Y, we pick Y
`
2. Pick an equation that contains that letter
`
I pick the first equation
X + Y - Z = 3
`
3. Solve for that letter in that equation.
`
X + Y - Z = 3
` ` ` ` Y = 3 - X + Z
`
4. Substitute what you get into any other equations that contains
` `that letter, and simplify.
`
The third equation, X + 2Y - Z = 3, contains Y, so replace Y by 3-X+Z
in it and simplify
`
` ` ` ` ` X + 2Y - Z = 3
X + 2(3 - X + Z) - Z = 3
`X + 6 - 2X + 2Z - Z = 3
` ` ` ` ` ` ` -X + Z = -3
`
5. Now you have only two equations in one unknown
`
These are
`
-3X + Z = -5 and -X + Z = -3
`
6. Solve that system for the two letters they contain.
`
-3X + Z = -5
`-X + Z = -3
`
Solve for Z in the second one just above,
`
` ` ` Z = -3 + X
`
Substitute -3+X for Z in the first one just above
`
` ` ` `-3X + Z = -5
-3X + (-3 + X) = -5
` `-3X - 3 + X = -5
` ` ` ` ` `-2X = -2
` ` ` ` ` ` `X = 1
`
Substitute 1 for X in Z = -3 + X
`
Z = -3 + (1) = -3 + 1 = -2
`
7. Substitute the values of those two letters in the result of step 3.
`
Substitute 1 for X and -5 for Z in Y = 3 - X + Z
`
Y = 3 - X + Z
Y = 3 - (1) + (-2)
Y = 3 - 1 - 2
Y = 0
`
Edwin

You can put this solution on YOUR website!
An empty swimming pool can be filled in 5hrs. When full, the pool can be drained in 17hrs. How long will it take to fill the empty pool if the drain is left open?
`
Suppose it will take x hours.
`
>>...An empty swimming pool can be filled in 5hrs...<<
`
Translation:
`
In 5 hours, 1 poolful of water goes in.
In 1 hour, 1/5 of a poolful of water goes in.
In x hours, x/5 of a poolful of water goes in.
`
>>...the pool can be drained in 17hrs...<<
`
Translation:
`
In 17 hours, 1 poolful of water goes out.
In 1 hour, 1/17 of a poolful of water goes out.
In x hours, x/17 of a poolful of water goes out.
`
In x hours:
`
water coming in in x hours - water going out in x hours = 1 poolful
x/5 of a poolful - x/17 or a poolful = 1 poolful
`
x/5 - x/17 = 1
`
Can you solve that? If not post again. Answer 85/12 hours
or 7 1/12 hours or 7 hours 5 minutes.
`
Edwin

You can put this solution on YOUR website!
Sonya has x amount of money. Bob has three times as much as Sonya has, less $14.62. Write an expression, using x, that tells how much money Bob has.

Sonya has x amount of money.

>>...Bob has three times as much as Sonya has, less $14.62...<<

Translation: Bob's money = 3 times Sonya's money, minus $14.62

             Replace the word's "Sonya's money" by x

             Bob's money = 3 times x, minus $14.62

Replace the words "3 times x" by "3x"

             Bob's money = 3x, minus $14.62

Replace the word "minus" by a minus sign

             Bob's money = 3x - $14.62

Erase the $ sign, since it is understood

             Bob's money = 3x - 14.62

Edwin        

You can put this solution on YOUR website!
Some bank robbers leave town, speeding at 80mph. 15min later, the polive give chase, traveling at 90mph. How long (hrs) will it take the police to overtke the robbers? Can you explain how you get the answer?
'
15 minutes after robbers leave town they have traveled 1/4 hour at 80 mph, and thus have traveled 20 miles, (using D = RT = (80 mi/hr)(1/4 hr) = 20 miles.)
'
So the robbers have a 20 mile lead on the cops when the cops set out.
'
Since the cops are going 90 mph and the robbers are going 80 mph, the cops are gaining on the robbers by 10 mph. Therefore the cops will gain the whole 20 mile lead the robbers have on them in 2 hours, (using T = D/R = 20/10 = 2).
'
Edwin
AnlytcPhil@aol.com

You can put this solution on YOUR website!

The sum of Carol's and Sandy's ages is 47. In 10 years Carol will be
10 years older than Sandy was 7 years ago. Find their present ages.
`
The sum of Carol's and Sandy's ages (C+S) is 47. In 10 years Carol (C+10)
will be 10 years older than(10 more than) Sandy was 7 years ago (S-7).
`
(C+S) = 47
(C+10) = 10 more than (S-7), which means "(S-7) plus 10"
`
or
`
C + S = 47
C + 10 = (S - 7) + 10
`
Can you solve this system, after simplifying the second one?
`
Answer: Carol is 20 and Sandy is 27
`
Edwin

You can put this solution on YOUR website!
How do I write an equation that corresponds to the given inequality?
example:
`
y < 4
`
Thank You
`
The left side is y, the right side in 4
`
Since the left side is LESS THAN the right side, you must add a positive
number to the left side to make it equal to the right side.
`
This positive number is often called a "slack variable", because it takes up
the slack between the smaller left side and the larger right side.
`
Let this positive number be represented by " s ". Then
`
y + s = 4
`
Edwin

You can put this solution on YOUR website!

Find all solutions of the equations.
1.
`
x<sup>6</sup> - 64 = 0
`
First factor as the difference of squares.
`
(x<sup>3</sup>)<sup>2</sup> - 8<sup>2</sup> = 0
`
(x³ - 8)(x³ + 8) = 0
`
Next factor these two parenthetical expressiona as the difference and
sum respectively of two cubes
`
(x³ - 2³)(x³ + 2³) = 0
`
(x - 2)(x<sup>2</sup> + 2x + 4)(x + 2)(x<sup>2</sup> - 2x + 4) = 0
`
Set each of the four factors = 0
`
x - 2 = 0, solving gives x = 2
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` _
x<sup>2</sup> + 2x + 4 = 0, solving by the quadratic formula gives x = -1±Ö3
`
x + 2 = 0, solving gives x = -2
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `_
x² - 2x + 4 = 0, solving by the quadratic formula gives x = 1±Ö3
`
-----------------------------------------------
`
2.
`
9x<sup>4</sup> - 24x<sup>3</sup> + 16x2 = 0
`
Factor out x²
`
x<sup>2</sup>(9x<sup>2</sup> - 24x + 16) = 0
`
Factor the expression in parentheses
`
x<sup>2</sup>(3x - 4)(3x - 4) = 0
`
x²(3x -4)² = 0
`
Set each factor equal to 0
`
x² = 0 gives x = 0
`
(3x - 4)<sup>2</sup> = 0, gives x = 4/3
`
Edwin

You can put this solution on YOUR website!
When constructing a circle ("pie") graph, how do you find the number of degrees the central angle should be which represents a certain percent of the total?
`
Answer:
`
1. Change the percent to a decimal, by moving the decimal point two places left and removing the "%" sign
`
2. Multiply this decimal by 360°.
`
Edwin

You can put this solution on YOUR website!

A, B, and C can finish a job in 6 days. If B and C work

together, the job will take 9 days; if A and C work together,

the job will take 8 days. How many days will it take each man

to do the job alone? 

A. A in 9 days, B in 1 day, and C in 8 days 

B. A in 25 days, B in 12 2/3 day, and C in 28 days 

C. A in 20 1/2 days, B in 16 day, and C in 25 days 

D. A in 18 days, B in 24 day, and C in 14 2/5 days 

I don't have a clue where to begin with this problem. I would

appreciate any help--thanks

Let x = the number of days it would take A to do 1 job alone.

Let y = the number of days it would take B to do 1 job alone.

Let z = the number of days it would take C to do 1 job alone.

Make this chart:

           Number of jobs | Rate(jobs/days) |  Time(days)

A alone                   |                 |    

B alone                   |                 |    

C alone                   |                 |    

A,B,& C                   |                 |     

B & C only                |                 |

A & C only                |                 |

In each case 1 job was done, so fill in 1 for each of the

numbers of jobs

           Number of jobs | Rate(jobs/days) |  Time(days)

A alone          1        |                 |    

B alone          1        |                 |    

C alone          1        |                 |    

A,B,& C          1        |                 |     

B & C only       1        |                 |

A & C only       1        |                 |

Now fill in the times (numbers of days.

           Number of jobs | Rate(jobs/day)  |  Time(days)

A alone          1        |       1/x       |      x  

B alone          1        |       1/y       |      y 

C alone          1        |       1/z       |      z

A,B,& C          1        |       1/6       |      6

B & C only       1        |       1/9       |      9

A & C only       1        |       1/8       |      8

Now fill in the rates using rate = (jobs done)/(time)

The rate for A,B,& C equals the sum of their individual

rates, which must equal 1/6, so 

1/x + 1/y + 1/z = 1/6

The rate for A & C equals the sum of their individual rates,

which must equal 1/8, so 

1/x + 1/z = 1/8

The rate for B & C equals the sum of their individual rates,

which must equal 1/9, so 

1/y + 1/z = 1/9

So we have this system of equations:

1/x + 1/y + 1/z = 1/6

1/x       + 1/z = 1/8

      1/y + 1/z = 1/9

Don't clear of fractions, but solve for 1/x, 1/y, and 1/z.

Can you do this system?  If not, post again and ask how to solve it.

You'll get 1/x = 1/18, 1/y = 1/24, and 1/z = 5/72, which

means x = 18 days, y = 24 days, z = 72/5 or 14 2/5 days, and the

correct choice is D.

Edwin

You can put this solution on YOUR website!

`x +` y + 2z = 5
`x + 2y +` z = 8
2x + 3y -` z = 1
`
One way is to eliminate the three lower left terms,
the ones I have colored red:
`
`x +` y + 2z = 5
`x + 2y +` z = 8
2x + 3y -` z = 1
`
Instead of solving yours, I'll solve one just like it, OK?
Then you can use it as a model to solve yours.
`
`x - 3y + 4z =` 45
3x + 2y - 5z = -21
4x + 5y - 3z = -32
`
`x - 3y + 4z = `45
3x + 2y - 5z = -21
4x + 5y - 3z = -32
`
To get rid of the 3x, multiply the top equation by -3
and add it to 1 times the middle equation, but restore the
top equation:
`
-3[ x - 3y + 4z =` 45]
`1[3x + 2y - 5z = -21]
` `4x + 5y - 3z = -32
`
`x - 3y +` 4z = ` 45
` ` 11y - 17z = -156
4x + 5y -` 3z =` -32
`
To get rid of the 4x, multiply the top equation by -4
and add it to 1 times the bottom equation, but again
restore the top equation:
`
-4[ x - 3y +` 4z = ` 45]
` ` ` `11y - 17z = -156
`1[4x + 5y - `3z = `-32]
`
x - 3y + `4z = ` 45
` `11y - 17z = -156
` `17y - 19z = -212
`
To get rid of the last one, 17y, multiply the middle equation by -17 and add it to 11 times the bottom equation, but
restore the middle equation:
`
` ` x - 3y + 4z = ` 45
-17[ ` 11y - 17z = -156
`11[ ` 17y - 19z = -212
`
x - 3y + `4z = ` 45
`` 11y - 17z = -156
` ` ` ` `80z = 320
`
Now that those three bottom left terms have been
eliminated, solve the bottom equation:
`
` ` ` ` `80z = 320
` ` ` ` ` `z = 4
`
Substitute z=4 into the middle equation and solve
for y
`
`11y - 17(4) = -156
` ` 11y - 68 = -156
` ` ` ` `11y = -88
` ` ` ` ` `y = -8
`
Fimally substitute z=4 and y=-8 into the top equation and solve for x:
`
x - 3(-8) + 4(4) = 45
` ` `x + 24 + 16 = 45
` ` ` ` ` x + 40 = 45
` ` ` ` ` ` ` `x = 5
`
So the solution is (x, y, z) = (5, -8, 4)
`
Now use this as a model to solve yours by. The solution is
`
(x, y, z) = (-7, 6, 3)
Edwin

You can put this solution on YOUR website!
x²+y²=13
2x+y=1
I then tried to solve by substitution:
y=1-2x
x²+(1-2x)²=13
I then got a bit muddled up and wasn't sure how to expand
(1-2x)²
-----------
Then you went astray. To expand (1-2x)², write it as
(1-2x) multiplied by itself:
`
(1-2x)² = (1-2x)(1-2x)
`
Now use "FOIL" on that. You'll eventually end up with a quadratic
equation which can be solved by factoring. You'll get two answers
for x, and then you'll substitute each of these into y=1-2x to get
the corresponding values for y.
`
If you still have trouble
post again. I'll give you the answers:
`
There are two solutions
`
(2, -3) and (-6/5, 17/5)
`
Edwin

You can put this solution on YOUR website!

If traveling on a bicycle at 20mph for 12 miles what is the total time spent

traveling, and what is the proper formula used to compute this?

The proper formula is

TIME = DISTANCE/RATE 

or

T = D/R

Substitute 12 miles for the distance D and 20mph for the rate R.

You should get T = 3/5 of an hour, or 36 minutes.

Edwin

You can put this solution on YOUR website!

 

 THE PRODUCT OF A NUMBER AND SIX  IS  TEN LESS THAN SIXTY

(THE PRODUCT OF A NUMBER AND SIX) IS (TEN LESS THAN SIXTY)

(THE PRODUCT OF     N    AND SIX) IS (TEN LESS THAN SIXTY)

(THE PRODUCT OF     N    AND  6 )  = (10  LESS THAN  60  )

(        N TIMES 6              )  = (10  LESS THAN  60  )

(            6N                 )  = (    60 MINUS 10    )

(            6N                 )  = (      60 - 10      )

(            6N                 )  = (         50        )

             6N                    =           50

                              6N   = 50

                              6N/6 = 50/6

                               N   = 25/3

Edwin

You can put this solution on YOUR website!

>>Please help me solve this equation: m + 18 = -9<< 

                             m + 18 = -9

An equation is like a balance scale.  If you perform a mathematical operation

to one side of the equation, then you must perform the same mathematical

operation to the other side. The left side is

                             m + 18

We wish there were only the letter

                             m

on the left side and nothing else.  We wish the

                               + 18

weren't there.  So we need to get rid of the



                               + 18.

The only thing that we can use to get rid of the 

                               + 18

is

                                    - 18



so we insert



                                    - 18

after the                      + 18

and that makes the left side become

                             m + 18 - 18

However since we put - 18 at the end of the left side, we have no choice but to

also put 

                                        - 18



 at the end of the right side too!  That will make the right side

becoms

                                     -9 - 18

So here are the steps so far:

                            m + 18 = -9

                       m + 18 - 18 = -9 - 18

Now the + 18 - 18 on the left is just 0, so we can just erase

the + 18 - 18 on the left and get

                                 m = -9 - 18

Now the right side is -9 - 18 and that is -27, so the last step is

                                 m = -27

So altogether here are the steps as you should show them on your paper:

                            m + 18 = -9

                       m + 18 - 18 = -9 - 18

                                 m = -27     

That is the solution.  Now we check it:

                            m + 18 = -9

Replace m by -27

                          -27 + 18 = -9

                                -9 = -9

Since both sides of the equation are the same we know the answer is

correct.

Edwin





                        

You can put this solution on YOUR website!
Could someone please help me out with this one? I am suppose to
evaluate this expression if a= -2, b = 5, c = -4, and d = 6
`
b^2 - 2bc+c^2 =
`
Here is what I have tried but it really looks wrong to me.
5^ - 2(5)(-4)+ -4^2 = and now I can't even figure out the answer to this. So I know there has to be a better way and I am hoping someone can show me.
Thanks
`
b<sup>2</sup> - 2bc + c<sup>2</sup>
`
Put (5) in place of b
`
(5)<sup>2</sup> - 2(5)c + c<sup>2</sup>
`
Put (-4) in place of c
`
(5)<sup>2</sup> - 2(5)(-4) + (-4)<sup>2</sup>
`
Replace (5)² by 25
`
25 - 2(5)(-4) + (-4)<sup>2</sup>
`
Replace - 2(5)(-4) by + 40
`
25 + 40 + (-4)<sup>2</sup>
`
Replace + (-4)² by + 16
`
25 + 40 + 16
`
Replace 25 + 40 by 65
`
65 + 16
`
Replace 65 + 16 by 81
`
81
`
Edwin

You can put this solution on YOUR website!
if given a right triangle with the bottom line length being 8, and the
hypotenuse being 15 how can i find the top angle (angle x).
`
The bottom side 8 is the side OPPOSITE the
top angle (angle x)
`
The HYPOTENUSE = 15
`
sin(x) = (OPPOSITE SIDE)/(HYPOTENUSE)
`
sin(x) = 8/15
`
Now making sure calculator is in DEGREE mode, enter
`
sin^-1(8/15)
`
read 32.23095264
`
So the top angle, x = 32.23°, rounded to the nearest
hundredths of a degree.
`
Edwin

You can put this solution on YOUR website!
help me solve for y
`
` ` ` ` (x-1)<sup>2</sup> + y<sup>2</sup> = 1
`
Subtract (x-1)² from both sides
`
` ` ` ` `y² = 1 - (x-1)²
Write 1 as 1²
`
` ` ` ` `y² = 1² - (x-1)²
`
The right side will factor as the difference of two squares:
`
` ` ` ` `y<sup>2</sup> = [1 - (x-1)][1 + (x-1)]
`
Remove inner parentheses
`
` ` ` ` `y² = [1 - x + 1)(1 + x - 1]
`
Combine like terms
`
` ` ` ` `y<sup>2</sup> = [2 - x][x]
`
Rewrite with short factor first
`
` ` ` ` `y² = x(2-x)
`
Take square roots of both sides, remembering ± on the right
` ` ` ` ` ` ` ` ______
` ` ` ` ` y = ±Öx(2-x)
`
Edwin

You can put this solution on YOUR website!
>>Here is my equation : A(M+N)=BN-4M
This is what I have so far: -BN+AN=-AM-4M
Is this right? If so what's next?<<
`
We have to know whether you are solving for A, M, or N.
You forgot to tell us which of the three letters you are
supposed to solve for. It looks as though you are
solving for N since you got all the terms with N on the
left side, so I'll assume you are solving for N
`
A(M+N) = BN-4M
`
`AM+AN = BN-4M
`
-BN+AN = -AM-4M (this is what you have so far)
`
Next step is to factor out N on the left side:
`
N(-B+A) = -AM-4M
`
Now we divide both sides by the parenthetical expression
(-B+A)
`
N(-B+A) ` `-AM-4M
-------- = -------
`(-B+A)` ` `(-B+A)
`
Now we can cancel the (-B+A)'s on the left
`
N(-B+A) ` `-AM-4M
-------- = -------
`(-B+A) ` ` (-B+A)
`
` ` -AM-4M
N = -------
` ` `(-B+A)
`
This will do for an answer. However we like to see if
we can make the answer look simpler. Factor -M out of
the numerator
`
` ` -M(A+4)
N = -------
` ` `(-B+A)
`
We can dispense with the parentheses in the denominator:
`
` ` -M(A+4)
N = -------
` ` ` -B+A
`
Next factor -1 out of the denominator
`
To understand how to do this, place 1's in front of the
letters in the denominator
`
` ` `-M(A+4)
N = ---------
` ` `-1B+1A
`
Now it's easy to see how to factor -1 out of the
denominator:
`
` ` -M(A+4)
N = -------
` ` -1(B-A)
`
We can now cancel the negative signs
`
` ` `M(A+4)
N = -------
` ` `1(B-A)
`
We don't need the 1 or the parentheses around the B-A
`
` ` `M(A+4)
N = -------
` ` ` B-A
`
This could be the simplest form, or you could remove
the parentheses in the numerator and have
`
` ` `MA+4M
N = -------
` ` ` B-A
`
One of these last two forms should be identical to
the answer given in your book.
`
Edwin

You can put this solution on YOUR website!
simplify:
`______
Ö81c<sup>5</sup>d<sup>4</sup>
`
Prime factor 81 = 9·9 = 3·3·3·3
Prime factor c⁵ = c·c·c·c·c
Prime factor d⁴ = d·d·d·d
`______
Ö81c<sup>5</sup>d<sup>4</sup> =
`_________________________
Ö3·3·3·3·c·c·c·c·c·d·d·d·d =
`_____________________________________
Ö(3·3)·(3·3)·(c·c)·(c·c)·c·(d·d)·(d·d) =
`_______________________________
Ö(3²)·(3²)·(c²)·(c²)·c·(d²)·(d²) =
`__ `__` __`__ `_` __` __
Ö3<sup>2</sup>·Ö3<sup>2</sup>·Öc<sup>2</sup>·Öc<sup>2</sup>·Öc·Öd<sup>2</sup>·Öd<sup>2</sup> =
` ` ` ` ` ` ` ` `_
`3 · 3 · c · c ·Öc· d · d =
` ` ``_
9·c<sup>2</sup>·Öc·d<sup>2</sup>
` ` ` _
9c²d²Öc
`
Edwin

You can put this solution on YOUR website!
Tom's father is three times as old as Tom. Four years ago
Tom's father was four times as old as Tom. How old is Tom?

Let:

Tom's age now = T

>>...Tom's father is three times as old as Tom...<<

TRANSLATION:

Tom's father's age now = 3T

Then 

Tom's age four years ago = T-4

and

Tom's father's age four years ago = 3T-4

>>... Four years ago Tom's father was four times as old as Tom...<<

TRANSLATION:

Tom's father's age four years ago = 4 times Tom's age 4 years ago

                             3T-4 = 4(T-4)

                             3T-4 = 4T-16

                            3T-4T = 4-16

                               -T = -12

                                T = 12

Check:

Tom is 12 years old.  His father is 3 times as old as Tom, or 36.

Four years ago, Tom was 8 and his father was 32.  So indeed Tom's father

was four times as old as Tom was then.



Edwin 

   

You can put this solution on YOUR website!
Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the
same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can
all three fill the pool together.

What we need is this equation:



Jim's rate + Sue's rate + Tony's rate = their combined rate



>>...How quickly can all three fill the pool together...<<



Let the time be x minutes. 

THEREFORE

their combined rate = 1 pool per x minutes or

their combined rate = 1/x pool per minute

>>...Jim can fill a pool...in 30 minutes...<<

TRANSLATION:

Jim's rate is 1 pool per 30 minutes or

Jim's rate = 1/30 pool per minute

>>...Sue can do the same job in 45 minutes...<<

TRANSLATION:

Sue's rate is 1 pool per 45 minutes or

Sue's rate = 1/45 pool per minute

>>...Tony can do the same job in 1 ½ hours.,,<<

TRANSLATION:

Tony's rate is 1 pool per 1½ hour

Tony's rate is 1 pool per 90 minutes

Tony's rate = 1/90 pool per minute

Now

Jim's rate + Sue's rate + Tony's rate = their combined rate

becomes

                       1/30 + 1/45 + 1/90 = 1/x

Get the LCD of all the denominators 30, 45, 90, and x, which is 90x.

Multiply through by 90x

  (90x)(1/30) + (90x)(1/45) + (90x)(1/90) = (90x)(1/x)

                              3x + 2x + x = 90

                                       6x = 90

                                        x = 90/6

                                        x = 15 minutes

Edwin

You can put this solution on YOUR website!
John is traveling to a meeting that is 28 miles away. He needs to be there in
30 minutes. How fast does he need to go to make it to the meeting on time?
`
Learn these three equivalent equations:
`
DISTANCE = RATE × TIME
`
RATE = DISTANCE/TIME
`
TIME = DISTANCE/RATE
`
You are asked "how fast". That's asking for a RATE, so use the
middle one above.
`
RATE = DISTANCE/TIME
`
The distance = 28 miles and the time = 30 minutes or .5 hour.
`
RATE = 28 miles/(.5 hour) = 28/(.5) miles/hour = 56 miles/hour.
`
Edwin

You can put this solution on YOUR website!
A=$6000 P= $1000 interest is 12% compounded quarterly
Find # of interest periods
`
The formula is
`
A = P(1+r/n)^nt
`
Where
`
A = ending amount = 6000
P = beginning amount = 1000
r = annual rate expressed as a decimal = .12
n = number of interest periods per year = 4
` ` (since it's quarterly)
t = number of years (which we find first)
`
A = P(1+r/n)<sup>nt</sup>
`
Taking logs of both sides
`
logA = log[P(1+r/n)<sup>nt</sup>]
`
logA = logP + log(1+r/n)^nt
`
logA = logP + nt[log(1+r/n)]
`
logP + nt[log(1+r/n)] = logA
`
nt[log(1+r/n)] = logA - logP
`
nt[log(1+r/n)] `` logA - logP
-------------- = -------------
`n[log(1+r/n)] ` n[log(1+r/n)]
`
nt[log(1+r/n)] `` logA - logP
-------------- = -------------
`n[log(1+r/n)] ` n[log(1+r/n)]
`
` ` ` ` ` ` ` ``` logA - logP
` ` ` ` ` ` `t = -------------
` ` ` ` ` ` ` `` n[log(1+r/n)]
`
` ` ` ` ` ` ` ``` log6000 - log1000
` ` ` ` ` ` `t = --------------------
` ` ` ` ` ` ` ` ` `4[log(1+.12/4)]
`
` ` ` ` ` ` ` ``` 3.77815125 - 3
` ` ` ` ` ` `t = --------------------
` ` ` ` ` ` ` ` ` `4[log(1.03)]
`
` ` ` ` ` ` ` `` ` .7781512504
` ` ` ` ` ` `t = ---------------
` ` ` ` ` ` ` ` ` `.0513488988
`
` ` ` ` ` ` ` `` ` .77815125
` ` ` ` ` ` `t = ---------------
` ` ` ` ` ` ` ` ` `.0513488988
`
` ` ` ` ` ` `t = 15.15419548 years
`
Multiply by 4 to get the number of interest periods
`
Answer = 60.61678192 which means that 60 interest periods will
yield slightly less that $6000, or $5891.60 and 61 interest period
will yield slightly more than $6000, or $6068.40.
`
Edwin J

You can put this solution on YOUR website!
write an equation of a line given (x1,y1)=(12,7) and (x2,y2)=(-4,5)




Now use






That will do as a final answer if you only want the slope-intercept
form, or,
you can multiply through by 8 and get rid of fractions

and to get it in standard form Ax + By = C

and since the standard form requires that A be positive,
we multiply thru by -1

Edwin

You can put this solution on YOUR website!
A boy can drive a motorboat 45 miles downstream in the same amount
of time that he can drive 27 miles upstream. What is the speed of
the current in the river if the speed of the boat in still water
is 12 mph.
`
Let x = the speed of the current.
Make a DRT chart
`
` ` ` ` ` `|`Distance | Rate `| ` Time `
downstream | ` ` ` ` `|` ` ` `| ` ` ` ``
upstream ` | ` ` ` ` `|` ` ` `| ` ` ` ``
`
Fill in the given distances
`
` ` ` ` ` `|`Distance | Rate `|` ` Time `
downstream | ` `45 ` `|` ` ` `|` ` ` ` ``
upstream ` | ` `27 ` `|` ` ` `|` ` ` ` ``
`
Now fill in the rates. The rate downstream is the sum of the rate of
the boat if in still water + the rate of the current, or 12+x. The rate
upstream is the difference of the rate of the boat if in still water -
the rate of the current, or 12-x.
`
` ` ` ` ` `|`Distance | Rate `|` ` Time `
downstream | ` `45 ` `|`12+x `|` ` ` ` ``
upstream ` | ` `27 ` `|`12-x `|` ` ` ` ``
`
Now fill in the times using Time = Distance/Rate
`
` ` ` ` ` `|`Distance | Rate `|` ` Time `
downstream | ` `45 ` `|`12+x `| 45/(12+x)
upstream ` | ` `27 ` `|`12-x `| 27/(12-x)
`
>>...downstream in the same amount of time...upstream...<<
`
The key words are "same amount of time". "Same" means "equal", so
we set the two times equal to each other
`
` ` ` ` ` ` ` ` `
`
Can you solve this equation? If not post again.
`
` ` ` ` ` ` ` ` ` Answer: x = 3 mph.
`
Checking: This means the boat never went 12 mph because there
was no still water. It went 15 mph upstream and 9 mph downstream.
The time to go 45 miles downstream at 15 mph was 3 hours. The time
to go 27 miles upstream at 9 mph was also 3 hours.
`
Edwin J