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# Recent problems solved by 'rapaljer'

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 Linear-equations/399750: Find the slope of a parallel line and the slope of perpendicular line with the equation y= -3x1 solutions Answer 283052 by rapaljer(4667)   on 2011-01-25 19:27:46 (Show Source): You can put this solution on YOUR website!Given y=-3x, the slope of this line is m=-3. Any line parallel to this line has the SAME SLOPE, so m= -3 for any line paralle. Any line perpendicular to this line has a slope that is the NEGATIVE RECIPROCAL of this slope. This slope would be m=+1/3. For a complete explanation of this topic in my own FREE curriculum, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Intermediate Algebra", and look in "Chapter 4" for Section 4.02. Scroll down the to page 389 for the EXACT explanation that you need. Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE! I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!! Dr, Robert J. Rapalje, Retired Seminole State College of Florida
 Angles/399735: 87 degree whats its supplement?1 solutions Answer 283048 by rapaljer(4667)   on 2011-01-25 19:10:25 (Show Source): You can put this solution on YOUR website!Subtract from 180 degrees. 180 - 87 = 93 degrees. Check: 87+93= 180 Dr, Robert J. Rapalje, Retired Seminole State College of Florida
 Equations/399726: 5/6x = (3-x) > (x-3)/31 solutions Answer 283041 by rapaljer(4667)   on 2011-01-25 19:01:11 (Show Source): You can put this solution on YOUR website!I think you may have an error in this one. You can't really have an equal sign and and a > sign in the same statement. Dr, Robert J. Rapalje, Retired Seminole State College of Florida
 Rational-functions/399689: what is the vertical asymptote and horizontal asymptote for f(x)= -x^2 + 2x -3/x^2+x-121 solutions Answer 283038 by rapaljer(4667)   on 2011-01-25 18:51:42 (Show Source): You can put this solution on YOUR website!The degree of the numerator is equal to the degree of the denominator, so the horizontal asymptote is y= the ratio of the leading coefficients. Thia is y = -1/1 , or y =-1 Horizontal Asymptote Vertical asymptotes can be found by setting the denominator equal to zero. x^2+x-12=0 (x+4)(x-3)=0 x=-4 or x=3 Vertical Asymptotes Dr, Robert J. Rapalje, Retired Seminole State College of Florida
 test/398902: A karate match is held on a square mat that has a area 676 ft. squared. What is the length of the mat?1 solutions Answer 282561 by rapaljer(4667)   on 2011-01-24 12:33:30 (Show Source): You can put this solution on YOUR website!Let x = length of the mat. x^2 = 676 x= +- sqrt(676) Got a calculator? x=26 feet. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Polygons/398897: If one angle of a parallelogram is 72, what is the measure of the opposite angle?1 solutions Answer 282555 by rapaljer(4667)   on 2011-01-24 12:21:24 (Show Source): You can put this solution on YOUR website!Opposite angles of a parallelogram are EQUAL. The answer is 72 degrees. Dr, Robert J. Rapalje, Retired Seminole State College of Florida
 Geometry_Word_Problems/398873: A rectangular field is 4 times as long as it is wide. Let the width be x and the length will therefore be 4x. If the length is decreases by 10 in. and the width is increased by 2 in. the perimeter will be 80 in. Find the dimensions of the original field.1 solutions Answer 282543 by rapaljer(4667)   on 2011-01-24 11:18:13 (Show Source): You can put this solution on YOUR website!Ler x= original width 4x= original length x+2 = new width 4x-10 = new length 2W + 2L = P 2(x+2) + 2(4x-10)=80 2x+4+8x-20=80 10x -16=80 10x = 96 x=9.6 original width 4x= 38.4 = original length Check: New width = 9.6 + 2 = 11.6 inches New lenth = 38.4-10 = 28.4 inches Perimeter = 2*11.6 + 2*28.4=80 inches NEAT PROBLEM!! Where did you find this one??? For additional explanation on WORD PROBLEMS, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 1" for TWO sections on WORD PROBLEMS. Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE! I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!! Dr, Robert J. Rapalje, Retired Seminole State College of Florida
 Linear-equations/398860: write y=3/5x+2 in standard form 1 solutions Answer 282528 by rapaljer(4667)   on 2011-01-24 10:44:51 (Show Source): You can put this solution on YOUR website!y=3/5 x + 2 First clear the fraction, by multiplying both sides by 5: 5y = 3x + 10 Next, subtract 3x from each side to get the variables all on the left side: 5y-3x=10 The tradition in standard form is to have the x coefficient positive, so multiply both sides by -1: 3x-5y = -10 Dr, Robert J. Rapalje, Retired Seminole State College of Florida
 Polynomials-and-rational-expressions/398862: Hi. Can you please help me? I need to solve the following equation when P(t) = 0.... P(t)=-t^4+9t^2+400 Thank you!1 solutions Answer 282526 by rapaljer(4667)   on 2011-01-24 10:41:48 (Show Source): You can put this solution on YOUR website!There are NO SOLUTIONS to this equation, since any value raised to an EVEN power must be greater than or equal to 0. Then, if you add +400 to this quantity, the result will always be positive, NEVER equal to 0. NO SOLUTION!! Dr, Robert J. Rapalje, Retired Seminole State College of Florida
 Triangles/388359: the measure of each base angle of an isosceles 21 more than the measure of the vertex angle. find the measure of each angle of the triangle. 1 solutions Answer 274659 by rapaljer(4667)   on 2010-12-21 19:53:25 (Show Source): You can put this solution on YOUR website!Let x = vertex angle x+21 = each base angle x+x+21+x+21=180 3x+42=180 3x=138 x= 46 degrees vertex angle x+21 =67 degrees base angles Dr. Rapalje
 Numbers_Word_Problems/388360: Four times an unknown number less five1 solutions Answer 274657 by rapaljer(4667)   on 2010-12-21 19:47:44 (Show Source): You can put this solution on YOUR website!4x-5
 logarithm/388234: Your question goes here. Write clearly! We are not mind readers, so be sure to ask a question that we can understand.exponential functions1 solutions Answer 274552 by rapaljer(4667)   on 2010-12-21 12:21:32 (Show Source): You can put this solution on YOUR website!For a complete explanation of exponential functions, please see my own website To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Then click on my website that you will find there, and it goes directly to my Homepage. From my Homepage, look for the link that says, "Basic, Intermediate, adn College Algebra." Choose "College Algebra", then "Chapter 4", and look for "Section 4.01 Logarithms and Exponential Functions." Also, my "Basic, Intermediate, and College Algebra: One Step at a Time" sections are supported by my "MATH IN LIVING COLOR" sections, where the most frequently asked problems are solved IN COLOR!! I also have a number of vidoes on selected topics from my own classes a few years before I retired. These can be found by looking on my "Rapalje Videos in Living Color." In particular, see the videos in College Algebra on Logarithms Part I. The videos and everything else on the website are all FREE! I hope you like my website, and that you will recommend it friends and family. If you have trouble finding it, then just do a Google search for "Math in Living Color". It comes right up there for you. Oh, and Merry Christmas to all!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus
 Graphs/388236: Im trying to find the y intercept and the x intercept in that order. -3x + 2y =6 Im also trying to find the median for for these set of numbers 23 51 237 397 4621 solutions Answer 274548 by rapaljer(4667)   on 2010-12-21 12:04:46 (Show Source): You can put this solution on YOUR website!To find the y intercept, always let x = 0 and solve for y. In this case, 2y=6, so y=3. To find the x intercept, always let y = 0 and solve for x. In this case, -3x=6, so x=-2 To find the median, arrange the numbers in NUMERICAL order, which they are in this case. Choose the middle number, which is 237. If there happen to be an even number of numbers, then take the middle TWO numbers when arranged in order, and average these two numbers. If you didn't understand intecetps, then you really need to see my website!! I have an explanation here that is probably easier than the one in your textbook!! To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Then click on my website that you will find there, and it goes directly to my Homepage. From my Homepage, look for the link that says, "Basic, Intermediate, adn College Algebra." Choose "Basic Algebra", then "Chapter 4", and look for "Section 4.03 Intercept Method of Graphing." If you have trouble with this section, then take a look at the previous sections in this chapter. Math is cumulative, so if you don't understand the earlier sections, that might explain your problems later on. Also, my "Basic, Intermediate, and College Algebra: One Step at a Time" sections are supported by my "MATH IN LIVING COLOR" sections, where the most frequently asked problems are solved IN COLOR!! I also have a number of vidoes on selected topics from my own classes a few years before I retired. These can be found by looking on my "Rapalje Videos in Living Color." In this case, look in Basic Algebra for the video called "Graphing and Slope of a Line." EVERYTHING, EVEN THE VIDEOS, IS FREE ON THIS WEBSITE. I hope you like my website, and that you will recommend it friends and family. If you have trouble finding it, then just do a Google search for "Math in Living Color". It comes right up there for you. Oh, and Merry Christmas to all!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus