Questions on Algebra: Real numbers, Irrational numbers, etc answered by real tutors!

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I have a couple of homework problems that I am having trouble with. Any help you can give me to understand how to work these problems would be appreciated.
The Cotes have 30 feet of picket fence with which to enclose a flower garden. What dimensions should the garden have in order to maximaze area? I believe the equation I would use is A(w) = (30-2)w.
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30 feet is the perimeter of the enclosed area. The max area is a circle for a given perimeter. You didn't specify the shape. If it's to be a rectangle, the max area is a square.
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Find the value of "a" such that f(x)=ax2+16x+38 has a minimum value of 6. Would this answer be 96/19?
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The minimum is the point where the 1st derivative is 0, so
2ax + 16 = 0
x = -8/a at the minimum.
Subbing -8/a for x and setting = 6:
a*(64/a^2) - 128/a + 38 = 6
64 - 128 + 38a = 6a
a = 2
Email me if you have questions, this is a complex problem. gsihoutx@aol.com

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A radical is just a square root. Here are some examples of radical expressions:

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The final grade for a particular course is calculated by dividing total points earned by total points available. There are 120 points available in the first half of the course, and 140 points in the second half of the course. If a student earns 81% in the first half of the course, how many points must the student earn in the second half in order to earn an 80% B final grade?
:
If the final grade is just the average of the two grades,
79% would give you an 80 average for the two semesters
:
.79*140 = 110.6 points required in the 2nd semester

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How many real numbers satisfies ||||x-1|-2|-3|-2|=1
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|||x-1|-2|-3|-2 = 1 or |||x-1|-2|-3|-2 = -1
A. Looking at the 1st of these you get:
||x-1|-2|-3|-2 = 1 or ||x-1|-2|-3|-2 = -1
B. Now, looking at the 1st of these you get:
|x-1|-2|-3|-2 = 1 or |x-1|-2|-3|-2 = -1
C. And , looking at the 1st of these you get:
}x-1|-2|-3| = 3
Then |x-1|-6 = 3
|x-1| = 9
x-1 = 9 or x-1 = -9
x = 10 or x = -8
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Now, you would need to look at the 2nd part of B:
|x-1|-2|-3|-2 = -1
}x-1|-6-2 = -1
|x-1|-8=-1
|x-1|= 7
x-1 = 7 or x-1 = -7
x = 8 or x = -6
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You would have to keep working thru both part of "A" .
Cheers,
Stan H.

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Please post the problem (the entire problem). Remember, we don't have access to your book.

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Hi, Hope I can help,
.
Not sure if this is the right section but will someone please help.
Find the LCM of and
Thanks
.
First, we can see if the two "numbers" can be factored
.
To find factors of something, you have to put the "m's" in paretheses ( since " = ,
.
For , (m )(m ) , next we have to find all factors of (-5), and the factors have to add up to (-4), the middle term
.
Factors of (-5), (-5) and (1), (-1) and (5), now add each pair of factors
.
,
.

.
The first pair of factors add up to (-4), our middle term
.
We can put (-5) and (1) in our paretheses
.
(m )(m ) = (m - 5)(m + 1), if we used the FOIL method we would come up with our original equation
.
(m - 5)(m + 1) = = = =
.
(Remember the negative and positive signs, = (Our answers are true)
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The factors for our first "number" = (m - 5)(m + 1)
.
Now we will find the factors of the second equation,
.
First, we put the "m's" in parentheses, (m )(m )
.
Remember, the factors of "7" add up to the middle term "8"
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Factors of "7", (-7) and (-1), (1) and (7)
.
Adding them we get,
.

.

.
The second factors work. We can put the factors in the parentheses
.
(m + 1)(m + 7), If we used the FOIL method,
.
(m + 1)(m + 7) = = = =
.
Remember signs, = ( our factors our true )
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Our factors for our second "number" = (m + 1)(m + 7)
.
We can now put the factored equations side by side
.
Equation (1), (m - 5)(m + 1)
.
Equation (2), (m + 1)(m + 7)
.
To find the LCM, we count all the DIFFERENT factors
.
All factors put together = (m - 5)(m + 1)(m + 1)(m + 7),
.
There are three different factors, (m - 5)(m + 1)(m + 7), ( both numbers have (m + 1) in common, so we only count that factor once )
.
The LCM would then be , if we expanded it,
.
The LCM =
.
Hope I helped, Levi

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m^2 - 4m - 5 factors out to be (m+1) * (m-5)
m^2 + 89m + 7 factors out to be (m+1) * (m+7)
the common factors appears to be (m+1).
i would say that's your answer.
it's no different than finding out the least common multiplier of 9 and 12.
9 is 9*1 or 3*3 and 12 is 12*1 or 6*2 or 4*3.
LCM is 3
hope that helps.

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adjustments before elimination
3x+6y=-6
5x-2y=14
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Multiply thru the 2nd equation by 3 to get the following system of equations:
3x + 6y = -6
15x- 6y = -42
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Add the two equations to get:
18x = -48
x = -24/9
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Substitute to solve for "Y".
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Cheers,
Stan H.

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y=(x+3)^2-4=0
(x+3)^2=4
x+3 =2 or x+3=-2
x=-1 or x=-5
Answer: x=-1 or x=-5

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Assuming that both numbers are in base 3, find the product of 21 x 21.
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In base 10, that's 7 x 7 which is 49.
49 in base 3 = 1211

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6(-2 1/2)=6(-2.5)=-15 ANSWER.

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134+80=214 degrees is the difference.

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-15+(-12) = -27

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To subtract a number, you add its "additive inverse".
The "additive inverse" of a number is the same number (absolute value) but having the opposite sign.
Examples:
6-9 = 6+(-9) The additive inverse of 9 is -9
-5-(-6) = -5+6 = 1 The additive inverse of -6 is 6
So you are changing the subtraction problem to an addition problem.
10-6 = 10+(-6) = 4
-12-4 = -12+(-4) = -16

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Write the  as :



Divide both sides by the coefficient of ,
which is :



On the left side the 's cancel.



On the right side  divided by 
gives , since a positive divided by a
negative is negative.  So the final equation is:



Edwin

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2x+3x=(2+3)(x)=5x

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Think of it this way.
If I have two apples and add three apples, how many apples will I have?
How about 2 CDs and add 3 CDs, how many CDs will I have?
How about two pet alligators and add three more pet alligators?
The variable x takes the place of whatever the thing is.
So if I have two things and add three things, I'll always get five things, no matter what the thing is.

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How about "A perfect square"?

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how do i solve this??
multiply and simplify if possible
(2/9) * 9x=?
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Cancel and "9" in the numerator and in the denominator to get:
2x
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Cheers,
Stan H.

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1. My irrational number is .
Addition :
Subtraction :
Multiplication:
Division:
Exponentiation:
.
.
.
2. My complex number is 3+5i.
Addition :
Subtraction :
Multiplication:
Division:

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50(3A-B) - 20(B-2A) = 50(3A)-50(B) - 20(B)-(-20)(2A)
                    = 150A - 50B - 20B + 40A
                    = 190A - 70B

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6 over x+3= 6/x + 6/3= 6/x+2 is it right or wrong?
notice: 6 over x+3 should be written as follows
6/(x+3)
6/(x+3) cannot be separated
notice: if problem was stated as follows... 6 over x plus three it would mean....
6/x + 3 (following order of operations) which in this case is like saying
(6/x) + 3 which is not the same as 6/x + 2= (6/x) + 2

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I must decide if the algebraic manipulation is correct or incorrect. if it is incorrect I need to fix it or explaine why it cannot be simplified.I don't know if this is the right spot to post but if you can help that would be great.
16^(exponet is a fraction)3/2= (16^1/2)^3 (exponent in () is a fraction)= 4^3= 64
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???
Those are the same, and they equal 64.

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3^x+3^x+3^x = 3^3^x
:
not right, think of it like this:
1(3^x) + 1(3^x)+ 1(3^x) = 3(3^x)

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I must decide if the algebraic manipulation is correct or incorrect. if it is incorrect I need to fix it or explaine why it cannot be simplified.I don't know if this is the right spot to post but if you can help that would be great.
12^x/2^x=6^x
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It is correct.

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7.55x 1000000=7550000

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Actually it should be:
= =

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I must decide if the algebraic manipulation is correct or incorrect. if it is incorrect I need to fix it or explaine why it cannot be simplified.I don't know if this is the right spot to post but if you can help that would be great.
(4x^2/5y^3)^3=4x^6/5y^9
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Not correct, the coefficients must also be raised to the 3rd power.

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I must decide if the algebraic manipulation is correct or incorrect. if it is incorrect I need to fix it or explaine why it cannot be simplified.I don't know if this is the right spot to post but if you can help that would be great.
2/3^-x=2(3^x)=6^x
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It's not correct.
If I interpret it correctly, it's
, which is
, but that's all that can be done.

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I must decide if the algebraic manipulation is correct or incorrect. if it is incorrect I need to fix it or explain why it cannot be simplified.I don't know if this is the right spot to post but if you can help that would be great.
6x^2-14x+4=(3x-4)(2x-1)
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That's not correct.
6x^2-14x+4 = 3x^2 - 7x + 2 (divide by 2)
= (3x-1)*(x-2)
Or, for the original, double either binomial:
6x^2-14x+4 = (6x-2)*(x-2), or
6x^2-14x+4 = (3x-1)*(2x-4)
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(3x-4)*(2x-1) = 6x^2 - 11x + 4, not the same.

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I must decide if the algebraic manipulation is correct or incorrect. if it is incorrect I need to fix it or explaine why it cannot be simplified.
6x-2(x-y)= 6x-2x-2y = 4x-2y
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It's incorrect, should be +2y in the center
6x-2(x-y)= 6x-2x+2y = 4x+2y

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multiplying by the complex conjugate of the denominator (5-2i)

__ __

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d/4 = -6
d = (-6)*4
d = -24

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Rewriting:
distribute
combine similar terms

------->

go back eqn to check:




Thank you,
Jojo

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8*(4*9)= (8*4)*9 demonstrates the Associative Property of Multiplication

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i got the same answer as you although i kept the denominator as 1 number.
original equation is
i multiplied top and bottom by to remove imaginary number from the denominator.
result was
which is the same answer you got.
looks good from what i can tell.
is correct.

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Multiply by the conjugate of the denominator over itself:
* = = =
=

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.
To get rid of the 'i' from the numerator, multiply by (-3+2i)/(-3+2i):

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-24*-2=48 answer.

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-22=11-6a
I guess you are trying to solve for a.
Begin by subtracting 11 from both sides of the equation.
-22 - 11 = -6a
Next, divide both sides of the equation by -6.
-33/-6 = a
33/6 = a
We can reduce this fraction.
Final answer: 11/2 = a
======================
How do we know that the answer is a = 11/2?
We plug the value of [a] back into the original equation given. If we get the same answer on both sides of the equation, then we will know that the answer is right.
THE PROVE:
-22 = 11 - 6a....This is your original equation.
Replace [a] with (11/2) and simplify.
-22 = 11 - 6(11/2)
-22 = 11 - 3(11)
-22 = 11 - 33
-22 = -22....IT CHECKS!!!
Now we know for sure that a = 11/2
Did you follow?
REMEMBER: Always check your answer.

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-2/3 is a fraction so it is a rational number and is in the set of rational numbers denoted by Q.
You could also say it is part of the set of negative real numbers denoted by R-

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Do you mean Queen Elizabeth??
Check www.wikipedia.org for a list of queens named Elizabeth.
Good luck.

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1 belongs to rational numbers, integers, natural numbers, and whole numbers.

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X+(X+1)=119
2X+1=119
2X=118-1
2X=118
X=118/2
X=59 FOR THE SMALLER INTEGER.
59+1=60 FOR THE LARGER INTEGER.

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For a woman with 40 inch hips the ideal waist is 32 inches. What is the maximum level if woman has 35 inch hips
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No, it should be set up like a ratio problem.
Since the ideal size is "40 inch hips the ideal waist is 32 inches" the ratio is:
32:40
.
To calculate waist for 35 inch hips.
32:40 = 35:?
32/40 = 35/?
cross multiply to give:
32? = 40(35)
? = 40(35)/32
? = 43.75 inches