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 Expressions-with-variables/643031: what does a positive plus a negative equal?1 solutions Answer 404309 by jim_thompson5910(28476)   on 2012-08-29 16:05:54 (Show Source): You can put this solution on YOUR website!If the positive number is larger than the negative value (ignore the negative sign), then positive + negative = positive ex: 5 plus -2 = 3, which is positive Notice how 5 is larger than 2 ------------------------------------------------------- If the positive number is smaller than the negative value (ignore the negative sign), then positive + negative = negative ex: 3 plus -12 = -9, which is negative Notice how 3 is smaller than 12
 Graphs/643012: problem 8Y-7=-7 8Y-7+7=-7+7 8y=0 I entered no solution I think I worked it right.1 solutions Answer 404298 by jim_thompson5910(28476)   on 2012-08-29 15:19:33 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is Note: a solution of zero is still a solution, so the answer is NOT "no solution".
 Equations/643008: Read and answer each. 1. Is 30 a perfect number? explain your answer. 2.Is 21 a prime number? Is 43 a prime number?Explain. 3.Give an example of a composite number and tell why it is a composite number. 4.Is 48 a multiple of 6? Is 8 a multiple of 40? Explain. 5. Is 8 a factor of 20? Is 7 a factor of 35? Explain.1 solutions Answer 404297 by jim_thompson5910(28476)   on 2012-08-29 15:14:19 (Show Source): You can put this solution on YOUR website!1. Is 30 a perfect number? explain your answer. No, 30 doesn't equal the sum of its factors. -------------------------------------------------------------------------- 2.Is 21 a prime number? Is 43 a prime number?Explain. No, 21 = 7*3 which means it's not prime. The number 43 is prime since its only factors are 1 and 43. -------------------------------------------------------------------------- 3.Give an example of a composite number and tell why it is a composite number. 27 is a composite number since 27 = 3*9, so it can be factored into the product of two smaller numbers (none of which are 1 or 27) -------------------------------------------------------------------------- 4.Is 48 a multiple of 6? Is 8 a multiple of 40? Explain. 48 is a multiple of 6 since 48 = 6*8. The number 8 is NOT a multiple of 40 since 8 = 40x has NO integer solution. -------------------------------------------------------------------------- 5. Is 8 a factor of 20? Is 7 a factor of 35? Explain. 8 is NOT a factor of 20 since 8x = 20 has no integer solution 7 is a factor of 35 since 35 = 7*5
 Equations/642930: 4/5y-4=-9/10y+11 solutions Answer 404279 by jim_thompson5910(28476)   on 2012-08-29 12:21:12 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Add to both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
 Functions/642926: Is the relation {(1,3),(-4,0),(3,1),(0,4),(2,3)} a function? Why or why not?1 solutions Answer 404278 by jim_thompson5910(28476)   on 2012-08-29 12:20:12 (Show Source): You can put this solution on YOUR website!Since each x value maps to one and ONLY ONE y value, this means that this given relation is indeed a function. If we had x = 2 mapping to both y = 3 and y = 4 at the same time, then this wouldn't be a function (since this x value is mapping to more than one y value). But that's not the case here. So again, this relation is a function. =============================================================================== Summary Is the relation {(1,3),(-4,0),(3,1),(0,4),(2,3)} a function? Yes Why or why not? See explanation above
 Functions/642925: Evaluate f(x) = -2x-5 for x=31 solutions Answer 404277 by jim_thompson5910(28476)   on 2012-08-29 12:15:03 (Show Source): You can put this solution on YOUR website!f(x) = -2x-5 f(3) = -2(3)-5 f(3) = -6-5 f(3) = -11
 Equations/642918: the average age (A) of 4 boys whose ages are m,n,p and q years1 solutions Answer 404276 by jim_thompson5910(28476)   on 2012-08-29 12:13:56 (Show Source): You can put this solution on YOUR website!If "the average age (A) of 4 boys whose ages are m,n,p and q years", then or without any other info, we can't say anything more
 Permutations/642859: There are 15 ‘True or False’ questions in an examination. In how many ways can a student do the examination if he or she can also choose not to answer almost 3 questions?1 solutions Answer 404275 by jim_thompson5910(28476)   on 2012-08-29 11:59:24 (Show Source): You can put this solution on YOUR website!If the student answers all 15 questions, then there is only one way to do this. ------------------------------------------------------- If the student skips one question, and exactly one question only, then there are 15 ways to do this (since there are 15 questions to skip). ------------------------------------------------------- If the student skips two questions, then there are 15 C 2 = 15*14/2 = 105 ways to do this. ------------------------------------------------------- If the student skips three questions, then there are 15 C 3 = 15*14*13/6 = 455 ways to do this. ======================================================= So if a student can skip at most 3 questions, then there are 1+15+105+455 = 576 different ways to do this.
 Sequences-and-series/642819: Cn=(-1)^n(n-17)^2 What are the first three terms?1 solutions Answer 404273 by jim_thompson5910(28476)   on 2012-08-29 11:38:35 (Show Source): You can put this solution on YOUR website!The 1st term is Cn = (-1)^n(n-17)^2 C1 = (-1)^1(1-17)^2 C1 = (-1)^1(-16)^2 C1 = (-1)(256) C1 = -256 -------------------------------------------- The 2nd term is Cn = (-1)^n(n-17)^2 C2 = (-1)^2(2-17)^2 C2 = (-1)^2(-15)^2 C2 = (1)(225) C2 = 225 -------------------------------------------- The 3rd term is Cn = (-1)^n(n-17)^2 C3 = (-1)^3(3-17)^2 C3 = (-1)^3(-14)^2 C3 = (-1)(196) C3 = -196
 Equations/642899: answer -3/4b=2 1 solutions Answer 404272 by jim_thompson5910(28476)   on 2012-08-29 11:32:39 (Show Source): You can put this solution on YOUR website!-3/4b = 2 -3b = 2*4 -3b = 8 b = 8/(-3) b = -8/3
 Permutations/642890: a product code is made from 3 non-distinct letters from this set { W,Y,T,U,X,R}. how many different codes contain exactly 1 R?1 solutions Answer 404270 by jim_thompson5910(28476)   on 2012-08-29 11:31:08 (Show Source): You can put this solution on YOUR website!If repetition is NOT allowed (ex: RTX is allowed, but RTT is NOT allowed) Case 1) First letter is R There are 6 letters total. After picking R, you have 5 left. So there are 5*4 = 20 ways to arrange the remaining letters in the remaining two slots. Case 2) Second letter is R Same as case 1, but now the R is in the second slot instead of the first. There are still 5 letters left and 5*4 = 20 ways to arrange these 5 remaining letters in the two outer slots. Case 3) Third letter is R Same as case 1, but now R is in slot 3. So there are 20 ways to arrange the remaining letters. So we have 3 cases with 20 ways each giving us 3*20 = 60 ways total. =========================================================================== OR If repetition is allowed (ex: RTT is finally allowed), then... You have 6 letters, but you can only have exactly one R. So once you choose that R (for say the first slot), then you have 5 letters left to choose from for the second slot. Since repetition is allowed, you also have 5 letters left to choose for the 3rd slot. So you have 5*5 = 25 ways to choose an R for the first slot, then 2 (maybe repeating) letters for the second and third slot. This can be generalized if R was in any slot. So there are 3 times as many ways, which means that there are 3*25 = 75 different ways ========================================================================= Summary: So again, if repetition is NOT allowed, then there are 60 ways to do this. If repetition is allowed, then there are 75 ways to do this.
 Quadratic_Equations/642898: Please help me solve this equation 4y + x = 4y - 101 solutions Answer 404268 by jim_thompson5910(28476)   on 2012-08-29 11:15:02 (Show Source): You can put this solution on YOUR website!4y + x = 4y - 10 4y + x - 4y = 4y - 10 - 4y 0y + x = 0y - 10 x = -10
 absolute-value/642734: can you explain how to get the absolute value of -91 solutions Answer 404203 by jim_thompson5910(28476)   on 2012-08-28 22:55:19 (Show Source): You can put this solution on YOUR website! Basically, the absolute value of -9 is the distance -9 is from zero, which is 9 units.
 Numeric_Fractions/642750: What is the answer to this fraction 5/7 + 3/4 simplify show your work plz1 solutions Answer 404202 by jim_thompson5910(28476)   on 2012-08-28 22:54:19 (Show Source): You can put this solution on YOUR website!5/7 + 3/4 (5/7)(4/4) + (3/4)(7/7) 20/28 + 21/28 (20 + 21)/28 41/28 So 5/7 + 3/4 = 41/28
 expressions/642740: 7{[5(a-5)+19]-[2(4a-3)+4]}1 solutions Answer 404201 by jim_thompson5910(28476)   on 2012-08-28 22:50:27 (Show Source): You can put this solution on YOUR website!7{[5(a-5)+19]-[2(4a-3)+4]} 7{[5a-25+19]-[8a-6+4]} 7{[5a-6]-[8a-2]} 7{5a-6-8a+2} 7{-3a-4} -21a-28 So the original expression simplifies to -21a-28
 Equations/642711: how you solve 7y+8y=?1 solutions Answer 404198 by jim_thompson5910(28476)   on 2012-08-28 21:56:45 (Show Source): You can put this solution on YOUR website!7+8 = 15 So 7y+8y = 15y
 Numeric_Fractions/642699: What is 9/10 minus 3/8 SIMPLIFIED AS A FRACTION.1 solutions Answer 404193 by jim_thompson5910(28476)   on 2012-08-28 21:48:43 (Show Source): You can put this solution on YOUR website!9/10-3/8 (9/10)(4/4)-(3/8)(5/5) 36/40-15/40 (36-15)/40 21/40 So 9/10-3/8 = 21/40
 Polynomials-and-rational-expressions/642697: Please Factor: 8x^3 + 27y^6 Thank You!1 solutions Answer 404191 by jim_thompson5910(28476)   on 2012-08-28 21:46:08 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Now factor by using the sum of cubes formula. Remember the sum of cubes formula is Multiply ----------------------------------- Answer: So factors to . In other words,
 Inequalities/642694: 6x-4+3/2x=5x+11 I have put x all on one side 6x+3/2x-5x=11+4 I made everything with x an fraction 12/2x+3/2x-10/2x=15 12+3-5=10 10/2=5 5x=15 x=31 solutions Answer 404190 by jim_thompson5910(28476)   on 2012-08-28 21:44:53 (Show Source): You can put this solution on YOUR website!You made a mistake in red below 12+3-5=10 when it *should* be 12+3-10 = 5 which becomes 5/2 So 12/2x+3/2x-10/2x=15 5/2x=15 5x = 15*2 5x = 30 x = 30/5 x = 6 So the solution is x = 6
 test/642683: write the equation for a line with a slope of 6/5 that passes through the point (-7, -1)1 solutions Answer 404186 by jim_thompson5910(28476)   on 2012-08-28 21:33:23 (Show Source): You can put this solution on YOUR website! So the equation of the line is
 Linear-equations/642681: Find the equation of the line that passes through the point (-3,-7) and has a slope of 2/3 . Show all work and graph the equation .1 solutions Answer 404185 by jim_thompson5910(28476)   on 2012-08-28 21:32:06 (Show Source): You can put this solution on YOUR website! So the equation of the line is
 Radicals/642667: How do you solve 7(1 − x) = 9(1 + 2x) + 8. 7-7x=9+18x+8 7-7x=17+18x 7-7-7x=17-7+18x 7x=10+18x 7x-18x=10+18x-18x -11x=10 1 solutions Answer 404178 by jim_thompson5910(28476)   on 2012-08-28 21:19:58 (Show Source): You can put this solution on YOUR website!You made a mistake highlighted in red 7-7x=9+18x+8 7-7x=17+18x 7-7-7x=17-7+18x 7x=10+18x 7x-18x=10+18x-18x -11x=10 It should be -7x and not 7x. So you lost a negative sign somehow. ------------------------------------------------------- Start with the given equation. Distribute. Combine like terms on the right side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Angles/642660: I need to find the measure of the third angle and they give me this: x°, (123 – x)° how can i do it?1 solutions Answer 404175 by jim_thompson5910(28476)   on 2012-08-28 21:11:03 (Show Source): You can put this solution on YOUR website!Let y = third missing angle Since the three angles (in any triangle) must add to 180, we know that x+(123-x) + y = 180 123 + y = 180 y = 180 - 123 y = 57 So the third angle is 57 degrees
 Linear-equations/642659: Please help solve using the fractions and step by step b/7=-11. Thank you very much.1 solutions Answer 404174 by jim_thompson5910(28476)   on 2012-08-28 21:08:43 (Show Source): You can put this solution on YOUR website!Multiply both sides by 7 to get b/7=-11 b = -11*7 b = -77
 Geometry_proofs/642658: The question is: Can you think of any way to prove from Euclid's postulates that for every line l (a) There exists a point lying on l? (b) There exists a point not lying on l? I'm thinking it has something to do with Euclid's parallel postulate, but I'm not sure. I have never written proofs before, so I am just having a difficult time trying to formulate this properly. Any help would be appreciated. Thank you!1 solutions Answer 404173 by jim_thompson5910(28476)   on 2012-08-28 21:08:01 (Show Source): You can put this solution on YOUR website!a) Any line is uniquely determined by 2 points. So if you have a line, then you know it has at least two points on it. ------------------------------------------------------- b) Parallel lines will NEVER intersect in euclidean geometry (in the plane). This means that parallel lines will not have any points in common. So the existence of parallel lines shows us that if you have a line, then there are points that do not lie on this given line (since these points will lie on the parallel lines).
 Functions/642640: Given: f(x) = x2 + 2x + 1, find f(x + h) and simplify1 solutions Answer 404170 by jim_thompson5910(28476)   on 2012-08-28 20:48:20 (Show Source): You can put this solution on YOUR website!f(x) = x^2 + 2x + 1 f(x+h) = (x+h)^2 + 2(x+h) + 1 f(x+h) = (x^2+2xh+h^2) + 2(x+h) + 1 f(x+h) = x^2+2xh+h^2 + 2x+2h + 1
 Linear-equations/642634: Please help me solved this equation using fractions and step by step. n/8=-1/41 solutions Answer 404163 by jim_thompson5910(28476)   on 2012-08-28 20:35:33 (Show Source): You can put this solution on YOUR website!n/8=-1/4 4n=-1*8 4n=-8 n=-8/4 n = -2
 Travel_Word_Problems/642629: If a train travels 100 MPH for 15 minutes, what is the distance traveled?1 solutions Answer 404162 by jim_thompson5910(28476)   on 2012-08-28 20:28:16 (Show Source): You can put this solution on YOUR website!15 min = 0.25 hour d = rt d = 100*0.25 d = 25 So it has traveled 25 miles.
 expressions/642616: what is 9 - 2b for b = 3?1 solutions Answer 404158 by jim_thompson5910(28476)   on 2012-08-28 20:20:37 (Show Source): You can put this solution on YOUR website!9 - 2b 9 - 2(3) 9 - 6 3 So 9 - 2b = 3 when b = 3
 expressions/642612: T - 7 for t = 20 Is the answer 13? 2 xsquared for x = 3 Is the answer 18? The word for is throwing me off1 solutions Answer 404156 by jim_thompson5910(28476)   on 2012-08-28 20:15:18 (Show Source): You can put this solution on YOUR website!t - 7 20 - 7 13 So you are correct. ------------------------------------------------------- 2x^2 2(3)^2 2(9) 18 So you are correct on both Note: T - 7 for t = 20 can be reworded to say "find t - 7 when t = 20"
 Exponents/642610: Square the binomial (7x-9)^2 1 solutions Answer 404153 by jim_thompson5910(28476)   on 2012-08-28 20:10:42 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Remember something like . Now let's FOIL the expression. Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms:. Multiply the Outer terms:. Multiply the Inner terms:. Multiply the Last terms:. --------------------------------------------------- So we have the terms: , , , Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, for all values of x. -------------------------------------------------------------------------------------------------------------- If you need more help, email me at jim_thompson5910@hotmail.com Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you Jim --------------------------------------------------------------------------------------------------------------