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# Recent problems solved by 'rapaljer'

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 Expressions-with-variables/45398: find the indicated sum, products and quotients 3x-2y+4(-x+3(y-2x)-3y)-2x1 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 R^2 at SCC
 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 . R^2 at SCC
 logarithm/45274: This question is from textbook College Algrebra Write as a single logarithm (DO NOT find approximations): 2 log 4 + log x - log 2.1 solutions Answer 30143 by rapaljer(4667)   on 2006-07-11 01:13:27 (Show Source): You can put this solution on YOUR website! R^2 at SCC
 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! R^2 at SCC
 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. R^2 at SCC
 Coordinate-system/45338: Sketch the region given by the set? !(X,Y)! 1 < x < 2)1 solutions Answer 30140 by rapaljer(4667)   on 2006-07-11 01:02:35 (Show Source): You can put this solution on YOUR website!Draw vertical dotted lines on the xy plane through x=1 and x=2. Shade all values between these vertical lines. I'm sorry, but I don't know how to post this graph in algebra.com. R^2 at SCC
 Coordinate-system/45337: Sketch the region given by the set? !( X, Y)! x _< 0 )1 solutions Answer 30138 by rapaljer(4667)   on 2006-07-11 01:00:02 (Show Source): You can put this solution on YOUR website!Since , it means that x must be a negative number or zero. On the xy plane, draw a vertical line on the y axis, and shade everything to the left of the y axis. R^2 at SCC
 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 – 631 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: R^2 at SCC
 Geometric_formulas/45277: find the perimeter length is x/2x-5 height is 8/2x-51 solutions Answer 30135 by rapaljer(4667)   on 2006-07-11 00:50:23 (Show Source): You can put this solution on YOUR website!What kind of figure is it? Is it a right triangle?? R^2 at SCC
 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) R^2 at SCC
 Triangles/45384: triangle has sides 3x + 7 and 4x - 9 and 5x- 7 find the expression that represents the perimeter1 solutions Answer 30133 by rapaljer(4667)   on 2006-07-11 00:42:54 (Show Source): You can put this solution on YOUR website!Add up the three sides: 3x+ 7 + 4x -9 + 5x - 7 Combine like terms: 12x -9 R^2 at SCC
 expressions/45385: Subtract (9z-5/8) from (z+7/8) I got z-3/16 Is this correct? Thanks!1 solutions Answer 30132 by rapaljer(4667)   on 2006-07-11 00:41:22 (Show Source): You can put this solution on YOUR website!(z+7/8) - (9z-5/8) z+7/8 - 9z + 5/8 Combine like terms: -8z + 12/8 This reduces to -8z + 3/2 R^2 at SCC
 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: R^2 at SCC
 Polynomials-and-rational-expressions/45264: This does not make sense to me...please help. Factor by grouping. x3 – 3x2 + 4x – 121 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. R^2 at SCC
 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!!): R^2 at SCC
 Polynomials-and-rational-expressions/45269: x3+6x2+5x+30=01 solutions Answer 30127 by rapaljer(4667)   on 2006-07-11 00:09:30 (Show Source): You can put this solution on YOUR website! This can be solved by factoring by grouping the first two terms and the last two terms together: or If you are looking for real roots, there is only one, x= -6. The other solutions would be , which are NOT real solutions. If you are solving complex solutions, then and of course, x= -6. R^2 at SCC
 logarithm/45275: This question is from textbook College Algebra Expand and simplify: ln(ex)1 solutions Answer 30126 by rapaljer(4667)   on 2006-07-10 23:58:59 (Show Source): You can put this solution on YOUR website! The operations and are inverse operations of one another. Therefore, one operation "undoes" the other operation. So, . R^2 at SCC
 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!! R^2 at SCC
 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. R^2 at SCC
 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: R^2 at SCC
 Quadratic_Equations/45223: !X!< 71 solutions Answer 30052 by rapaljer(4667)   on 2006-07-10 01:16:09 (Show Source): You can put this solution on YOUR website!You are looking for a problem such that the size of the number, regardless of the sign must be less than 7. This would be all numbers on a numberline between -7 and 7. In interval notation, it would be written (-7,7). R^2 at SCC
 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. R^2 at SCC
 Polynomials-and-rational-expressions/45244: I can not get the right answer for this. My answer does not match any of the choices. Please help. Factor completely. y3 – 12y2 + 36y A) y(y – 9)(y + 4) B) y(y – 6)2 C) y(y + 6)2 D) y(y + 12)(y – 3) 1 solutions Answer 30050 by rapaljer(4667)   on 2006-07-10 01:07:27 (Show Source): You can put this solution on YOUR website!First take out the common factor of y: or , which is B). R^2 at SCC
 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. R^2 at SCC
 Polynomials-and-rational-expressions/45248: This one is confusing me....can I get help please? Factor completely. 12x3 – 3xy2 A) 3x(4x – y)(x + y) C) 12x(x – 3y)(x – y) B) 3x(2x – y)2 D) 3x(2x + y)(2x – y) 1 solutions Answer 30048 by rapaljer(4667)   on 2006-07-10 00:58:12 (Show Source): You can put this solution on YOUR website!First take out the common factor of 3x This leaves a difference of two squares, which factors: The correct answer is D R^2 at SCC
 Polynomials-and-rational-expressions/45246: Can someone double check my answer? Factor completely. 5a2 – 125 A) (5a – 1)(a – 125) B) 5a(a – 25) C) 5(a + 5)(a – 5) D) 5(a – 5)2 1 solutions Answer 30047 by rapaljer(4667)   on 2006-07-10 00:54:43 (Show Source): You can put this solution on YOUR website!First take out the common factor of 5 This leaves a difference of two squares, which factors: R^2 at SCC
 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!! R^2 at SCC
 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 R^2 at SCC
 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 =-201 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. R^2 at SCC
 Quadratic_Equations/45227: !x!_> 31 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). R^2 at SCC In interval notation
 test/45230: 3x + 2y = 61 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: R^2 at SCC