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# Recent problems solved by 'rapaljer'

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 Graphs/211359: how do you represent the following numbers in interval notation? -7≤x≤31 solutions Answer 159716 by rapaljer(4667)   on 2009-09-06 20:14:37 (Show Source): You can put this solution on YOUR website![-7,3]
 Radicals/210547: 8 over 6 radical 151 solutions Answer 159084 by rapaljer(4667)   on 2009-09-02 19:53:31 (Show Source): You can put this solution on YOUR website! In order to rationalize the denominator, you must multiply numerator and denominator of this fraction by . Divide out the factor of 2 in the numerator and denominator: If you need additional help with rationalizing denominators, please see my own website by clicking on my tutor name "Rapaljer" anywhere in algebra.com. Then look for the link on my homepage called "MATH IN LIVING COLOR." Select Intermediate Algebra, and look for Chapter 3, then the section called "Rationalizing Denominators." I think you will find my explanations which are IN COLOR helpful!! R^2 Dr. Robert J. Rapalje, Retired Altamonte Springs Campus Seminole Community College Florida
 Permutations/210495: This question is from textbook pre algebra four less then the aamount of cents in a number of dimes1 solutions Answer 159055 by rapaljer(4667)   on 2009-09-02 17:42:07 (Show Source): You can put this solution on YOUR website!WHAT??? Can you clarify this please??? R^2
 Radicals/205354: 6=1-2n+51 solutions Answer 158724 by rapaljer(4667)   on 2009-08-31 23:15:45 (Show Source): You can put this solution on YOUR website!6=1-2n+5 6=6-2n Subtract 6 from each side: 0=-2n Divide both sides by -2 R^2 Dr. Robert J. Rapalje
 Functions/209951: Find the domain of the function. f(x)=square root of x+6 (divided by) 6+x Please help I am really confused I got "All real numbers except x=-6 but I also got x is greater than or equal to 6.1 solutions Answer 158723 by rapaljer(4667)   on 2009-08-31 23:09:13 (Show Source): You can put this solution on YOUR website!Assuming that your problem is , there are TWO restrictions here. First, since there is a square root in the numerator, the quantity inside the radical, x+6 MUST BE greater than or equal to zero. , so . However, there is a second restriction because of the denominator. Denominators must NEVER equal zero. Anything that causes the denominator to equal zero is ILLEGAL and must NOT be allowed. So in this case, 6+x CANNOT equal zero, so x CANNOT equal -6. The second restriction must be applied as well as the first restriction, so therefore, the TOTAL restriction is . Final Answer! Please see my non-traditional explanation of "Functions, Domain, and Range" by visiting my website. Go to my website by clicking on my tutor name "Rapaljer" anywhere in algebra.com, and look on my Homepage for the "MATH IN LIVING COLOR" topic. You can't miss it. Then select "College Algebra" and look in Chapter 2 for the topic "Functions, Domain, and Range". There you will find my very "non-traditional" explanation (that means "easier to understand" than your textbook that you spent so much money for!!), and it's in LIVING COLOR--and ALL FREE!!! R^2 Dr. Robert J. Rapalje Seminole Community College Altamonte Springs Campus Florida
 Numbers_Word_Problems/210015: what number must be added to the numerator of 3/10 to produce the fraction 4/51 solutions Answer 158721 by rapaljer(4667)   on 2009-08-31 22:54:59 (Show Source): You can put this solution on YOUR website!Let x = the number to be added. Remember that if then So, means that 15+5x = 40 5x=40-15 5x=25 x=5 Check: Add 5 to the numerator of 3 which gives you 8. . It checks!!! R^2
 Miscellaneous_Word_Problems/209975: This question is from textbook foundations for algebra five people who were all different heights lined up at the front of the room and discovered that their median height was 145 centimeters. How many people were taller than 145 centimeters? Explain? 1 solutions Answer 158719 by rapaljer(4667)   on 2009-08-31 22:50:23 (Show Source): You can put this solution on YOUR website!The median height is the "middle" height, when the heights are all lined up from smallest to largest or largest to smallest. If there were 5 people each of different heights lined up in order of heights, then the middle person is 145 cm with two people taller and 2 people shorter than 145 cm. R^2 Dr. Robert J. Rapalje Seminole Community College Altamonte Springs Campus
 Rational-functions/210010: 1 solutions Answer 158716 by rapaljer(4667)   on 2009-08-31 22:25:33 (Show Source): You can put this solution on YOUR website!You forgot to state the problem! R^2
 Radicals/210004: This question is from textbook Intro Alegbra Rationalize the Denominator for this: 4-sqrt(3)/6+sqrt(y) I don't even know how to begin this. Could you help?1 solutions Answer 158715 by rapaljer(4667)   on 2009-08-31 22:24:50 (Show Source): You can put this solution on YOUR website!Rationalizing the denominator means to get rid of all the square roots in the denominator. You can do this by multiplying the numerator and denominator by the same quantity, and in the case of binomial denominators, you must multiply by the same binomial as the denominator EXCEPT with the OPPOSITE SIGN. You may ask, why do we do this??? Because it works!! This will probably get ugly, so hang in there! I have a pretty good lesson for this (if I do say so myself!!)on my website! To see it, click on my tutor name "Rapaljer" anywhere in algebra.com, and look for the link on my homepage that says "MATH IN LIVING COLOR." Select "Intermediate Algebra" and look for "Chapter 3" which is on Square Roots and Radicals. Choose the topic that says "Rationalizing Denominators." Now back to the problem at hand. You will have to multiply the numerator and denominator by It looks like this: * This simplifies (but not much, but at least you eliminated the square roots from the denominator!) R^2 Dr. Robert J. Rapalje Seminole Community College Altamonte Springs Campus Florida
 Equations/209944: 5d - 2g = 9 please show each step1 solutions Answer 158711 by rapaljer(4667)   on 2009-08-31 22:07:12 (Show Source): You can put this solution on YOUR website!What is the question? Solve for d? Solve for g? Why don't you re-state the problem or send me an Email! R^2
 Inequalities/209999: write (and solve) and inequality to find three consecutive odd integers with a sum between 64 and 74.1 solutions Answer 158709 by rapaljer(4667)   on 2009-08-31 22:04:46 (Show Source): You can put this solution on YOUR website!Let x = first odd integer x+ 2 = second odd integer x+ 4 = third odd integer The sum of these integers (add them up!) will be 3x + 6. The inequality will be 64<3x+6 <74 Subtract 6 from each part of the inequality: 64-6<3x+6-6<74-6 58<3x<68 Divide by 3: 19.333. . . < x < 22.666. . . Since these are INTEGERS you are looking for, the only ones that fit this description would be x= 20, 21, and 22. You must reject the x=20 and x=22 since these are NOT odd integers. The only solution would be x=21 x+2 = 23 x+4=25 The sum is 69. R^2 Dr. Robert J. Rapalje Seminole Community College
 Miscellaneous_Word_Problems/209994: Find the exact value of each expression. log4(100) - log4(32) - log4(50)1 solutions Answer 158702 by rapaljer(4667)   on 2009-08-31 21:50:44 (Show Source): You can put this solution on YOUR website!log4(100) - log4(32) - log4(50) Using the Laws of Logarithms: Now, by the basic definition of logarithms: means So, means that Therefore, y = -2, since I think my explanation of LOGARITHMS is easier to understand than the ones given in traditional textbooks. It's all posted free for you on my website. Just go to my website by clicking on my tutor name "Rapaljer" anywhere in algebra.com, and look for the link on my homepage that says "Basic, Intermediate, and College Algebra: One Step at a Time." Select "College Algebra" and look for "Chapter 4" which is my Logarithms chapter. You will probably need to study the Laws of Logarithms, once you understand the basic Definition of Logarithms. See also my MATH IN LIVING COLOR PAGES that correspond to this sections! R^2 Dr. Robert J. Rapalje Seminole Community College Altamonte Springs Campus Florida R^2
 Miscellaneous_Word_Problems/209996: I am stuggling with how to set this problem up in an equation to solve it. Together, a baseball and a football weigh 1.25 pounds, the baseball and a soccer ball weigh 1.35 pounds, and the football and the soccer ball weigh 1.9 pounds. How much does each of the balls weigh?1 solutions Answer 158699 by rapaljer(4667)   on 2009-08-31 21:37:58 (Show Source): You can put this solution on YOUR website!You will have to write three equations with three unknowns. Let b = weight of baseball f = weight of football s = weight of soccer ball b+f=1.25 b+s=1.35 f+s=1.9 Start by subtracting the first equation minus the second equation. b+f=1.25 b+s=1.35 b-b+f -s = 1.25-1.35 f-s=-.1 Now take this equation and add it to the third equation: f-s=-.1 f+s=1.9 2f=1.8 f=.9 Now go back to the first three equations: b+f=1.25 b+s=1.35 f+s=1.9 In the first equation, substitute f =.9 b+f=1.25 b+.9=1.25 b=1.25-.9 b=.35 In the second equation, substitute b.35 b+s=1.35 .35+s=1.35 s=1 Check with the third equation f+s=1.9 .9+1=1.9 It checks!!! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Mixture_Word_Problems/209992: the leght of a rectangle is 5 cm greater than its width. the perimeter is 58 cm. find the dimension of the rectangle1 solutions Answer 158694 by rapaljer(4667)   on 2009-08-31 21:16:21 (Show Source): You can put this solution on YOUR website!Let x = width of the rectangle x+5 = length 2W + 2L = P 2(x) + 2(x+5) = 58 2x+2x+10 = 58 4x+10=58 4x = 48 x=12 width x+5 = 12+5=17 length Check: 2*12+2*17 24+34= 58 = Perimeter For additional explanation on solving Word Problems please 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." Go to "Basic Algebra", and look for "Chapter 1" and select the sections marked "Word Problems." See also my MATH IN LIVING COLOR pages, where a LOT of these problems are solved in COLOR--it really makes a difference!! My students have ALL told me that my explanations are easier than traditional books. I WROTE ALL OF THESE SECTIONS SPECIFICALLY FOR PEOPLE WHO DON'T GET MATH!! I hope it helps you!! R^2 Dr. Robert J. Rapalje, Retired Altamonte Springs Campus Seminole Community College Florida
 Pythagorean-theorem/209993: This question is from textbook holt 1 solutions Answer 158689 by rapaljer(4667)   on 2009-08-31 21:08:28 (Show Source): You can put this solution on YOUR website!You forgot to state the problem!
 Exponents-negative-and-fractional/209194: I need to use the number 7 four times as exponents to equal 1, then 2, then 3...all the way up to 100. How do I figure out the equations? For example: 77/77 = 1 7/7 + 7/7 = 2 and so on...1 solutions Answer 158138 by rapaljer(4667)   on 2009-08-27 22:03:16 (Show Source): You can put this solution on YOUR website!This sounds like fun! Get as many different combinations as you can think of, and see which ones are missing. Here are a that I could think of: 77/7-7=4 (7-7)/7 +7 = 7 ((7*7+7)/7 =8 (7+7)/7 +7 =9 (77-7)/7 =10 (77+7)/7 =12 (7*7)/7+7=14 77/7+7=18 7+7+7+7 =28 7*7 +7/7 = 50 77-7/7 = 76 77+7/7=78 77+7+7=91 This sounds like a good group project or a contest to see who can come up with the most different numbers. Am I right?? Have fun with the rest of these!! R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Altamonte Springs Campus Florida
 Functions/209129: This question is from textbook Integrated Mathematics 3 What is the domain and range of the function f(x)=2x-5 in the absolute value form? 1 solutions Answer 158130 by rapaljer(4667)   on 2009-08-27 21:43:52 (Show Source): You can put this solution on YOUR website!Domain and range are both ALL REAL NUMBERS. I'm not sure by I suppose you could write this in absolute value form: D: |x|< inf R: |y| < inf R^2
 Pythagorean-theorem/209147: which of the two triangles shown below has greater area? how many square units is the greater triangle? show or expalin how yuo got your answer. 1 solutions Answer 158125 by rapaljer(4667)   on 2009-08-27 21:37:31 (Show Source): You can put this solution on YOUR website!We can't see the triangles!
 Angles/209173: Find the measure of Y if Y is six more than three times it complement.1 solutions Answer 158122 by rapaljer(4667)   on 2009-08-27 21:24:56 (Show Source): You can put this solution on YOUR website!Let y be the angle, and 90-y = the complement of the angle. The statement you gave is "Y is six more than three times the complement". Just translate it into math symbols: y= 3(90-y) + 6 Now, solve for y: y = 270 -3y +6 Add +3y to each side and combine the 270 + 6 y + 3y = 276 - 3y + 3y 4y = 276 Divide by 4: y = 276/4= 69 = The angle 90-y = 90 - 69=21 = The complement Check the equation: y= 3(90-y)+6 69= 3(21) + 6 69= 63+6 It checks!! R^2 Dr. Robert J. Rapalje Seminole Community College
 Equations/209189: 14.00 millimeters equals how many meters? 1 solutions Answer 158120 by rapaljer(4667)   on 2009-08-27 21:16:42 (Show Source): You can put this solution on YOUR website!To convert from millimeters to meters (smaller to larger units!) you must move the decimal 3 places to the left, which would be 0.014 meters. The most frequently visited page on my entire website it my "METRIC SYSTEM" page. You can find it by clicking on my tutor name "Rapaljer" anywhere in algebra.com. Look for the link on my homepage that says "Geometry Topics." Select "Metric System". I think you will like my explanation on this topic. R^2 Dr. Robert J. Rapalje Altamonte Springs Campus Seminole Community College Florida
 Equations/209185: how do you solve this problem 24a-22=4(1-6a)1 solutions Answer 158117 by rapaljer(4667)   on 2009-08-27 21:02:22 (Show Source): You can put this solution on YOUR website!24a-22=4(1-6a) 24a - 22= 4- 24a Let's get all the variables on the left side by adding +24a to each side: 24a + 24a -22 = 4 48a -22 = 4 Next, get all the number terms on the right side by adding +22 to each side: 48a -22+22 = 4 + 22 48a = 26 Finally, divide both sides by 48: Reduce the fraction on the right side by dividing out a factor of 2: For additional help, please see my own website by clicking on my tutor name "Rapaljer" anywhere in algebra.com. Look for the link on my homepage that says "Basic, Intermediate and College Algebra: One Step at a Time." Select "Basic Algebra" and look in "Chapter 1" for the "Equation Solving" topic. I think you will like and understand my explanation and format for this topic. I also have a LOT of problems like this solved in my "MATH IN LIVING COLOR" pages. R^2 Dr. Robert J. Rapalje Altamonte Springs Campus Seminole Community College Florida
 Coordinate-system/209152: how can you describe a pattern formed by points1 solutions Answer 158116 by rapaljer(4667)   on 2009-08-27 20:54:01 (Show Source): You can put this solution on YOUR website!Maybe the equation of best fit??? I'm really not sure what you mean. R^2
 Linear-systems/209179: A coin bank has \$37 dollars consisting of quarters and dimes. There are 10 times as many dimes more than 2 times as many quarters. how many quarters and dimes are there1 solutions Answer 158115 by rapaljer(4667)   on 2009-08-27 20:51:35 (Show Source): You can put this solution on YOUR website!Let x = number of quarters 2x+10 = number of dimes The equation is based upon the values of each coin times the number of each coin. You can do it in either dollars or cents. Your teacher may have a preference, but to me, working with dollars requires the use of decimals, whereas the use of cents comes out in whole numbers. I'll do it in "cents". Doesn't that make "cents" to you?? Of course the quarters are each worth 25 and the dimes are each worth 10 cents. Be sure to change the \$37 to cents also. 25(x) + 10(2x+10) = 3700 25x + 20x + 100 = 3700 45x +100 = 3700 45x=3600 x=3600/45=80 Quarters 2x+10 = 2(80)+10= 170 Dimes Check by calculating the values of the coins: Quarters = 80*.25 = \$20 Dimes = 170*.1= \$17 Total = \$37 It checks!! For additional help with coin problems or any kind of word problems, please see my website by clicking on my tutor name "Rapaljer" anywhere in algebra.com. Look for "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", and look for the appropriate topic in "Chapter 1". This is a user friendly explanation with examples and exercises integrated into it. My students ALL tell me it's easier to understand than the traditional textbooks! See also my "MATH IN LIVING COLOR" pages where a lot of these exercises are solved in "Living Color." R^2
 expressions/209161: This question is from textbook Algerbra for college students how do you solve this problem -28 over 9 over 41 solutions Answer 158109 by rapaljer(4667)   on 2009-08-27 20:37:17 (Show Source): You can put this solution on YOUR website!If this is a problem with a complex fraction (fractions within fractions!), then one of the lines must be longer than the other one. From what you have stated without any parentheses, it's not possible to know for sure what you mean. Is it 1) = = or is it 2) = = Do you understand the difference? R^2
 Functions/209169: Hi all, Im having trouble with the following Function and Domain problem(s). The function f is defined by y = f(x) = 2 ln 4x, 0:01 <= x >= 1 . (a) Solve for x in terms of y, and hence and the formula for the inverse function f^(-1)(x). b) Write down the domain of f^(-1) Any help would be most appreciated. -Nick.1 solutions Answer 158108 by rapaljer(4667)   on 2009-08-27 20:26:40 (Show Source): You can put this solution on YOUR website!Hi Nick!! Given , you must solve for x by "undoing" all the operations that were done to it. You must undo mult by 2, undo the "ln" function, and undo multiplication by 4. That brings you down to x. Start by dividing both sides by 2: In order to "undo" the "ln", you must raise both sides as a power of e: Last, divide both sides by 4: In the above statements, y represents f(x). NOW, if you interchange the x and the y, the NEW y represents the inverse function . R^2 Dr. Robert J. Rapalje, Retired Seminole Community College Florida
 Numeric_Fractions/208965: 3/4 divided by -1/21 solutions Answer 157988 by rapaljer(4667)   on 2009-08-27 01:08:34 (Show Source): You can put this solution on YOUR website!3/4 divided by -1/2 Invert the second number and multiply: You may want to just multiply numerator times numerator and denominator times denominator, and reduce the fraction: or -1 1/2 R^2
 Equations/208970: 6x/7=24/5 12-6x+3(2x+3)=2x+5 in this problem i worked in two ways not sure which is the right answer -8 or 131 solutions Answer 157987 by rapaljer(4667)   on 2009-08-27 01:03:21 (Show Source): You can put this solution on YOUR website!12-6x+3(2x+3)=2x+5 12-6x+6x+9=2x+5 21=2x+5 21-5=2x-5 16=2x 8=x R^2
 Equations/208969: 5x-2x+7x=-81 I was having trouble with this problem is it 10x=-81, but they not divide what am i doing wrong1 solutions Answer 157986 by rapaljer(4667)   on 2009-08-27 01:00:01 (Show Source): You can put this solution on YOUR website!You aren't doing anything wrong! Math is like life--sometimes it comes out even, sometimes it doesn't!! In this case the answer is a fraction!! R^2
 Angles/208182: find the measure of an angle if it's measure is 9 degrees less than 8 times its complement1 solutions Answer 157503 by rapaljer(4667)   on 2009-08-23 23:04:21 (Show Source): You can put this solution on YOUR website!Let x= the complement of the angle 8x - 9 = the angle itself x + 8x -9 = 90 9x = 99 x=11 the complement of the angle 8x-9= 8*11 -9=88-9 =79 degrees = the angle Check: 79+11=90 R^2
 logarithm/208181: the number of homes built can be modeled by an exponential function, H= p * a(t) , where p is the number of new homes built in the first year recorded. p=10 t =3 a=2 im not sure how to caculate it. 1 solutions Answer 157501 by rapaljer(4667)   on 2009-08-23 23:01:01 (Show Source): You can put this solution on YOUR website!H=p*a^t H=10*2^3 H=10*8=80 homes R^2
 logarithm/208183: the number of homes built can be modeled by an exponential function, H= p * at , where p is the number of new homes built in the first year recorded. p=10 t =3 a=2 I'm not sure how to calculate : the number of homes built can be modeled by an exponential function, H= p * a^t , where p is the number of new homes built in the first year recorded. p=10 t =3 a=2 I'm not sure how to calculate 1 solutions Answer 157500 by rapaljer(4667)   on 2009-08-23 22:59:26 (Show Source): You can put this solution on YOUR website!H= p*a^t H = 10*2^3 H = 10*8 H = 80 homes R^2