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rapaljer answered: 4664 problems
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3x-2y+4(-x+3(y-2x)-3y)-2x
1 solutions
Answer 30148 by rapaljer(4667)   on 2006-07-11 02:37:37 (Show Source):
You can put this solution on YOUR website!First remove the parentheses on the inside by distributive property:
3x-2y+4(-x+3(y-2x)-3y)-2x
3x-2y+4(-x+3y-6x-3y)-2x
Next, combine like terms within the remaining parentheses (the +3y -3y subtract out):
3x -2y +4(-7x) -2x
3x -2y-28x -2x
Combine the x terms:
-27x -2y
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Polynomials-and-rational-expressions/44811: This question is from textbook
Given that (3x-a)(x-2)(x-7)=3x^3-32x^2+81x-70, determine the value of a.
Thanks!
1 solutions
Answer 30144 by rapaljer(4667) on 2006-07-11 01:32:26 (Show Source):
You can put this solution on YOUR website!This one looks intimidating, but it is much easier than it looks!!
If you expanded the left side of this equation, you would have a polynomial in which the last times last times last would be (-a)(-2)(-7), which would equal the number term on the right side, which is -70.
It would be -14a = -70, so  .
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logarithm/45390: Please explain the difference between a logarithm of a product and the product of logarithms and give examples of each.
1 solutions
Answer 30142 by rapaljer(4667) on 2006-07-11 01:10:17 (Show Source):
You can put this solution on YOUR website!The logarithm of a product is like log(M*N).
The product of logarithms is like log(M)*log(N).
It is a very important distinction to make, since the first case brings up the very important LAW OF LOGARITHMS:
log(M*N) = log(M) * log(N).
There is no such property for the second case, the product of logarithms!
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Coordinate-system/45339: Sketch the region given by the set?
!cx,y)! y > 1)
1 solutions
Answer 30141 by rapaljer(4667) on 2006-07-11 01:06:32 (Show Source):
You can put this solution on YOUR website!On the xy-plane, draw a horizontal dotted line through the point y = 1. Then shade everything that is ABOVE this dotted line. This will be the solution.
Here is the line: 
You will have to make this a dotted line, and shade above the line.
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Polynomials-and-rational-expressions/45260: I can not figure this problem out, what am I not doing right?
Rewrite the middle term as the sum of two terms and then factor by grouping. x2 – 2x – 63
1 solutions
Answer 30136 by rapaljer(4667) on 2006-07-11 00:55:22 (Show Source):
You can put this solution on YOUR website!Notice taht 63 can be written as 9*7, and also notice that -9 +7 = -2. Isn't that an interesting coincidence for this problem!!
So, let's write this  and do factoring by grouping. Group the first two and take out a common factor of x, and take out a common factor of 7 from the last two terms.
Now, there is common factor of x-9, so take out this common factor:
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logarithm/45273: This question is from textbook College Algebra
1. Find the domain of the function f(x) = ln(x - 7).
1 solutions
Answer 30134 by rapaljer(4667) on 2006-07-11 00:48:20 (Show Source):
You can put this solution on YOUR website!f(x) = ln(x-7)
This function has a restriction that for ln(u), u must be a positive number. ln(0) is undefined, ln of a negative number would be a complex number. Therefore, x-7>0, so x>7.
Domain: (7, inf)
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Polynomials-and-rational-expressions/45263: I don't understand this problem. Please help me?
Complete the following statement. 6a2 – 5a + 1 = (3a – 1)( )
1 solutions
Answer 30131 by rapaljer(4667) on 2006-07-11 00:23:29 (Show Source):
You can put this solution on YOUR website!
In this problem, the first times first must equal  . You are given that one of the factors is 3a, so the OTHER factor must be 2a. It should look like this:
Now, notice that the last term on the left side is a +1. This means that the last times last on the right side must be -1 times -1. So it must be this way for the final answer:
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Polynomials-and-rational-expressions/45264: This does not make sense to me...please help.
Factor by grouping. x3 – 3x2 + 4x – 12
1 solutions
Answer 30130 by rapaljer(4667) on 2006-07-11 00:17:46 (Show Source):
You can put this solution on YOUR website!
Group the first two together and take out a common factor of  . Then from the last two, take out a common factor of 4:
Notice that there is now a common factor of (x-3). Take out this common factor, and you have:
The sum of squares does not factor at this level, so this is the final answer.
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Linear-equations/45267: Find the equation of the line with x-intercept 2 and y- intercept 3.
1 solutions
Answer 30129 by rapaljer(4667) on 2006-07-11 00:14:17 (Show Source):
You can put this solution on YOUR website!If the x intercept is (2,0) and the y intercept is (0,3), then the slope is the rise over run, so
The equation of the line is y=mx + b, where m=-3/2 and b is the y intercept which is 3. Therefore, the equation of the line is  .
The graph looks like this (no extra charge!!):
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real-numbers/45383: This question is from textbook algebra 1 concepts and skills
well i got into algebra 1 in eighth grade and the graphing and he multiplying is a problem for me. i think i need help on it.
1 solutions
Answer 30125 by rapaljer(4667) on 2006-07-10 23:54:59 (Show Source):
You can put this solution on YOUR website!You might want to check my website for some additional explanations. Click on my tutor name "rapaljer" anywhere in algebra.com, and look for "Basic Algebra", then "Samples from Basic Algebra: One Step at a Time", then Chapter 1. It's all free!!
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Distributive-associative-commutative-properties/45302: hi mam,sir. how can i understand the math algebra? becuse i have a problem her that its har fpr me to uderstand example.state the properties of a real number
example:
if a=b and b=3,thena=3 how can i state that ian a properties of real numbers hope u can help me.
1 solutions
Answer 30124 by rapaljer(4667) on 2006-07-10 23:51:54 (Show Source):
You can put this solution on YOUR website!This is called the Transitive Property of Equations for real numbers.
"If a = b, and b= c, then a=c."
It comes from the word "trans" which means "across". If you can get from point a to point b, then from point b you can get to point c, then you can get "across" from point a to point c.
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Coordinate-system/45157: I got this wrong. Solve this by the following system by graphing.
1 solutions
Answer 30053 by rapaljer(4667) on 2006-07-10 01:21:49 (Show Source):
You can put this solution on YOUR website!In this problem, both equations represent the same line, as you can see if you multiply both sides of the second equation by 3.
To graph, let x= 0, in each equation, and y turns out to be -1.5.
Let y = 0, and in each equation, x turns out to be 3.
The graph should look like this:
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Polynomials-and-rational-expressions/45240: This one is confusing me because of the exponents. Can someone help me?
Factor. 8m4n – 16mn4
Below are my choices:
A) 8m4n(1 – 2n3) B) 8m4n4(m – 2n) C) 8mn(m3 – 2n3)
D) 8m4n(1 – 16mn4)
1 solutions
Answer 30051 by rapaljer(4667) on 2006-07-10 01:13:07 (Show Source):
You can put this solution on YOUR website!As always, begin by taking out the common factor which will be 8mn:
 The answer is C).
For help with factoring the common factor, see my website by clicking on "rapaljer" anywhere in algebra.com, then look for "Basic Algebra" then "Basic Algebra: One Step at a Time", then Chapter 2, Section 2.03 Factoring the Common Factor.
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Polynomials-and-rational-expressions/45245: Should this be multiple steps?
Factor. 18x3 – 36x2
Choices:
A) 18x2(x – 36) B) –18x(x2 – 36x) C) –9x2(–2x + 4) D) –9x2(–2x – 36)
1 solutions
Answer 30049 by rapaljer(4667) on 2006-07-10 01:04:33 (Show Source):
You can put this solution on YOUR website!A lot of these factoring problems require multiple steps, but not this one. This has a common factor, and that's about it. The common factor is 18x^2, so take out this common factor:
 The final answer is NOT given.
Now, look at the choices that ARE given. The C answer is a factored form of this problem, but it is NOT factored completely. It could be a trick question, or it could be a poorly stated problem. Ask your teacher for his/her opinion of this one. It might even be an oversight or an error by the one who made up the problem.
If you need more problems that work out better than this one did, please see my website under Basic Algebra, Chapter 2.
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Linear-equations/45249: find the equation of the line that passes through the point whose coordinates are (1, -1) and has slope 2.
y - (-1) = 2(x - 1) or y - (-1) = 2 (x + 1)
y + 1 = 2(x + 1)
y + 1 = 2x + 2
not sure if I even started that off right but the answer should be
y=2x-3
1 solutions
Answer 30046 by rapaljer(4667) on 2006-07-10 00:51:52 (Show Source):
You can put this solution on YOUR website!You are correct again!! I don't know if they teach this in school, but I discovered a quick way to check the answer when you have to find the equation of a line. First, check to see if the slope is correct. Then second, substitute the value of x from the given point into your equation, and see if you get the correct y value for the given point. If so, then it checks! In your case, it checks!!
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Polynomials-and-rational-expressions/45247: My answer is not matching any of these choices....
Factor completely. b2 – ab – 6a2
A) (b + 3a)(b – 2a) B) (b – 6a)(b + a) C) (b + 6a)(b – a) D) (b – 3a)(b + 2a)
1 solutions
Answer 30036 by rapaljer(4667) on 2006-07-09 21:45:21 (Show Source):
You can put this solution on YOUR website!Try the D answer. By the way, since these all seem to be multiple choice, you don't actually have to factor them. You can just multiply out the four multiple choice answers, and see which one gives you the problem you are supposed to factor.
Multiply out D)
(b-3a)(b+2a)
b^2 +2ab-3ab-6a^2
b^2 -ab -6a^2
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Equations/45160: Solve each of the following systems by addition.If a unique solution does not exist ,state whether the system is inconsistent or dependent.
x + 5y =10
-2x -10y =-20
1 solutions
Answer 30035 by rapaljer(4667) on 2006-07-09 21:41:56 (Show Source):
You can put this solution on YOUR website!If you multiply both sides of the first equation by -2, you will find that the first equation is exactly the same as the second equation. In this case, the system is said to be dependent and there is NOT a unique solution. The solution is actually the entire line.
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Quadratic_Equations/45227: !x!_> 3
1 solutions
Answer 30034 by rapaljer(4667) on 2006-07-09 21:36:52 (Show Source):
You can put this solution on YOUR website!
Do you understand that absolute value of a positive number is positive, the absolute value of 0 is zero, and the absolute value of a negative number is actually the positive number associated with it. Like absolute value of 3 is 3, absolute value of -3 is 3, absolute value of -5 is 5, etc. Be sure you understand this first.
Now, draw a numberline, and by trial and error try to find the numbers on the numberline where the absolute value of the number will result in a number that is greater than or equal to 3.
Trial and error results in all numbers that are from 3 on the numberline, and to the right on the numberline, like 4, 5, 6, etc.
Also, trial and error results in the number -3, and all numbers to the left of -3, like -4, -5, -6, etc.
This means that  . In interval notation, this would be
(-inf, -3] U [3, inf).
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In interval notation
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test/45230: 3x + 2y = 6
1 solutions
Answer 30033 by rapaljer(4667) on 2006-07-09 21:27:29 (Show Source):
You can put this solution on YOUR website!What was the question? Draw the graph? If so,
Let x=0, then 2y = 6, so y = 3.
Let y=0, then 3x = 6, so x = 2.
Graph these two points: (0,3) and (2,0), and connect the dots!! It should look like this:
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