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Question 1158010: When the number 𝑛 is written in base 𝑏, its representation is the two-digit number 𝐴𝐵 where 𝐴=𝑏−2 and 𝐵=2. What is the representation for 𝑛 in base (𝑏−1)?
Answer by KMST(5396)

(Show Source):

You can put this solution on YOUR website!
The value of a number in any base is really a polynomial.
If ABCD is how a number is written in base

, its value is
Ax%5E3%2BBx%5E2%2BCx%2BD

.
Of course, if ABCD is how a number is written in base

,
we know that

is an integer,
that

is greater than A, B, C, and D,
and that

would be written as 10 in base

The value of number 324 in base 10 is 3%2A10%5E2%2B2%2A10%2B4

.

The value of the number

written as

in base

, and we know that b%3EA=b-2

and

.
So,

and

.
Substituting b-2

for

and

for

, we get

Now we are dealing with polynomials.
n=%28b-2%29b%2B2

-->

-->

-->

-->

Highlight%28n=1%2A%28b-1%29%5E2%2B0%2A%28b-1%29%2B1%29

and that polynomial in %28b-1%29

is the value of the number that in base b-1

would be written as highlight%28101%29

Question 24587: Solve the system of equations by substitution: y= xsquared+2x-2 and y=3x+4
thanx
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39838)   (Show Source):
You can put this solution on YOUR website!
two expressions for y, are then equal.

Try to factor.

Check each of x=3, and x=-2, and find which work and which do not, if any or either.

Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

Solve the system of equations by substitution: y= xsquared+2x-2 and y=3x+4 thanx ***** There're 2 sets of solutions: (3, 13), and (- 2, - 2), NOT 1 as the other person states.

Question 49223: We are suppose to find the gcf of the product but I am unsure of where to start. Should I start by sloving the equation or just factoring each term.
(6y^2-3y)(y+7)
Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
We are suppose to find the gcf of the product but I am unsure of where to start.
Should I start by sloving the equation or just factoring each term.
(6y^2-3y)(y+7)
~~~~~~~~~~~~~~~~~~~~~~~~~~

This "problem" is posed mathematically incorrectly.

For polynomials, GCF (Greatest Common Factor) is determined, when two or more polynomials are considered.
Here, in this problem, only one polynomial is under the consideration - THEREFORE, it makes no sense
to ask about the GCF - it is not defined.

Simply a person, who created/composed this "problem", does not know the basic definitions
(which happens at this forum practically every day).

The : as worded, this composition in the incoming post makes no sense.

How @consc198 responds this question, only demonstrates that this person does not know basic definitions, too.

Question 47801: Can you please tell me if the answer to this question that I got is correct?
(-10xy^3z^2)^3= x^3y^9z^6/1000, just to clarify, x to the third, y to the ninth, z to the sixth over 1000 Thank you so much for the help!!!

Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
Can you please tell me if the answer to this question that I got is correct?
(-10xy^3z^2)^3= x^3y^9z^6/1000, just to clarify, x to the third, y to the ninth, z to the sixth over 1000
Thank you so much for the help!!!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From @consc198, you got the answer "Yes that is correct !".

This answer is TOTALLY WRONG !

The answer you got is WRONG.

The correct identity is

(-10xy^3z^2)^3= -1000*x^3*y^9*z^6.

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

Keep in mind that this "enthusiast" @consc198 is practically illiterate in Math.

Looking in his output at this forum, I see that he produced 58 posts/solutions,
and then suddenly stopped his activity.

I hope that the managers of the other site, where he was affiliated, got understanding
that his qualification in Math is below any acceptable level and removed him from the staff.

Question 299158: Solve by the LCM method:

I am unable to come up with the LCD: (y+3)(y-3)? Unsure of how to work this. Once I have the LCD, I believe I will be able to solve it. Thank you in advance for your help.
Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
Solve by the LCM method:
+ = .
I am unable to come up with the LCD: (y+3)(y-3)? Unsure of how to work this.
Once I have the LCD, I believe I will be able to solve it. Thank you in advance for your help.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        The solution in the post by @mananth is incorrect.
        I came to bring a correct solution.

LCM (the Least Common Multiple) is y*(y^2-9) = y*((-3)*(y+3). So, we multiply both sides of the given equation by this expression y*(y-3)*(y+3). We get 6y*(y-3) + 2(Y^2-9) = (5y-3)y, 6y^2 - 18y + 2y^2 - 18 = 5y^2 -3y, 3y^2 - 15y - 18 = 0, y^2 - 5y - 6 = 0, (y-6)*(y+1) = 0. The roots are y = 6 and/or y = -1. ANSWER. The solutions for the given equation are y= 6 and/or y = -1. To , I used a free of charge plotting tool at web-site http:\\www.desmos.com/calculator/ I printed the formulas for the left side and right side functions and got two plots. They have exactly two intersection points at y = 6 and y = -1 , confirming my solution.

Solved correctly.

Question 411220: I need to solve this rational equation 18/x-3+18/x+3=8

Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13367)   (Show Source):
You can put this solution on YOUR website!

Almost certainly, your equation is 18/(x-3)+18/(x+3)=8. (If you are working a problem like this, then you should be far enough in your study of algebra to know that proper use of parentheses is important!)

Inspection and a little logical reasoning and mental arithmetic show that x=6 is a solution. However, formal algebra shows that there are two solutions....

Multiply both sides by to clear fractions:

or

ANSWERS: 6 and -3/2

Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

I need to solve this rational equation 18/x-3+18/x+3=8 ****************************************************** Solution depends on whether it's or ! The person who responded has the former, but who knows!

Question 278288: 7w^3/28w^2
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39838)   (Show Source):
You can put this solution on YOUR website!

Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
7w^3/28w^2
~~~~~~~~~~~~~~~~~

The answer ' 1/2 * w ' in the post by @mananth is incorrect.

The correct answer is 1/4 * w.

Question 276444: Factor by grouping x^2-y^2-ax-ay
Found 2 solutions by n2, ikleyn:
Answer by n2(91)   (Show Source):
You can put this solution on YOUR website!
.
Factor by grouping x^2-y^2-ax-ay
~~~~~~~~~~~~~~~~~~~~~~~~

x^2-y^2-ax-ay = = (x+y)(x-y) - a(x+y) = (x+y){ x-y -a) This is the final ANSWER: x^2-y^2-ax-ay = (x+y)*(x-y-a).

Solved.

Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
Factor by grouping x^2-y^2-ax-ay
~~~~~~~~~~~~~~~~~~~~~~~~

        In the post by @mananth, factoring is made incorrectly, giving wrong answer.
        I came to bring a correct solution.

x^2-y^2-ax-ay = = (x+y)*(x-y) - a(x+y) = (x+y)*{x-y-a) This is the final ANSWER: x^2-y^2-ax-ay = (x+y)*(x-y-a).

Solved correctly.

Question 243807: The Epson Stylus 850 can print Helen's class project in 18 minutes. The Epson Stylus 500 can print the project in 36 minutes. If the two printers work together, how long would they take to print out the project?
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13367)   (Show Source):
You can put this solution on YOUR website!

The response from tutor @MathTherapy shows the standard formal algebraic method for solving "working together" problems like this.

Here are two (very similar) less formal methods for solving such problems, if a formal algebraic solution is not required.

(1) Notice that the model 850 can do the job in half the time required by the model 500. That means the model 850 does work twice as fast as model 500, so it is like having two model 500s working together. So one model 850 and one model 500 is like have 2+1 = 3 model 500s. And since one model 500 can print the job in 36 minutes, 3 model 500s can print the job in 36/3 = 12 minutes.

ANSWER: 12 minutes

(2) Consider the least common multiple of the two given times; the least common multiple of 18 and 36 is 36.

Consider what the two model could do in 36 minutes. The model 500 in 36 minutes could do the job 36/36 = 1 time; the model 850 in 36 minutes could do the job 36/18 = 2 times. So the two models together in 36 minutes could do the job 1+2 = 3 times; therefore, they could do the one job together ins 36/3 = 12 minutes.

ANSWER: 12 minutes

Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

The Epson Stylus 850 can print Helen's class project in 18 minutes. The Epson Stylus 500 can print the project in 36 minutes.If the two printers work together, how long would they take to print out the project? *************************************************************************************************** At least this person admitted that he/she is NOT a tutor, and is omly trying to help. But, instead of engaging in a task that might be too much for him/her, why NOT just leave the problem alone, so someone who knows how to solve it, can do so? Needless to say, this person's answer is WRONG. 18 is NOT added to 36, and then the result is divided by 2 to get 22 hours. This makes absolutely NO SENSE! One should realize that, since 1 printer can do the job (print the project) in 18 minutes, it's IMPOSSIBLE for both printers, working together, to do the same job (print the project) in more time than it takes 1 printer, working alone. With both working together, it will MOST DEFINITELY take less time than it takes just 1 to print the project. Makes sense? Anyway, let the time it takes both printers to print the project, be T The FASTER printer, working alone, takes 18 minutes to print the project, or can do of the job in 1 minute Likewise, the SLOWER printer, working alone, takes 36 minutes to print the project, or can do of the job in 1 minute We then get the following TOTAL-JOB equation: 2T + T = 36 ---- Multiplying by LCD, 36T 3T = 36 Time it takes both printers, working together, to do the job, or Do you notice that the model numbers: Epson Stylus 850 and Epson Stylus 500 were included? Including IRRELEVANT numbers, is DELIBERATELY done, at times, to confuse the reader.

Question 384433: I am having a problem with dividing polynomials.
(6x^2 - 25x - 10) divided by (3x + 2)=?????
send the complete question.
I know that 3x/6x^2 = 2x after that I am lost. Can you help!
Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

I am having a problem with dividing polynomials. (6x^2 - 25x - 10) divided by (3x + 2)=????? send the complete question. I know that 3x/6x^2 = 2x after that I am lost. Can you help! ************************************************************* 2x ------------------------- 3x + 2 | 6x² - 25x - 10 | 6x² + 4x <===== Multiplying quotient, 2x by divisor, 3x + 2 | - 29x - 10 <== Subtracting 6x² + 4x from 6x² - 25x, and BRINGING DOWN - 10 | - 29x - <== Multiplying quotient, by divisor, 3x + 2 | ------------------ | - 10 <== Subtracting - 29x from - 29x - 10 , or <=== Remainder So, =

Question 264797: a^2/a-3 = 9/a-3
Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
a^2/a-3 = 9/a-3
~~~~~~~~~~~~~~~~~~~

        The solution by @mananth in his post is FATALLY WRONG.
        See my correct solution below.

Your original equation is = . Its domain is the set of all real numbers except of 'a = 3', where the denominator is zero and expressions on the left side and the right side are not defined. So, we will look for the solution (a solution) in the domain, excluding a = 3. In the domain, multiply both sides by (a-3). You will get an equivalent equation in the domain a^2 = 9, which gives two possible solutions a = 3 and a = -3. But a = 3 is a prohibited value, while a = -3 works perfectly. ?ANSWER. The solution to the given equation is a = -3. This solution is UNIQUE: there is NO other solution.

Solved correctly.

This problem is a TRAP, and @mananth felt in this trap, inviting you, the reader, to follow him.

My task is to teach you to recognize such traps and to avoid them.

Question 1003361: If 1 is a zero of p(x) =ax^3-(a-1)x-1 then find value of a
Found 2 solutions by MathTherapy, ikleyn:
Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

If 1 is a zero of p(x) =ax^3-(a-1)x-1 then find value of a ********************************************************** Given that 1 is a 0/1 is a solution, becomes: --- Substituting 1 for x 0 = a - a + 1 - 1 ------ Substituting 0 for p(1), and simplifying 0 = 0 (TRUE) As the above equation proves TRUE, there's NO 1 SPECIFIC value for "a." As such, ANY value of "a" will SATISFY the function,

Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
If 1 is a zero of p(x) = ax^3-(a-1)x-1 then find value of a
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In his post, @mananth deduces that, under given condition, the value of ' a ' must be 1.

        It is a crude and a danger logical mistake.

Actually, a ' 1 ' is a root of a polynomial   p(x) = ax^3 - (a-1)x - 1 for value of ' a ',

Indeed, for every such a polynomial p(x),   p(1) = a - (a-1) - 1 === 0 identically for any value of 'a'.

So, from the given condition, we can not determine a value of ' a ' : it can be number/value.

I don't know if this problem is a mathematical joke or a TRAP to catch
a hapless student, or a mistake of the problem's creator, but what I said is the FACT.

If it is a trap, then @mananth has fallen in this trap and invites all his readers to follow him.

Question 722429: Divide.
6x3-7x2-9/
3x+1
Please help thank you!
that / is suppose to be in the middle of 6x3-7x2-9 and 3x+1
the 6x3 the 3 is suppose it be an exponent also the 7x2 the 2 is suppose to be an exponent
**Sorry I dont know how to do exponents on this website.
Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

Divide. 6x3-7x2-9/ 3x+1 Please help thank you! that / is suppose to be in the middle of 6x3-7x2-9 and 3x+1 the 6x3 the 3 is suppose it be an exponent also the 7x2 the 2 is suppose to be an exponent **Sorry I dont know how to do exponents on this website. ******************************************************* . So, FINAL answer is:

Question 139405: I need to solve this equation and state any extraneous solutions. When it says over, it's a fraction. I didn't know how else to put it.
a over 3a+6
minus
a over 5a+10
equals 2 over 5

Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

I need to solve this equation and state any extraneous solutions. When it says over, it's a fraction. I didn't know how else to put it. a over 3a+6 minus a over 5a+10 equals 2 over 5 *********************** The LCD is simply 3(5)(a + 2), NOT what the other person states. As a result, the quadratic equation formula is NOT needed here, as he/she believes. ====> , with 5a - 3a = 2(3)(a + 2) ---- Multiplying by LCD, 3(5)(a + 2) 2a = 6a + 12 2a - 6a = 12 - 4a = 12

Question 1026531: 4/x-3 + 2x\xsquared-9 = 1/x+3
Found 2 solutions by n2, ikleyn:
Answer by n2(91)   (Show Source):
You can put this solution on YOUR website!
.
4/(x-3) + (2x)/(x^2-9) = 1/(x+3)
~~~~~~~~~~~~~~~~~~~~~~~~~

Your starting equation is + = . Notice that the domain of this equation is the set of all real numbers except of x = 3 and/or x = -3, where the denominators are not defined. So, we will work on the domain x =/= -3 and x =/= 3. Multiply both sides by (x^2-3). You will get 4(x+3) + 2x = x - 3, 4x + 12 + 2x = x - 3, 6x - x = -3 - 12 5x = -15, x = -15/5 = -3. But x = -3 is not in the domain. So, we conclude that the given equation HAS NO solutions in its domain. <<<---=== ANSWER

Solved.

Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
4/(x-3) + (2x)/(x^2-9) = 1/(x+3)
~~~~~~~~~~~~~~~~~~~~~~~~~

        This problem is very tricky.
        It contains a hidden trap that's easy to fall into.
        Tutor @mananth didn't avoid this trap — he fell into it and produced an incorrect solution,
        for which he deserves a solid F.

        Below is my correct solution to replace @mananth's incorrect one.

Your starting equation is + = . Notice that the domain of this equation is the set of all real numbers except of x = 3 and/or x = -3, where the denominators are not defined. So, we will work on the domain x =/= -3 and x =/= 3. Multiply both sides by (x^2-3). You will get 4(x+3) + 2x = x - 3, 4x + 12 + 2x = x - 3, 6x - x = -3 - 12 5x = -15, x = -15/5 = -3. But x = -3 is not in the domain. So, we conclude that the given equation HAS NO solutions in its domain. <<<---=== ANSWER

Solved correctly.

Question 1033430: Write a polynomial that represents the sum of the square of the next even integer after the integer x and the square of the integer right before the integer x.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39838)   (Show Source):
You can put this solution on YOUR website!
---------------------------------------
the sum of the square of the next even integer after the integer x and the
square of the integer right before the integer x.
---------------------------------------

x, an EVEN integer
x+2, the even integer after x
x-1, the integer "right before" x

Transcribing the description:

Some algebra steps

Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
Write a polynomial that represents the sum of the square of the next even integer
after the integer x and the square of the integer right before the integer x.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To the next generations of visitors who will read this post.

The formulation of the problem in the post is mathematically incorrect (illiterate).

So, do not try to catch an exact/precise meaning in it - you better simply ignore it.

Nonsense should be called by its proper name and consigned to the trash,
rather than trying to interpret it and/or give it some kind of meaning.

Question 619589: i need help with this i need to add and simplify thanks
3w/w^2-64 + w/w-8
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39838)   (Show Source):
You can put this solution on YOUR website!

Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

i need help with this i need to add and simplify thanks 3w/w^2-64 + w/w-8 FYI, the other person's answer, is DEAD WRONG!!

Question 131106: Please can you help me with this equation, I have tried but can't figure it out. The answer from the back of my text book says that it is T=P/.25 or T=P*4, but I have to show my work. the equation is (T+P)/T=1.25 and I need to solve for T.
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13367)   (Show Source):
You can put this solution on YOUR website!

To solve the given equation for T, the objective is to manipulate the given equation to get an equivalent equation in which all the terms with T are on one side of the equation.

Then divide by the coefficient to get T by itself.

or , which is equivalent to

Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

Please can you help me with this equation, I have tried but can't figure it out. The answer from the back of my text book says that it is T=P/.25 or T=P*4, but I have to show my work. the equation is (T+P)/T=1.25 and I need to solve for T. T + P = 1.25T ---- Cross.multiplying P = 1.25T - T P = .25T

Question 312845: I need some help with this problem,
Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

I need some help with this problem, = = That's it!!

Question 1178647: The formula F=Kq1q2/r^2 gives the force between two point charges of q1 and q2 coulombs that are r metres apart. If two equally charged balls are placed 0.1m apart and the force between the balls is 9.8*10^-4 Newtons, calculate the charge on each ball to 2 significant figures, given K=9.0*10^9.
Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
The formula F=Kq1q2/r^2 gives the force between two point charges of q1 and q2 coulombs that are r metres apart.
If two equally charged balls are placed 0.1m apart and the force between the balls is 9.8*10^-4 Newtons,
calculate the charge on each ball to 2 significant figures, given K=9.0*10^9.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        Calculations in the post by @mananth are incorrect.
        I came to bring a correct solution.

F = r = 0.1 F = 9.8*10^-4 Newtons, K = 9.0*10^9. q=? Substitute the values into the basic formula = = = = = q = <<<---=== ANSWER

Solved.

Question 434848: hi..im in 7th grade algebra and i work out of the algebra 1 book published by glenco. i am in chapter 8 and working on dividing monomials. i really dont understand my homework and need help.. i dont want you to give me the answer, i want to be able to understand it. i dont understand wether i am supposed to divide the final product or what. here is some questions i am having trouble with on my homework for tonight.

#20. -2a cubed over 10a to the eighth power.
#22. x cubed times y to the zero power times x to the negative 7th power.
please help!!
Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

hi..im in 7th grade algebra and i work out of the algebra 1 book published by glenco. i am in chapter 8 and working on dividing monomials. i really dont understand my homework and need help.. i dont want you to give me the answer, i want to be able to understand it. i dont understand wether i am supposed to divide the final product or what. here is some questions i am having trouble with on my homework for tonight. #20. -2a cubed over 10a to the eighth power. #22. x cubed times y to the zero power times x to the negative 7th power. please help!! ****************** "i dont want you to give me the answer, i want to be able to understand it" I HOPE you do!! #20. -2a cubed over 10a to the eighth power. Go from LEFT to RIGHT 1. SIGNS: First seen are the signs: "-" (in numerator) and "+" (in denominator). They are DIFFERENT! What's the result when 2 DIFFERENT/UNLIKE signs are DIVIDED? 2. COEFFICIENTS: These are 2 (in numerator) and 10 (in denominator). What do you get when you DIVIDE 2 by 10? 3. VARIABLES: These are (in numerator) and (in denominator). What's the result when EXPONENTIAL EXPRESSIONS/MONOMIALS with the same base ("a", in this case) are DIVIDED? What happens to the EXPONENTS when SAME-BASE MONOMIALS are DIVIDED? In other words, how does one "treat" ? ****************** #22. x cubed times y to the zero power times x to the negative 7th power. 1. LIKE-TERMS: DETERMINING like-terms, and then COMBINING them. These are and . What's the result when EXPONENTIAL EXPRESSIONS/MONOMIALS with the same base ("x", in this case) are MULTIPLIED? What happens to the EXPONENTS when SAME-BASE MONOMIALS are MULTIPLIED? In other words, how does one "treat" ? 2. EXPRESSIONS raised to the "0" POWER: This is . What's the result when EXPRESSIONS/MONOMIALS are raised to the "0" POWER? In other words, how does one "treat" ?

Question 764376: 9x to the fourth power minus 25x to the second power plus 16 is equal to zero
Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

9x to the fourth power minus 25x to the second power plus 16 is equal to zero While the other person's solutions/roots are correct, I don't see any sense in the method that he/she used to get them!! ----- Substituting ----- Factoring out GCF for binomials and (3x - 4)(3x + 4)(x - 1)(x + 1) = 0 ----- Factorizing each binomial (3x - 4) = 0 ; 3x + 4 = 0 ; x - 1 = 0 ; x + 1 = 0 ----- Setting each factor equal to 0

Question 455657: Using the Point-Slope form to write equations
m=3/4, (2,-6)
y--6=3/4(x--2)
How do I solve this problem?
Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
Using the Point-Slope form to write equations
m=3/4, (2,-6)
y--6=3/4(x--2)
How do I solve this problem?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        From the post by @mananth, it is clear that he simply does not know
        what a "Point-Slope form" is. Therefore, his solution and his answer are irrelevant,
        non-adequate and incorrect.

        I came to bring a correct solution.

When the slope 'm' and coordinates of a point are given (a,b), the Point-Slope form equation of a line with the given slope 'm' passing through point (a,b) is y - b = m(x - a). <<<---=== by the D E F I N I T I O N So, in this given problem, the required equation is y - (-6) = , or, equivalently, y + 6 = 0.75*(x-2). ANSWER

Solved.

Question 453363: (sub subject is Factoring)
solve
please justify your answer thank you
Found 2 solutions by MathTherapy, ikleyn:
Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

(sub subject is Factoring) solve please justify your answer thank you Another WRONG answer by the other person. is in the form: , NOT , as the other person states. So, it should be , NOT. Therefore, we get: ----- Taking square root of both sides 7a - 4 = 0 7a = 4 DOUBLE Roots/Solutions are located at

Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.
(sub subject is Factoring)
solve
please justify your answer thank you
~~~~~~~~~~~~~~~~~~~~~~

49a^2 - 56a + 16 = 0. Left side is . So, this equation 49a^2 - 56a + 16 = 0 has the root a = . ANSWER

Solved.

Question 83444: perform the indicated division. rationalize the denominator if necessary then simplify each radical expression
-9-square root of 108
over
3
Answer by MathTherapy(10858)   (Show Source):
You can put this solution on YOUR website!

perform the indicated division. rationalize the denominator if necessary then simplify each radical expression -9-square root of 108 over 3 = = = = = <==== Correct answer! That is, if it's NOT

Question 452963: I am having a problem factoring this one 14a^(2)-45a-14
Found 2 solutions by MathTherapy, ikleyn:
Answer by MathTherapy(10858)   (Show Source):
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I am having a problem factoring this one 14a^(2)-45a-14 Use the "ac" method ---- Replacing - 45a with - 49a + 4a

Answer by ikleyn(53937)   (Show Source):
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I am having a problem factoring this one 14a^2-45a-14.
~~~~~~~~~~~~~~~~~~~~~~~~

        The standard treatment of this problem and many other similar problems is to find
        the roots of a polynomial and then to decompose the polynomial.
        @mananth in his post started the job, but not completed it, so I came to do everything
        from the beginning to the end.

Find the roots of the given polynomial using the quadratic formula d = b^2 - 4ac = 45^2 - 4*14*(-14) = 2809 = = = = = ; = = = = = . Therefore, the decomposition of our polynomial is 14a^2 - 45a - 14 = = (2a-7)*(7a+2). ANSWER. 14a^2 - 45a - 14 = (2a-7)*(7a+2).

Solved.

Question 661692: (343/y^9)^-1/3 Write the expression using radical notation. Then simplify if possible.
Answer by MathTherapy(10858)   (Show Source):
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(343/y^9)^-1/3 Write the expression using radical notation. Then simplify if possible. The other person's answer, √7/y^3, is WRONG!! = = =

Question 446771: (y^2-4/y+3)=2-(y-2/y+3)
Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
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(y^2-4/y+3) = 2-(y-2/y+3)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As it is written in the post, it is inaccurate writing and it does not correspond to real intent.

The correct equation is

         = .

Now, @mananth gives the solutions y = 4 OR y = -3.

But if you will present it in this form to your teacher, you can easily get the score of '2'.

It is because y = -3   IS NOT   a solution. It is not even in the domain of this equation.

Therefore, the solution to this problem should start with these words

The domain of this equation is the set of all real numbers except of y = -3, because (y+3) is in the denominator of the formulas.

After that, you make all this analysis, which @mananth makes, but at the end you say

Since the root y = -3 is out of the domain, the only solution to the given equation is y = 4.

It is how to present the complete solution correctly and to get the highest score.

Question 446368: factor the expression completely:
x^4-9x^2
please help me as as u cannnnnnnnnnnnnnnnn
waiting for replyyy
Answer by ikleyn(53937)   (Show Source):
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factor the expression completely:
x^4-9x^2
~~~~~~~~~~~~~~~~~~~~~~~

x^4 - 9x^2 = x^2*(x^2-9) = x^2*(x-3)*(x+3).

Factored completely.

Question 729570: A firm anticipates a capital expenditure of $10,000 for new equipment in 5 years. How much should be deposited quarterly in an account earning 10 % interest per year, compounded quarterly to provide for the purchase?
Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
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A firm anticipates a capital expenditure of $10,000 for new equipment in 5 years.
How much should be deposited quarterly in an account earning 10 % interest per year,
compounded quarterly to provide for the purchase?
~~~~~~~~~~~~~~~~~~~~~~~~

It is about finding the present value of the compounded account. The present value is = 6102.71 (rounded to the closest cent). ANSWER
Solved.

Question 732181: simplify this expression(12)/(7d)-(3)/(14d)
Answer by ikleyn(53937)   (Show Source):
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simplify this expression(12)/(7d)-(3)/(14d)
~~~~~~~~~~~~~~~~~~~~~~~~~

- ---> write with the common denominator 14d ---> = - ---> work with this common denominator ---> = = ---> cancel common factor 7 ---> = . ANSWER

Solved.

It is the story on how to do it.

Question 732364: how do I simplify
x^2+9
Answer by ikleyn(53937)   (Show Source):
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.
how do I simplify
x^2+9
~~~~~~~~~~~~~~~~~~~~~~

Over real numbers, it can not be simplified further.

Over real numbers, it is just the most simplified form.

Question 733227: (4x9 + 2x8 � 5x7 + 6x6 � 3x5 + 2x4 + 4x3 � x2 + 4x � 7) (3x9 - 8x8 � 2x7 - 9x6 � 4x5 + x4 + 2x3 �2 x2 + x + 5)
Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website!
.

This task borders on madness and teaches nothing useful.