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# Recent problems solved by 'rapaljer'

rapaljer answered: 4664 problems
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 real-numbers/241267: when I worked on to problems using the elimination method I came up with 0=0 in both equations. Is this a solution or non solution or infinite solution1 solutions Answer 176694 by rapaljer(4667)   on 2009-11-21 00:12:33 (Show Source): You can put this solution on YOUR website!When you get 0=0, this means that the statement is ALWAYS TRUE, so the lines are actually the SAME LINE. There are infinitely many solutions. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Equations/241275: (x-1/x)=5 find the value of x2+1/x2=? here i wrote x square not x 2 please note that.Thanks1 solutions Answer 176690 by rapaljer(4667)   on 2009-11-20 23:39:40 (Show Source): You can put this solution on YOUR website!If (x-1/x)=5, then square both sides and get this: Add +2 to each side: Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Graphs/241037: Use the rule y = -x + 7 to fill in the blank. If (-1, y) is on the graph, then y = 1 solutions Answer 176534 by rapaljer(4667)   on 2009-11-20 01:00:23 (Show Source): You can put this solution on YOUR website!Plug in x=-1. y=-x+7 y=-(-1)+7 y=1+7 y=8 Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Graphs/241031: Use the rule y = -x + 7 to fill in the blank. If (1, y) is on the graph, then y = 1 solutions Answer 176532 by rapaljer(4667)   on 2009-11-20 00:32:19 (Show Source): You can put this solution on YOUR website!This is a LOT easier than it looks! All you have to do is realize that (1,y) means that x=1, and you have to find the value of y! If y=-x +7, just plug in the value of x=1, and find y: y=-1+7 y=6 That's it! FINAL ANSWER!!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Rate-of-work-word-problems/240843: It takes 6 hours to fill a pool. It takes 8 hours to drain it. How long does it take to fill the pool if the drain is left opened when the pool is started to be filled?1 solutions Answer 176423 by rapaljer(4667)   on 2009-11-19 16:51:39 (Show Source): You can put this solution on YOUR website!Let x = number of hours to fill the pool with both draining and filling. 1/6 = the part of the pool that can be filled in 1 hour 1/8= the part of the pool that can be drained in 1 hour 1/x= the part of the pool that is filled with both pipes open 1/6-1/8=1/x Multiply both sides of the equation by 24x: hours Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Graphs/240786: Find the slope and y intercept of each equation. Then graph. y=x+2 y=4/5x+2 y=7/4x+21 solutions Answer 176386 by rapaljer(4667)   on 2009-11-19 15:10:06 (Show Source): You can put this solution on YOUR website!When the equation is in slope-intercept form, y=mx+b, the slope is always the coefficient of x, and the y-intercept is always the number term. y=x+2 Slope = 1, y-intercept = 2. y=4/5x+2 Slope = 4/5, y-int = 2 y=7/4x+2 Slope = 7/4, y-int = 2 Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Linear-equations/240761: put the equation 5x-7y=9 into slope intercept form1 solutions Answer 176384 by rapaljer(4667)   on 2009-11-19 15:05:51 (Show Source): You can put this solution on YOUR website!To put this in slope intercept form, you have to solve for y. Start by subtracting 5x from each side. 5x-7y=9 -7y=-5x+9 Now divide by -7: Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Rectangles/240741: If the dimensions of the larger rectangle are 9 by 18, what are the dimensions of the smaller rectangle?1 solutions Answer 176360 by rapaljer(4667)   on 2009-11-19 12:47:18 (Show Source): You can put this solution on YOUR website!Is there a diagram or picture that we are not seeing here? Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Coordinate-system/240697: Solve x2 - 2x - 8 = 0 by graphing. The x intercepts are ? and ?.1 solutions Answer 176354 by rapaljer(4667)   on 2009-11-19 11:36:56 (Show Source): You can put this solution on YOUR website!Graph y=x^2 -2x-8 with a calculator. As you can see, the x-intercepts are at x=-2 and x=4. This can also be determined algebraically by letting y=0 and solving 0=x^2-2x-8 0=(x-4)(x+2) x=4 or x=-2 Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Numbers_Word_Problems/240674: what are six consecutive integers starting with -4? 1 solutions Answer 176350 by rapaljer(4667)   on 2009-11-19 11:31:18 (Show Source): You can put this solution on YOUR website!-4, -3, -2, -1, 0, 1
 Graphs/240715: Graph each point. (0, 4, 0)1 solutions Answer 176348 by rapaljer(4667)   on 2009-11-19 11:29:42 (Show Source): You can put this solution on YOUR website!This is a 3-dimensional graph, with x, y, and z axes. This point will be on the y axis at a distance of 4 units from the origin. I can't draw this on the algebra.com format.
 test/240716: What is the slope of a binomial 2x+3'1 solutions Answer 176347 by rapaljer(4667)   on 2009-11-19 11:27:17 (Show Source): You can put this solution on YOUR website!The slope is the coefficient of x, which is 2.
 Evaluation_Word_Problems/240691: Jane went fishing and caught a whopper of a fish! The head of her fish was ten inches long. The length of the fish's tail was equal to the length of the head plus half the length of the body. The body was as long as the head and tail together. What is the total length of her fish? 1 solutions Answer 176325 by rapaljer(4667)   on 2009-11-19 09:50:42 (Show Source): You can put this solution on YOUR website!Let x = length of the body, since that is at the end of the sentence. Now, the tail = length of the head plus half the length of the body. tail = 10 + 1/2*x The equation is that the body = head + tail x= 10 + 10+ 1/2x Subtract 1/2x from each side: 1/2x= 20 Multiply both sides by 2: x=40 inches = Body Tail = 10 + 1/2x Tail = 10 + 20 = 30 inches Total fish = Head + Body + Tail Total fish = 10+40+30 = 80 inches! (BIG FISH!!) Check: Body = Head + Tail 40=10+30 It checks!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 logarithm/240559: Solve: 2log(base4)x+log(base4)3=log(base4)x-log(base4)2 1 solutions Answer 176294 by rapaljer(4667)   on 2009-11-19 02:29:10 (Show Source): You can put this solution on YOUR website! Multiply both sides by 2: Factor the x: There are two solutions: x=0 NOTE: THIS ANSWER MUST BE REJECTED, SINCE log(0) is UNDEFINED!! 6x-1=0 6x=1 x=1/6 This one seems to work!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Quadratic_Equations/240648: How do you find the turning point (vertex) of a Quadratic function, not using complete the square?1 solutions Answer 176293 by rapaljer(4667)   on 2009-11-19 02:10:37 (Show Source): You can put this solution on YOUR website!If the equation is y=ax^2 +bx +c, then the vertex is always at the value where x=-b/(2a). After you find x, substitute this back into the original equation (or let the calcluator do it for you!!) to find y. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Numbers_Word_Problems/240645: One number is 4 more than twice the second number. Their total is 25. Find the numbers. I just need help on writing the problem, then I will be able to solve it.1 solutions Answer 176292 by rapaljer(4667)   on 2009-11-19 02:08:30 (Show Source): You can put this solution on YOUR website!Let x= the 2nd number. (I always like to let x = the quantity at the end of the sentence or phrase!) Now, the first number is 4 more than twice the second number, where the second number is x. Therefore, first number = 2x+4. Now the equation is that the total (or sum!) of the numbers is 25. x+2x+4=25 You said that you can solve it, so go for it! I have a LOT of resources on my own website on the topic of WORD PROBLEMS. To find my website, do a "BING" or a "GOOGLE" search for my last name "Rapalje". Near the top of the search list, you should see "Rapalje Homepage." Click on this, and look near the top of my homepage for the link "Basic, Intermediate and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in "Chapter 1" for "Sections 1.09 and 1.10, Word Problems." This is my own explanation especially written for students who have trouble understanding math. I wrote this to students, NOT mathematicians, and I think you will find it easier to understand than your own traditional textbooks!! In addition to this page, the entire website is supported by my "MATH IN LIVING COLOR" pages, where the hardest problems are solved IN COLOR. If you like my website, please recommend it to family and friends who have trouble understanding math!! It's ALL FREE!!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Rectangles/240569: if thw area of the rectangle is 30 square inches what is the perimeter and value?1 solutions Answer 176291 by rapaljer(4667)   on 2009-11-19 01:37:59 (Show Source): You can put this solution on YOUR website!Not enough information is given to solve this one. The area could be 30 square inches because it is 5 by 6 or it could be 3 by 10, or many different possiblities. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Functions/240578: excluding values 3x _______ 7x+21 1 solutions Answer 176290 by rapaljer(4667)   on 2009-11-19 01:35:15 (Show Source): You can put this solution on YOUR website!Excluding values means to find the values of x that are NOT allowed. What is NOT allowed in mathematics is DIVISION BY ZERO. You will NEVER be allowed to have a denominator equal to zero. Therefore, you must EXCLUDE the value that makes 7x+21=0 7x=-21 x=-3 This is the EXCLUDED VALUE of X. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Exponential-and-logarithmic-functions/240582: i am really stumped here! f(x)=e^2x what is f(1/4)?1 solutions Answer 176289 by rapaljer(4667)   on 2009-11-19 01:31:54 (Show Source): You can put this solution on YOUR website!If f(x)=e^2x, then f(1/4) just means to substitute the value of 1/4 in place of the x. f(1/4)=e^(2*1/4) f(1/4)=e^(1/2)=e^0.5=1.6487 approximately! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Equations/240587: Solve and state properties c) 2(3x-1)-5(2x+3)=4x-7 I know that distributive property has to take place but afterwards I don't know what to do. thank you 1 solutions Answer 176288 by rapaljer(4667)   on 2009-11-19 01:27:15 (Show Source): You can put this solution on YOUR website!2(3x-1)-5(2x+3)=4x-7 6x-2-10x-15=4x-7 Next, combine like terms on the left side: -4x-17=4x-7 Now, you need to get all the variable terms on one side and the number terms on the other side. It doesn't matter which side you get the variables on, but let's say you want ot get all the variables on the LEFT side. You need to get rid of the 4x on the right side, by subtracting 4x from each side: -4x-4x-17=4x-4x-7 -8x-17=-7 Now, since you have all the variables on the LEFT side, you need to get all the NUMBER terms on the right side. To get rid of the -17, add a +17 to each side: -8x-17+17=-7+17 -8x=10 Now, to "undo" the multiplication of x by -8, you must DIVIDE both sides by -8: I have my own non-traditional explanation of this topic that you may find easier to understand than the one in your own textbook. To see my explanation of this important topic of EQUATION SOLVING, please see my own website! To find my website, do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of the search list. Near the top of my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time." In "Basic Algebra" look in Chapter 1 for "Section 1.08 Equation Solving." Most of these explanations are supported by my "MATH IN LIVING COLOR" pages in which the most difficult problems are solved IN COLOR. I hope you will try it, and see what you think--it's all FREE!! If you like my website, please recommend it to friends!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Number-Line/240590: which numbers are between 0.5 and 3/4 on a number line1 solutions Answer 176287 by rapaljer(4667)   on 2009-11-19 01:16:06 (Show Source): You can put this solution on YOUR website!Did you have a list of numbers to choose from? There are infinitely many such numbers, so you can't possibly list them all. The one that is halfway between these would be the average of 0.5=1/2 and 3/4, which is 5/8. Dr. Robert J. Rapalje
 Polynomials-and-rational-expressions/240598: Grouping: x^3+x^2+x+11 solutions Answer 176286 by rapaljer(4667)   on 2009-11-19 01:12:45 (Show Source): You can put this solution on YOUR website!Group the first two and the last two together. From the first two take out a common factor of x^2. From the last two, take out a common factor (since there is actually NOT one!) of 1. x^3+x^2 + x +1 x^2(x+1)+1(x+1) Notice that you have a common factor of (x+1). Take out this common factor: (x+1)(x^2 + 1) There are a several links on my own website that explain FACTORING in detail. To find my website, do a "Bing" or "Google" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of the search list. Near the top of my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time." In "Basic Algebra" look in Chapter 2 for "Section 2.07 Factoring by Grouping." My non-traditional explanations are probably easier to understand than your own textbook. In addition, I have a FREE video that might help. From my homepage, look for the link "Rapalje Vidoes in Living Color". Choose "Basic Algebra" and look for "Factoring". Try it and see what you think--it's all FREE!! If you like my website, please recommend it to friends!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus