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# Recent problems solved by 'rapaljer'

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 Equations/84875: determine which of the ordered pairs are solutions for the given equations. x - y = 12; (15,3),(9,6),(18,6) 1 solutions Answer 61152 by rapaljer(4667)   on 2007-06-09 22:27:02 (Show Source): You can put this solution on YOUR website!x - y = 12; (15,3): 15-3=12 ->->-> It is a solution! (9,6): 9-6 = 3 ->->-> It is NOT a solution! (18,6): 18-6=12 ->->-> It is a solution! R^2 at SCC
 Miscellaneous_Word_Problems/84872: Hello. I've tried this problem but came to no logical solution. Please help. A monk has a very specific ritual for climbing up the steps to the temple. First he climbs up to the middle step and meditates for 1 minute. Then he climbs up 8 steps and faces east until he hears birds singing. Then he walks down 12 steps and picks up a pebble. He takes one step up and tosses the pebble over his left shoulder. Now, he walks up the remaining steps three at a time which only takes 9 paces. How many steps are there? Thank you very much for your help.1 solutions Answer 61151 by rapaljer(4667)   on 2007-06-09 22:21:57 (Show Source): You can put this solution on YOUR website!The monk goes up to the middle step. Then he goes up 8 more steps and down 12 steps, which places him 4 steps below the middle step. From this step, he goes UP 27 steps to the top. This means that there are 27-4=23 steps from the middle step to the top. There must be a total of 2*23 = 46 steps. R^2 at SCC
 Complex_Numbers/84867: This question is from textbook Elementary and intermediate Algebra Please assist I have been working on this for four days now and cannot make any progress. Write 4u/9cd - 2c^3z^2/3ad^2 as a single rational expression 1 solutions Answer 61150 by rapaljer(4667)   on 2007-06-09 22:16:59 (Show Source): You can put this solution on YOUR website! The first step is to find the LCD, which is . Multiply the first numerator and denominator by "ad", and the second numerator and denominator by "3c". This brings each denominator up to the common denominator. The numerator could be factored, but the fraction does not reduce so factoring is not necessary. If you have trouble with this, please see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, and look for "MATH IN LIVING COLOR", "Basic Algebra", "Chapter 3", "Least Common Denominator", and "Adding and Subtracting Fractions." R^2 at SCC
 Complex_Numbers/84869: This question is from textbook Elementary and intermediate Algebra Solve y^4 = -2 where y is a real number. Simplify your answer as much as possible. 1 solutions Answer 61149 by rapaljer(4667)   on 2007-06-09 22:04:29 (Show Source): You can put this solution on YOUR website!There is NO REAL SOLUTION, since there is no real number that you can raise to an even power and get a negative result. If imaginary (complex) solutions are allowed, then there will be solution(s), but NOT for real numbers. R^2 at SCC
 sets-and-operations/84874: a set has 9 elements a) how many subsets does it have? b) how many proper subsets does it have? so confused please help1 solutions Answer 61148 by rapaljer(4667)   on 2007-06-09 22:02:04 (Show Source): You can put this solution on YOUR website!The number of subsets is always 2 raised to the power of the number of elements in the set. In this case, the answer is . The number of proper subsets is always 1 less than the number of subsets, since a proper subset is any subset except the set itself! In this case, the answer is . R^2 at SCC
 Miscellaneous_Word_Problems/84858: I have 7 bags of marbles. There are 200 marbles in total. Using the clues below, work out how many marbles are in each bag. Bag 1 + Bag 2 = 57 marbles Bag 2 + Bag 3 = 83 marbles Bag 3 + Bag 4 = 71 marbles Bag 4 + Bag 5 = 43 marbles Bag 5 + Bag 6 = 66 marbles Bag 6 + Bag 7 = 43 marbles Thank you so much for your help. I tried to figure this out but came to no avail.1 solutions Answer 61147 by rapaljer(4667)   on 2007-06-09 21:58:30 (Show Source): You can put this solution on YOUR website!What you have here is 7 equations and 7 unknowns, unless someone sees a faster way to do this!! Let the 7 variables be x1, x2, x3, x4, x5, x6, and x7 respectively. Now, here are the equations: x1+ x2+ x3+ x4+ x5+ x6+x7=200 x1+x2=57 x2+x3=83 x3+x4=71 x4+x5=43 x5+x6=66 x6+x7=43 If you have a graphing calculator, like a TI85, 86, 83+, or 84, you may have a program that will solve this system called [SIMLT] or perhaps [POLYSMLT]. If you don't have a calculator, then try getting everything in terms of x1. Do this by starting with x2 =57-x1 Then x3 = 83-x2 x3=83-(57-x1) x3=26+x1 Next, x4= 71-x3 x4=71-(26+x1) x4=45-x1 x5=43-x4 x5=43-(45-x1) x5=-2+x1 x6=66-x5 x6=66-(-2+x1) x6=68-x1 x7=43-x6 x7=43-(68-x1) x7=-25+x1 Now, x1+ x2+ x3+ x4+ x5+ x6+x7=200 x1+(57-x1)+(26+x1)+(45-x1)+(-2+x1)+(68-x1)+(-25+x1)=200 x1+169=200 x1=31 x2=26 x3=57 x4=14 x5=29 x6=37 x7=6 That should do it!!! R^2 at SCC
 Linear-equations/84808: Solve for s D equals C-s over n 1 solutions Answer 61096 by rapaljer(4667)   on 2007-06-08 22:34:19 (Show Source): You can put this solution on YOUR website! Divide both sides by -1: R^2 at SCC
 Radicals/84804: I am having some trouble simplifying the radical expression index is 4, and the radicand is 32m^11 Thank you for your help1 solutions Answer 61095 by rapaljer(4667)   on 2007-06-08 22:29:26 (Show Source): You can put this solution on YOUR website! R^2 at SCC
 Radicals/84805: Hello, I am unable to start this problem in which I must simplify radical 12a^3/25 Thank you for your help1 solutions Answer 61094 by rapaljer(4667)   on 2007-06-08 22:25:46 (Show Source): You can put this solution on YOUR website! R^2 at SCC
 Square-cubic-other-roots/84793: Simplify squareroot of <3x/2>1 solutions Answer 61083 by rapaljer(4667)   on 2007-06-08 18:34:33 (Show Source): You can put this solution on YOUR website! You must rationalize the denominator by multiplying numerator and denominator by . R^2 at SCC
 Geometric_formulas/84678: Directions: Illustrate the following and label the diagram.(basic terms in geometry)?? if don't understand, never mind!!!!!!! l and m intersect at E. 1 solutions Answer 61005 by rapaljer(4667)   on 2007-06-07 06:47:14 (Show Source): You can put this solution on YOUR website!You have to state or describe the problem. R^2 at SCC
 Polynomials-and-rational-expressions/84598: Arrange in descending-exponent form and give the degree. 8-x1 solutions Answer 60982 by rapaljer(4667)   on 2007-06-06 22:37:27 (Show Source): You can put this solution on YOUR website!Write with the highest powers of x first: -x+8 The degree is the highest power of x, which in this case is 1. R^2 at SCC
 Distributive-associative-commutative-properties/84628: 4 * (3+ 2) = (3+ 2)* 4 = 1 solutions Answer 60981 by rapaljer(4667)   on 2007-06-06 22:33:33 (Show Source): You can put this solution on YOUR website!Since the order of the multiplication is reversed, this is the Commutative Property of Multiplication. R^2 at SCC
 Distributive-associative-commutative-properties/84629: 5 + (6+ 7) = 5+ (7 + 6) = 1 solutions Answer 60980 by rapaljer(4667)   on 2007-06-06 22:31:27 (Show Source): You can put this solution on YOUR website!Your question was probably, "Name the property used in the following equation." The answer is the Commutative Property of Addition, since the order of the addition within the parentheses is changed. R^2 at SCC
 Linear-equations/84632: X*X=4X+321 solutions Answer 60979 by rapaljer(4667)   on 2007-06-06 22:21:30 (Show Source): You can put this solution on YOUR website!X*X=4X+32 Because this has an in the problem, it is a QUADRATIC EQUATION, and you must first set it equal to zero: Next, factor it: Now, set each factor equal to zero: or or R^2 at SCC
 Circles/84635: Find the equation of a circle with center:(5,-2) and radius:161 solutions Answer 60978 by rapaljer(4667)   on 2007-06-06 22:17:59 (Show Source): You can put this solution on YOUR website!center:(5,-2) and radius:16 R^2 at SCC
 Equations/84639: please help me with this problem: x^2-9x+8=01 solutions Answer 60977 by rapaljer(4667)   on 2007-06-06 22:15:55 (Show Source): You can put this solution on YOUR website!First, this is a QUADRATIC EQUATION, so you must make sure the equation is set equal to zero, then you must factor it: or or R^2 at SCC
 Equations/84640: please help me with this equation x^2-9x+8=01 solutions Answer 60976 by rapaljer(4667)   on 2007-06-06 22:14:21 (Show Source): You can put this solution on YOUR website!First, this is a QUADRATIC EQUATION, so you must make sure the equation is set equal to zero, then you must factor it: or or R^2 at SCC
 Radicals/84661: This question is from textbook Algebra 1 Explorations and Applications 1 solutions Answer 60974 by rapaljer(4667)   on 2007-06-06 22:11:09 (Show Source): You can put this solution on YOUR website!We do not have your book! You will have to state the problem!! R^2 at SCC
 Probability-and-statistics/84652: If you are making a jam using 3 fruit and you have 10 fruits to choose from, how many different jams could you make?1 solutions Answer 60973 by rapaljer(4667)   on 2007-06-06 22:09:44 (Show Source): You can put this solution on YOUR website!In this problem, the key word is "choose". When you "choose", usually the order is NOT important. Therefore, when the word "choose" is used, it almost ALWAYS means that it is a COMBINATION. (See the solution that I posted a few minutes ago explaining the difference between a COMBINATION and a PERMUTATION. This will be a combination of 10 fruits, choosing 3 at a time, or a C(10,3). Again, most calculators will do this for you, but in case you need to do it without a calculator, you start out as with a permutation with 3 spaces: Remember that with a permutation it will be: P(10,3)= ___*___*___ P(10,3)= 10*9*8=720 Now, a combination is similar. Make 3 spaces. C(10,3) = ___*___*___ What is different with a combination, is that you must ALSO divide by 3*2*1. It looks like this: C(10,3) = **= R^2 at SCC
 Graphs/84648: Find an equation for the line with undefined slope and passing through the point (-8,-4).1 solutions Answer 60971 by rapaljer(4667)   on 2007-06-06 21:59:31 (Show Source): You can put this solution on YOUR website!An equation of a line passing through (-8,-4) with undefined slope must be a VERTICAL LINE. A vertical line can always be written in the form x= a number. In this case the "number" is -8, so x=-8 is the equation of the line. R^2 at SCC
 Quadratic-relations-and-conic-sections/84657: Classify the conic section as a circle, an elipse, a hyperbola, or a parabola 9x^2=144-144y^21 solutions Answer 60969 by rapaljer(4667)   on 2007-06-06 21:56:53 (Show Source): You can put this solution on YOUR website! This is the SUM of x^2 and y^2 with UNLIKE coefficients, so it is an ELLIPSE!! R^2 at SCC
 Probability-and-statistics/84653: You are choosing the batting order for a team with 13 players. How many different ways can you choose 9 players for the batting order?1 solutions Answer 60968 by rapaljer(4667)   on 2007-06-06 21:54:00 (Show Source): You can put this solution on YOUR website!Combinations and permutations really give students a hard time. First of all, with combinations, the ORDER does NOT matter. With permutations, the ORDER DOES matter!! In this case, what you are trying to count is the number of ways to arrange a batting ORDER!! Obviously, the ORDER matters, so this is a permutation. You must choose a batting order choosing 9 people out of 13 players. This is a permutation of 13, taking 9 at a time. You could write this as P(13,9). Most calculators will do this for you if you know how to enter it in the calculator. If you don't know how to do this, you can always calculate it yourself, by making 9 blank spaces in a product as follows: P(13,9) = ___*___*___*___*___*___*___*___*___ Then start with 13, and count down, filling all the 9 spaces. P(13,9) = 13*12*11*10*9*8*7*6*5=259,459,200. R^2 at SCC
 Probability-and-statistics/84655: A bicycle lock consists of 4 spinners each numbered 0-8. How many different lock combinations could you make if you know the number aren't repeated?1 solutions Answer 60965 by rapaljer(4667)   on 2007-06-06 21:39:06 (Show Source): You can put this solution on YOUR website!If the numbers on the spinners cannot be repeated, then each time you set a number on a spinner, then you can't use that number again. Therefore, there will be 8 possibilities on the first spinner, then (having used up one possibility) there will be 7 on the second spinner, 6 on the third spinner, and only 5 on the third. The number of possibilities will be 8*7*6*5 = 1680 possible combinations. R^2 at SCC
 Probability-and-statistics/84654: A bicycle lock consists of 4 spinners each numbered 0-8. How many different lock combinations could you make?1 solutions Answer 60964 by rapaljer(4667)   on 2007-06-06 21:36:04 (Show Source): You can put this solution on YOUR website!Since there are 8 different settings on each spinner, and there are 4 different spinners, there will be 8*8*8*8 = 4096 combinations. R^2 at SCC
 Systems-of-equations/84651: I need some help on how to solve simultanous equations.1 solutions Answer 60963 by rapaljer(4667)   on 2007-06-06 21:33:02 (Show Source): You can put this solution on YOUR website!What kind of simultaneous equations are you solving? Are they linear? That is, just x and y equations, where the variables are raised to the first power? Or, are they what we call "non-linear", which includes variables raised to powers other than the first power? Why don't you check out my website by clicking on my tutor name "rapaljer" anywhere in algebra.com, and look for "MATH IN LIVING COLOR". Now, if you are looking for LINEAR equations, go to "Intermediate Algebra" and look in Chapter 5 for the "Section 5.04 Systems of Equations". If you need NON-LINEAR equations, go to "College Algebra" and look in Chapter 3 for "Section 3.10 Non Linear Systems". R^2 at SCC P.S. Thanks for using my website!!
 Graphs/84560: Solve the system by graphing. 2x + 4y = 2 x + 2y = 1 1 solutions Answer 60962 by rapaljer(4667)   on 2007-06-06 21:23:55 (Show Source): You can put this solution on YOUR website!As Checkley correctly pointed out, these two equations represent the same straight line. However, if the solution is the SAME LINE, then the entire line is the solution to the problem. There are infinitely many solutions, since EVERY point on the line is a solution of both equations!! R^2 at SCC
 Polynomials-and-rational-expressions/84583: Hi everyone, Can someone help me multiply the following problem? (a^2+2ab-b^2)(a^2-7ab+b^2)1 solutions Answer 60961 by rapaljer(4667)   on 2007-06-06 21:19:58 (Show Source): You can put this solution on YOUR website!When I solved your problem, I did NOT get the same answer as the one posted by Checkley75. Here is what I got: Multiply the first times everything in the second parentheses: Next, multiply 2ab times everything in the second parentheses: Last, multiply times everything in the second parentheses: Now, combine like terms: ==> =======> __________________________________________ R^2 at SCC
 Quadratic_Equations/84579: Solve by making appropriate substitution. x^4 - 14x^2 - 32 = 01 solutions Answer 60960 by rapaljer(4667)   on 2007-06-06 21:04:02 (Show Source): You can put this solution on YOUR website!The method you are asked to use for this problem is the method of substitution. You should begin by noticing that in this equation, if you let , then Now, make these substitutions and you get: This factors into or Don't stop here! You must still solve for the original variable which is x. Substitute these values of u back into the formula or or Now, are you supposed to give REAL solutions, or are you supposed to also include imaginary (complex) solutions? IF COMPLEX solutions are allowed, then or or , or If you are finding ONLY REAL solutions, then the answer is only x=4 or x=-4. Note: You don't really need the 0 in the answers above. It's just that in the algebra.com format, you can't write this + or - notation without using the 0! Sorry about that. R^2 at SCC
 Graphs/84559: Graph f(x) = –3x – 2.1 solutions Answer 60905 by rapaljer(4667)   on 2007-06-05 21:58:57 (Show Source): You can put this solution on YOUR website!f(x) = –3x – 2 is a straight line graph, with y intercept of -2, and slope of -3. It should look like this: R^2 at SCC