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 Numbers_Word_Problems/252619: I am checking my sons math. Find four consecutive even integers such that 6 time the sum of the first and second is 8 more than 10 times the fourth. Rob Dewey...Mitchell's Dad.1 solutions Answer 184637 by jim_thompson5910(28598)   on 2009-12-29 18:43:55 (Show Source): You can put this solution on YOUR website!Consecutive even integers follow the form: x, x+2, x+4, x+6, etc... So because "6 time the sum of the first and second is 8 more than 10 times the fourth", this translates to Start with the given equation. Distribute. Combine like terms on the left side. 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 which means that the four consecutive even integers are x = 28 x+2 = 30 x+4 = 32 x+6 = 34
 Trigonometry-basics/252605: The height of the ocean at the dock is modeled by the function, h= 3sin(pi*t/4) +5 where h is measured in feet and t is the time in hours. If t=0 refers to 12:00 a.m., what is the height of the ocean at 10:00 a.m.? find the exact value of the vertical asymptotes for 0<=x<=pi for the function y=cot(3x) if sin(x)= -3/5 with x in the quadrant 4, find the sec(x) Thanks so much!!1 solutions Answer 184615 by jim_thompson5910(28598)   on 2009-12-29 16:47:52 (Show Source): You can put this solution on YOUR website!I'll do the first two to get you going. # 1 Since "t=0 refers to 12:00 a.m", this means that refers to 10:00 a.m. (just add 10 hours to 0) Start with the given equation. Plug in Reduce. Rearrange the terms Subtract from the argument (this is valid because you'll end up on a coterminal angle). Combine like terms. Use the unit circle to evaluate the sine of to get 1. Multiply Add So the height of the ocean at 10:00 a.m. is 8 feet. ================================================================= # 2 Remember that and . So this means that or in short, To find the vertical asymptotes of , we'll set the denominator equal to zero and solve for 'x' (since division by zero is undefined). Set the denominator equal to zero. Take the arcsine of both sides. or Evaluate the arcsine of 0 to get or . Don't forget to add on multiples of to each solution. or Divide both sides by 3 to isolate 'x' in each case. As a shortcut, you can condense the solution to where 'n' is an integer. So if , where 'n' is an integer, then . But since , this means that we're only going to look at the solutions (for n=0), (where n=1), (when n=2), and (when x=3). Note: any other solution is outside the interval . So the four vertical asymptotes of are , , , and
 Linear-systems/252604: There are 35 tickets to be sold for the dance. The number of tickets sold to seniors must be four times the number of tickets sold to juniors. please give me 2 linear equations and a solution. A diamond today costs 10$more than twice what it cost last year. The sum of the cost (last year and this year) is 2500$. What is the cost of last years diamond? i need 2 linear equations and a solution for this question also. THANK U SO MUCH! 1 solutions Answer 184609 by jim_thompson5910(28598)   on 2009-12-29 16:24:26 (Show Source): You can put this solution on YOUR website!# 1 Let s = # of senior tickets and j = # of junior tickets Since there are 35 tickets in total, and we're assuming that only junior and senior tickets are sold, this means that . In other words, adding up the two totals will give you the grand total of 35. Also, because "The number of tickets sold to seniors must be four times the number of tickets sold to juniors", we know that . In English, the number of senior tickets 's' is 4 times the number of junior tickets 'j'. Start with the first equation. Plug in Combine like terms on the left side. Divide both sides by to isolate . Reduce. So there are 7 junior tickets. Go back to the second equation Plug in Multiply So there are 28 senior tickets. As a check, take note that 28 is indeed 4 times 7 AND 28+7=35. So we've met our conditions. ====================================================================== # 2 Let t = cost of diamond today and y = cost of diamond last year Since "A diamond today costs 10$more than twice what it cost last year", we can say that (ie double the cost from last year 'y' and add 10 to get the new cost today 't'). Also, because "The sum of the cost (last year and this year) is 2500$", we know that (just add up the two individual costs to get the grand total of $2500) Start with the second equation. Plug in Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the cost of the diamond last year was$830. If you want to keep going then... Go back to the first equation Plug in Multiply Add So the cost of the diamond today is $1670.  Linear-systems/252597: Solve the following system of equations algebraically: 3x+2y=4 4x+3y=71 solutions Answer 184601 by jim_thompson5910(28598) on 2009-12-29 15:58:03 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the first equation by 3. Distribute and multiply. Multiply the both sides of the second equation by -2. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)  Expressions-with-variables/252600: Solve for x: 2x over 3 +4 = x-51 solutions Answer 184600 by jim_thompson5910(28598) on 2009-12-29 15:57:14 (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. 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  Equations/252601: 9y+5-2y=2y+5-y+3 solve this equation 1 solutions Answer 184598 by jim_thompson5910(28598) on 2009-12-29 15:55:54 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. 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 which approximates to .  Expressions-with-variables/252593: 3x+6 over 4x+12 DIVIDED BY x^2-4 over x+31 solutions Answer 184593 by jim_thompson5910(28598) on 2009-12-29 15:41:40 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the first fraction by the reciprocal of the second fraction . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. Distribute. So simplifies to . In other words,  Inequalities/252591: what do the word at most means? 1 solutions Answer 184584 by jim_thompson5910(28598) on 2009-12-29 15:20:17 (Show Source): You can put this solution on YOUR website!The phrase "at most" means that it is the largest value a variable can take on. When I say: "I have 'at most' 10 dollars", this means that the maximum amount of money I have is$10. I could have less than $10, but the most I have is$10. Algebraically, if 'x' is the amount of money I have, then this translates to
 Numbers_Word_Problems/252512: when N is divided by 5, the remainder is 3. what is the remainder when 7N is divided by 5?1 solutions Answer 184486 by jim_thompson5910(28598)   on 2009-12-29 00:42:39 (Show Source): You can put this solution on YOUR website!Since dividing N by 5 gives a remainder of 3, this means that where 'q' is the quotient (which is some whole number). Multiplying everything by 5 gets us So . If we divide 7N by 5, we then get . In other words, . The remainder is , but it's too big which means that we need to break it up. So . Since the fractional portion is , this tells us that the remainder is 1. ================================== Answer: So the remainder of dividing 7N by 5 is 1. Note: Try some examples to give you an idea that it works.
 Graphs/252515: I sure hope some one is feeling good this evening as im not good with this stuff and i need help with this problem. would you be so kind as to give me the steps and answer to it. Thank you so very much you all have been such great help to me. b/7.8 = -2.15 again thank you for your help wiggles1 solutions Answer 184482 by jim_thompson5910(28598)   on 2009-12-29 00:35:36 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by 7.8 to isolate 'b'. Multiply -2.15 and 7.8 to get -16.77 So the solution is
 Equations/252508: what multiplier should be used for each of the following equations to eliminate one unknown by subtraction? 3x-y=7 2x+7y=421 solutions Answer 184481 by jim_thompson5910(28598)   on 2009-12-29 00:28:58 (Show Source): You can put this solution on YOUR website!The multiplier is 7 since this will change -y into -7y. Add this to 7y to get -7+7y=0y=0 which means that it cancels out. Start with the given system of equations: Multiply the both sides of the first equation by 7. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent.
 Graphs/252509: HOW DO YOU GRAPH X=8 EXPLAIN IN DETAILS1 solutions Answer 184480 by jim_thompson5910(28598)   on 2009-12-29 00:27:02 (Show Source): You can put this solution on YOUR website!Simply draw a straight vertical line at to graph the equation like so: Graph of (green vertical line)
 Coordinate-system/252501: Solve the following system of equations algebraically and check: 2x + 3y = 11 5x - 2y = -20 1 solutions Answer 184479 by jim_thompson5910(28598)   on 2009-12-29 00:25:21 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the first equation by 2. Distribute and multiply. Multiply the both sides of the second equation by 3. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)
 Linear-systems/252498: Solve the following system of equations algebraically and check: 4x - 5y = 18 3x - 2y = 10 1 solutions Answer 184478 by jim_thompson5910(28598)   on 2009-12-29 00:24:12 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the first equation by 2. Distribute and multiply. Multiply the both sides of the second equation by -5. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)
 Numbers_Word_Problems/252490: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jelly beans she must take out of her pocket to ensure that she has one of each color? Could you please show me the set up and solution. Thank You1 solutions Answer 184454 by jim_thompson5910(28598)   on 2009-12-28 19:04:15 (Show Source): You can put this solution on YOUR website!Here's the worst case scenario: First, she pulls out all 8 red jellybeans. So she has taken out all of the red jellybeans. Then she either pulls out 4 consecutive green or blue jellybeans (either one or the other but not both colors). So far, she's pulled out 8+4=12 jellybeans total. To ensure that she has taken at least one of each color, she'll need to pull out at least one more (either blue or green) since there is only one color left. So in total, she'll have to pull out minimum of 8+4+1=13 jellybeans to ensure that she has at least one of each color.
 Trigonometry-basics/252486: 2sin^2x+3cosx=31 solutions Answer 184430 by jim_thompson5910(28598)   on 2009-12-28 17:02:17 (Show Source): You can put this solution on YOUR website!Hint: Recall that . So this means that . So plug in to get . Now let and plug that in to get: . At this point, we have a quadratic which can be solved by the quadratic formula. You'll get solutions in terms of 'z', so you'll need to remember to use to find the solutions in terms of 'x'. Let me know if you still need help.
 Functions/252416: Q:State the domain and range for each of the following relations.State whether or not each relation is a function. {(1,9),(2,12),(3,15),(4,22)} 1 solutions Answer 184314 by jim_thompson5910(28598)   on 2009-12-27 21:20:28 (Show Source): You can put this solution on YOUR website!Domain: Set of all possible inputs (ie x values): {1, 2, 3, 4} Range: Set of all possible outputs (ie y values): {9, 12, 15, 22} Since each x value only maps to one (and ONLY one) y value, this means that this relation is a function.
 Proofs/251009: This stuff is crazy O & I O -> (S v G) I -> ~G We have to show S1 solutions Answer 184296 by jim_thompson5910(28598)   on 2009-12-27 17:57:51 (Show Source): You can put this solution on YOUR website!1. O & I 2. O -> (S v G) 3. I -> ~G / :. S ---------------------- 4. I & O 1 Commutation 5. O 1 Simplification 6. I 4 Simplification 7. ~G 3,6 Modus Ponens 8. S v G 2,5 Modus Ponens 9. S 8,7 Disjunctive Syllogism