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# Recent problems solved by 'rapaljer'

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 Equations/184295: What are extraneous solutions of an equation? Why do they sometimes occur in the process of solving rational or radical equations? can you provide examples? 1 solutions Answer 138312 by rapaljer(4667)   on 2009-02-28 23:06:47 (Show Source): You can put this solution on YOUR website!Extraneous solutions of an equation are EXTRA solutions that work in subsequent equations that are obtained in trying to solve an equation, but that do NOT work in the original equation!! These extraneous solutions are caused by squaring both sides of an equation or by multiplying both sides of an equation by an expression containing a variable. For example, if you took the simple equation x=3, and square both sides, you would get x^2=9, which has two solutions, x=3 and x=-3. The second solution x=-3 is an extraeous solution in that it does NOT solve the original equation. I have a TON of extraneous solutions on my website, which you can find by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for my MATH IN LIVING COLOR pages, and choose Intermediate Algebra. Look for Section 2.07 on Fractional Equations, the last two problems that are posted there. Also look for Section 3.07 Radical Equations! This one is LOADED with extraneous solutions!! I hope this helps!! R^2
 Mixture_Word_Problems/184290: A ladder is resting against a wall. The top of the ladder touches the wall at a height of 9ft. Find the lenght of the ladder if the lenght is 3ft. more than its distance from the wall.1 solutions Answer 138311 by rapaljer(4667)   on 2009-02-28 22:02:19 (Show Source): You can put this solution on YOUR website!Let x = distance from the wall x+3 = length of the ladder By Theorem of Pythagoras: Subtract x^2 from each side: 81=6x+9 72 = 6x x= 12 feet = distance from wall x+3 = 15 feet = length of the ladder Check: R^2
 Mixture_Word_Problems/184289: The area of a square is numerically 3 less than the perimeter. Find the length of the side, if this length is greater than 1 unit.1 solutions Answer 138308 by rapaljer(4667)   on 2009-02-28 21:55:52 (Show Source): You can put this solution on YOUR website!Let x = side of the square. = area of the square = perimeter of the square or The only answer that is greater than 1 is x= 3. R^2
 Exponential-and-logarithmic-functions/184251: 2e^5a+2=81 solutions Answer 138306 by rapaljer(4667)   on 2009-02-28 21:51:27 (Show Source): You can put this solution on YOUR website!Subtract 2 from each side: 2e^5a= 6 Divide by 2: e^5a = 3 Take the ln of each side: ln(e^5a) = ln 3 5a = ln 3 Divide by 5: a = 0.2197 approximately If you need additional help with logarithms and exponential functions, please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look down the homepage for a topic called "Logarithms." I have an entire chapter on Logarithms in a format that my students UNANIMOUSLY tell me it easier to understand than the traditional textbooks. In addition to this, please see my MATH IN LIVING COLOR PAGES (College Algebra, Chapter 4). Let me know if this helps you!!! R^2
 Graphs/184270: This question is from textbook I have a problem graphing y= 3x and y = -x + 41 solutions Answer 138301 by rapaljer(4667)   on 2009-02-28 21:40:12 (Show Source): You can put this solution on YOUR website!Since both of these equations are in slope-intercept form, I recommend the slope-intercept method of graphing them. If you need additional explanations on this, I have a good Lesson PLan on this method here in algebra.com, or go to my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look on my homepage for "Basic Intermediate and College Algebra: One Step at a Time." Select "Basic Algebra" and look for Chapter 5 on Graphing. Now to solve the prlblem. The first graph y=3x is actually y=3x+ 0, so it has a y-intercept of 0 and a slope of 3. Plot the point (0,0). From this point move UP 3 units and RIGHT 1 unit and plot another point. Connect the two points with the first line. FOr the second graph y=-1x+4, the y intercept is 4, so go UP 4 units on the y axis and plot the first point. Then, with your pencil on this point, move DOWN 1 unit and RIGHT 1 unit, and plot the second point. Connect the dots, and you have the second line. It should look like this: R^2
 Equations/184268: on Monday a sea otter ate a certain amount of food. Tuesday the otter ate 4lbs less than he ate on Monday. Wednesday the otter ate 3 lbs more than he ate on Monday. from Monday to Thursday combined, the otter ate his own weight in food: 87 lbs. how much did he eat on each day?1 solutions Answer 138299 by rapaljer(4667)   on 2009-02-28 21:29:32 (Show Source): You can put this solution on YOUR website!Let x = Monday's food x-4 = Tuesday's food x+3 = Wednesday's food _____ = Thursday's food x + x-4 + x+3 + _______ = 87 You apparently forgot to tell us how much the otter ate on Thursday. We can't solve it unless we know that!! R^2
 Graphs/184269: can you please help me on:3.21 solutions Answer 138298 by rapaljer(4667)   on 2009-02-28 21:24:55 (Show Source): You can put this solution on YOUR website!In order to get the r alone on the right side, I recommend that you subtract 4.7 from each side: 3.2 < r+4.7 3.2-4.7 < r +4.7-4.7 -1.5 < r It may help to reverse this and write it as r>-1.5 R^2
 Graphs/184277: -9n>-361 solutions Answer 138295 by rapaljer(4667)   on 2009-02-28 21:16:55 (Show Source): You can put this solution on YOUR website!Divide both sides of the inequality by -9. Remember that very important rule, that when you divide or multiply both sides of an inequality by a NEGATIVE number, you must REVERSE the inequality sign! R^2
 Quadratic_Equations/184208: Answers should be written in sentence form. Explanations must be detailed and well-thought out. Include examples wherever possible. 1.a) Describe the graph of a linear system that has one solution, no solution and infinitely many solutions. Please and thanks.1 solutions Answer 138248 by rapaljer(4667)   on 2009-02-28 15:08:45 (Show Source): You can put this solution on YOUR website!One solution means you have two lines that intersect in a single point. No solution means that the two lines are parallel. Infinitely many solutions means that the two lines are actually the same line. Is this a take home test??? R^2
 Quadratic_Equations/184211: Answers should be written in sentence form. Explanations must be detailed and well-thought out. Include examples wherever possible. 4. Alyssa multiplies both equations in a linear system by 10 to eliminate the decimal. She determines that x=3 and y=2. She then divides her results by 10 to get a solution of (0.3, 0.2). Is her reasoning correct? Explain. Please and thank you very much!!!!1 solutions Answer 138247 by rapaljer(4667)   on 2009-02-28 15:04:56 (Show Source): You can put this solution on YOUR website!She is NOT correct to divide her answer by 10. When she multiplied both sides of the equation by the same number, this retains an EQUIVALENT equation. This is an equation that has the SAME solution as the original equation. So the solution that she gets for the new equation is actually the SAME solution as the solution for the original equation. She should NOT divide the answers by 10!! R^2
 Graphs/183858: This question is from textbook Intermediate Algebra I think the answerr for this problem is zero but I am not sure. 1 solutions Answer 137970 by rapaljer(4667)   on 2009-02-26 00:25:41 (Show Source): You can put this solution on YOUR website!What problemm??? R^2
 percentage/183879: I need to simplify 43-(-12)I tried it this way 43+(-12)= -55 I'm not sure this is right? -12+(-5)-3-(-8) (-4)square - 6 square next ques. 8/9 x ( 1/3-5/6) cubed divided by (-2/3) Not sure how to evaluate ex. I 9 I + I-12 I Thanks for helping me1 solutions Answer 137969 by rapaljer(4667)   on 2009-02-26 00:23:17 (Show Source): You can put this solution on YOUR website!43-(-12)= 43 + 12 = 55 -12+(-5)-3-(-8) -12-5-3+8 -17-3+8 -20+8 -12 That's enough for one question!! Post the rest in another question. R^2
 Polynomials-and-rational-expressions/183890: This question is from textbook I need help on understanding Opposites of Polynomials. I have an example of one its -5x^2-3x+7 opposite of that is -5x^2--3+-7 which simplifies to -5x^2+3x-7. I dont get how that is the answer, should'nt it just simplify to zero? im lost. please help me 1 solutions Answer 137966 by rapaljer(4667)   on 2009-02-26 00:17:36 (Show Source): You can put this solution on YOUR website!Do you mean the opposite of 5x^2-3x+7? By that you probably mean -(5x^2 -3x + 7). It may help to think of this as -1*(5x^2-3x+7), which would be according to the Distributive Property -1*5x^2 + -1*(-3x) + -1*7 -5x^2 + 3x -7 If you ADD the original number plus its opposite, then you get zero. I think the problem was to find the opposite. R^2
 Linear-systems/183257: Use elimination method in solving this; 2x+5y=7 3x-2y=11 solutions Answer 137597 by rapaljer(4667)   on 2009-02-22 20:13:54 (Show Source): You can put this solution on YOUR website!2x+5y=7 3x-2y=1 To make the y coefficients subtract out, multiply both sides of the first equation times 2, and the second equation times 5: 2(2x+5y=7) 5(3x-2y=1) 4x+10y=14 15x-10y=5 Add these equations together: 19x=19 x=1 Substitute x=1 into the first equation: 2x+5y=7 2*1+5y=7 2+5y=7 5y=5 y=1 Substitute both values back into the second equation to check: 3x-2y=1 3*1-2*1=1 3-2=1 It checks!! For more detailed explanations, examples, and exercises, including solutions in LIVING COLOR on my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the pages on my home page, either "Basic, Intermediate, and College Algebra" or "Math in Living Color". In either of these pages, select "Basic Algebra" and then "Chapter 4." Look for the appropriate sections, for an easier to understand explanation than traditional textbooks!! R^2
 Linear-systems/183258: Use elimination method in solving this; 2x+5y=7 3x-2y=11 solutions Answer 137596 by rapaljer(4667)   on 2009-02-22 20:12:56 (Show Source): You can put this solution on YOUR website!2x+5y=7 3x-2y=1 To make the y coefficients subtract out, multiply both sides of the first equation times 2, and the second equation times 5: 2(2x+5y=7) 5(3x-2y=1) 4x+10y=14 15x-10y=5 Add these equations together: 19x=19 x=1 Substitute x=1 into the first equation: 2x+5y=7 2*1+5y=7 2+5y=7 5y=5 y=1 Substitute both values back into the second equation to check: 3x-2y=1 3*1-2*1=1 3-2=1 It checks!! For more detailed explanations, examples, and exercises, including solutions in LIVING COLOR on my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the pages on my home page, either "Basic, Intermediate, and College Algebra" or "Math in Living Color". In either of these pages, select "Basic Algebra" and then "Chapter 4." Look for the appropriate sections, for an easier to understand explanation than traditional textbooks!! R^2
 Linear-systems/183255: help me to answr this this ; 2x+5y=7 3x-2y=11 solutions Answer 137595 by rapaljer(4667)   on 2009-02-22 20:11:54 (Show Source): You can put this solution on YOUR website!2x+5y=7 3x-2y=1 To make the y coefficients subtract out, multiply both sides of the first equation times 2, and the second equation times 5: 2(2x+5y=7) 5(3x-2y=1) 4x+10y=14 15x-10y=5 Add these equations together: 19x=19 x=1 Substitute x=1 into the first equation: 2x+5y=7 2*1+5y=7 2+5y=7 5y=5 y=1 Substitute both values back into the second equation to check: 3x-2y=1 3*1-2*1=1 3-2=1 It checks!! For more detailed explanations, examples, and exercises, including solutions in LIVING COLOR on my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the pages on my home page, either "Basic, Intermediate, and College Algebra" or "Math in Living Color". In either of these pages, select "Basic Algebra" and then "Chapter 4." Look for the appropriate sections, for an easier to understand explanation than traditional textbooks!! R^2
 Rational-functions/183241: Write an equation for the inverse of the relation y=4x+21 solutions Answer 137593 by rapaljer(4667)   on 2009-02-22 20:02:33 (Show Source): You can put this solution on YOUR website!y=4x+2 There are two steps: Step 1: Interchange the x and y variables! x= 4y+2 Step 2: Solve for y! x-2=4y Divide both sides by 4: or R^2
 Linear-systems/183252: Can you please help me and identifies if it is one solution,no solution or infinte solution: 3x+y=1 2x-y=-61 solutions Answer 137591 by rapaljer(4667)   on 2009-02-22 19:54:54 (Show Source): You can put this solution on YOUR website!Just add these two equations together: 3x+y=1 2x-y=-6 5x=-5 x=-1 Substitute back into the first equation: 3x+y=1 3(-1)+Y=1 -3+y=1 y=4 Check in the second equation: 2x-y=-6 2(-1)-(4)=-6 -2-4=-6 It checks!! (-1, 4) For an easier explanation of this topic, please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. On my homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra" and look for the appropriate sections in Chapter 4 of my Basic Algebra book. It's all FREE, just like algebra.com!! R^2
 Exponents-negative-and-fractional/183251: Simplify. Then evaluate the expression when a= 1 and b= 2 (a^2b^2)^31 solutions Answer 137589 by rapaljer(4667)   on 2009-02-22 19:47:22 (Show Source): You can put this solution on YOUR website!(a^2b^2)^3 If a=1 and b=2, (1^2*2^2)^3 (1*4)^3 4^3 64 R^2
 Rational-functions/183240: Simplify the expression. Assume all variables are positive. Leave answer in radical form, no decimals. Let r(x)=2x and s(x)=x^3-3. Find s(r(2)).1 solutions Answer 137588 by rapaljer(4667)   on 2009-02-22 19:44:39 (Show Source): You can put this solution on YOUR website!Let r(x)=2x and s(x)=x^3-3. Find s(r(2)). r(2) = 2*2=4 s(r(2)) =s(4) =4^3-3 =64-3 =61 R^2
 Polynomials-and-rational-expressions/183242: This question is from textbook hold algebra 1 1 solutions Answer 137587 by rapaljer(4667)   on 2009-02-22 19:41:31 (Show Source): You can put this solution on YOUR website!You need to state the problem!! We don't have your book!!
 Radicals/182859: how do I simplify sqrt(6)/sqrt(7)*sqrt(14)/sqrt(3) 1 solutions Answer 137503 by rapaljer(4667)   on 2009-02-22 08:38:06 (Show Source): You can put this solution on YOUR website!There may be several ways to simplify this, but the easiest way is to divide 3 into the 6 and 7 into 14: If you need additional help with square roots, see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. On my homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra" and look in Chapter 5 for topics on Square Roots. In addition to full explanations, examples, and exercises written so ordinary students can understand them, many of the exercises are solved in my MATH IN LIVING COLOR pages. R^2
 Polynomials-and-rational-expressions/183102: This question is from textbook Algebra 2 Factor 8x^3-6x^2-2x1 solutions Answer 137501 by rapaljer(4667)   on 2009-02-22 08:14:11 (Show Source): You can put this solution on YOUR website!The first step is to take out all the common factors. In this case, you have common factors of 2 and x. 2x(4x^2 - 3x -1) Next, see if the trinomial factors (and it does!): 2x(4x +1)(x-1) If you need additional explanation and help with factoring common factors OR factoring trinomials, check out my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the link on my main page that says, "Basic, Intermediate, and College Algebra: One Step at a Time." Then select "Basic Algebra" and look in Chapter 2 for the factoring sections. There you will find detailed explanations, examples, and exercises written in a format that is easier to understand than the traditional textbooks. R^2
 real-numbers/182959: what is 1/12 best described as? 1 solutions Answer 137356 by rapaljer(4667)   on 2009-02-21 00:43:04 (Show Source): You can put this solution on YOUR website!How about a fraction? Maybe a ratio of two integers? Maybe a rational number!! R^2
 Radicals/182831: This question is from textbook saxon algebra 2 3 over square root 7 - square root 2 simplify. The 3 on top confuses me.1 solutions Answer 137252 by rapaljer(4667)   on 2009-02-19 23:23:48 (Show Source): You can put this solution on YOUR website!Do you mean ??? If so, then the trick is to multiply numerator and denominator times the same thing as the denominator but with the opposite sign in the middle. This is called the "conjugate" of the denominator. In other words multiply numerator and denominator times . It looks like this: When you multiply out the denominator you get . . If you need extra explanation on SQUARE ROOTS, go to my website by clicking on my tutor name "Rapaljer" anywhere in algebra.com. On my Homepage, look for about the third link that says "Basic, Intermediate, and College Algebra: One Step at a Time." Click on this, then click on "Basic Algebra." Go to "Chapter 5 (Square Roots)". The explanations, examples, and exercises are integrated and easier to understand than traditional textbooks. Answers to all problems are provided, and many of the exercises are solved in the "MATH IN LIVING COLOR" pages. Check it out! Like Algebra.com, it's all free!! R^2
 Rational-functions/182845: This question is from textbook Mcdougal Littell Algebra 2 please help me do this problem1 solutions Answer 137251 by rapaljer(4667)   on 2009-02-19 23:06:05 (Show Source): You can put this solution on YOUR website!We don't have your book, so you have to state the problem!! R^2
 Rational-functions/182843: This question is from textbook Mcdougal Littell Algebra 2 i need help factorizing1 solutions Answer 137250 by rapaljer(4667)   on 2009-02-19 23:05:18 (Show Source): You can put this solution on YOUR website!Please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take about the third link on my homepage which is the one that says "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", then go to "Chapter 2" and look for the sections dealing with Factoring. The first lesson MUST be Factoring the Common Factor. Then after you have done that, do the section called "Factoring Trinomials." I have tried to write very "user-friendly" explanations integrated with examples and exercises in a workbook format. Also look for my pages that are called "Math in Living Color," which are my "full color" solutions to the most difficult sections in the "One Step" explanations. If you like this, send me an Email. R^2
 Miscellaneous_Word_Problems/180859: The height h, in feet, of a stone thrown with an upward speed of 40 ft/s is given by the formula h=40t-16t^2, where t is the time, in seconds, since the stone was thrown. How long does it take the stone to reach the highest point of its path of motion?1 solutions Answer 137142 by rapaljer(4667)   on 2009-02-19 01:14:16 (Show Source): You can put this solution on YOUR website!Rewrite this equation as h =-16t^2 + 40t It is well-known that the highest point on a parabolic graph y=ax^2 +bx +c occurs at the value of . In this equation for h=-16t^2 + 40t, the maximum value of h occurs when seconds R^2
 Inequalities/181110: -36< 4x<121 solutions Answer 137141 by rapaljer(4667)   on 2009-02-19 00:55:08 (Show Source): You can put this solution on YOUR website!Divide each of the 3 parts of this inequality by 4 in order to solve for x. , which means all numbers on a numberline that are BETWEEN -9 and 3, but not including the endpoints. R^2
 Trigonometry-basics/180645: The equation secA =x is equivalent to the equation. A=cos x A=1/cos x A=1/sec x A= sec^-1x1 solutions Answer 137140 by rapaljer(4667)   on 2009-02-19 00:49:46 (Show Source): You can put this solution on YOUR website!If secA =x, then to solve for A you must do the INVERSE operation to both sides in order to "undo" the sec. The inverse operation is called the "Arccos" or sometimes it is written "sec^-1". So the answer is A = Arcsec x or A =sec^-1 x R^2