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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=7 1 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-5 1 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+3 1 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 wiggles 1 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=42 1 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 DETAILS 1 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 You 1 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=3 1 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.

Quadratic_Equations/249185: Solve equation by using the quadratic formula. 9x^2+5x-11=0 1 solutions Answer 184313 by jim_thompson5910(28598)   on 2009-12-27 21:17:55 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . or Break up the expression. So the solutions are or which approximate to or

Linear-equations/252412: I have been sitting here for hours trying to figure the following problems. I am working on Non-Linear Systems and have to solve the following systems. No matter how I work it I can't seem to come to a solution. 1) {7x-8y=24 {xy^2=1 2) {(x+1)^2 - (y-1)^2 = 20 {x^2 - (y+2)^2 - 24 Thank you - Lori 1 solutions Answer 184310 by jim_thompson5910(28598)   on 2009-12-27 20:42:42 (Show Source): You can put this solution on YOUR website! Even though these are non-linear equations, we can still use substitution to solve them. I'll do the first one to get you started. If that doesn't help either repost or ask me. # 1 Start with the second equation. Divide both sides by {{y^2}}} to isolate 'x'. Move onto the first equation. Plug in Multiply EVERY term by the LCD to clear out the fractions. Get every term to the left side. Multiply every term by -1. Now use the rational root theorem to find that is a root to the polynomial equation above. In other words, if you plug in into , you will get 0. Because of this fact, this means that is a factor of Now use polynomial long division to find that . So This tells us that . Since we know that gives a root of , we can ignore this equation. So the next step is to solve for 'y'. Use the quadratic equation to find the next two solutions of or So the three solutions in terms of 'y' are , or From here, plug each solution (in terms of 'y') into to find the corresponding solution in terms of 'x'. I skipped a bit of steps (since they're a bit long and I'm out of time for now), so feel free to ask about any step.

Parallelograms/252408: If the following statement were to be proven using a coordinate proof which formulas would be used the diagonals of a rhombus are congruent (a) distance (b) midpoint (c) both (d) the statement cant be proved can you explain? thank you 1 solutions Answer 184302 by jim_thompson5910(28598)   on 2009-12-27 18:36:05 (Show Source): You can put this solution on YOUR website! You would use the distance formula since this formula computes the distance between two points. If you know the coordinates of all four points, then you can find the distance from the opposite vertices. In other words, you can find the lengths of the diagonals using the distance formula. Since there is no point in using the midpoint formula, the answer is A)

Graphs/252406: Solve the following system of equations for x: 2x + y = 10 3x = y 1 solutions Answer 184298 by jim_thompson5910(28598)   on 2009-12-27 18:00:30 (Show Source): You can put this solution on YOUR website! Note: Since , this means that Start with the first equation. Plug in Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is Note: if you need to find 'y' as well, simply plug into to find its value.

Proofs/251009: This stuff is crazy O & I O -> (S v G) I -> ~G We have to show S 1 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

Travel_Word_Problems/252335: if a person hikes at approximately 3 km/hour, and has been hiking for 10 hours, how far have they hiked? 1 solutions Answer 184193 by jim_thompson5910(28598)   on 2009-12-26 20:24:04 (Show Source): You can put this solution on YOUR website! Remember that the distance traveled (D) equals the rate (r) multiplied by the time (t). In other words, D = rt Start with the given equation. Plug in (the given speed) and (the given time) Multiply So if a person hikes for 10 hours at 3 km/hr, then they have gone 30 miles.

logarithm/252336: solve: ln(2x-1)=8 1 solutions Answer 184192 by jim_thompson5910(28598)   on 2009-12-26 20:21:58 (Show Source): You can put this solution on YOUR website! Start with the given equation. Recall that the equation can be rewritten as Use the property shown above to convert the equation into exponential form. Add 1 to both sides. Divide both sides by 2. So the exact solution is which approximates to

Probability-and-statistics/252330: Please help me solve this problem: In an exercise gym, 5 different people used a particular weight-training machine. Name Weight Mona 40 Sam 80 Tony 80 Alba 60 Peter 110 Use the data above to find the mean, median, mode. and range of the data. What effects does multiplication by a fixed number have on the mean, median, mode, and range of the data? Explain the reasoning for your answer. - I already found the mean, median, mode, and range. mean=74 median=80 mode=80 range=70 I just DON'T GET the question about the fixed number... PLEASE HELP ME AND EXPLAIN!!! -thankyou! :) 1 solutions Answer 184185 by jim_thompson5910(28598)   on 2009-12-26 18:20:42 (Show Source): You can put this solution on YOUR website! Let k = some fixed number (ie a constant). In other words, k is some number (we just don't know what it is). Now multiply EVERY data value by k to get: Mona 40k Sam 80k Tony 80k Alba 60k Peter 110k Now let's find the following: Mean: Add up the values and divide by 5 (the number of people there) to get So the mean of the data values of 40k, 80k, 80k, 60k, and 110k is 74k. What this means is that the mean is just the original mean multiplied by the constant k. So if k=2, then the new mean is 2*74=148 ------------------------------------------------------------------------------ Median: First write the values in ascending order: 40, 60, 80, 80, 110 Now multiply each value by k: 40k, 60k, 80k, 80k, 110k From this list, the middle most value is 80k. Since the original median is 80, the new median is just the result of multiplying the original median of 80 by the constant k. I bet you can guess what's going to happen with the mode and the range. ------------------------------------------------------------------------------ Mode: Looking at the list 40k, 60k, 80k, 80k, 110k we see that the mode is 80k since 80k repeats itself twice and it is the most frequent number. Because the original mode is 80, the new mode is just the product of the old mode and k. ------------------------------------------------------------------------------ Range: The range of the list 40k, 60k, 80k, 80k, 110k is just the difference between the largest element (110k) and the smallest element (40k). In other words the range is: 110k - 40k = 70k which is exactly the product of the original range and the constant k. So multiplying every element in a data set by a fixed number will just multiply the mean, median, mode, and range by that same fixed number. Try picking some specific numbers (like k=2, k=3, etc) to give you some examples.

Percentage-and-ratio-word-problems/252326: 1.if set A has 3 elements and set B has 4 elements: a. what is the greatest number of elements that A n B can have? explain the greatest number of elements that A n B can have is 3 b/c a is a subset of B and A and B b. what the lest number of elements that A n B can have? explain if a and B are disjoint than A and B has zero elements 2.solve the inequality and graph the solution set : (x- 4 is less than or equal to -6) or (2x > 8) p.s i wrote less than or equal to b/c i couldnt find the symbol for it. please and thank you 1 solutions Answer 184182 by jim_thompson5910(28598)   on 2009-12-26 17:24:50 (Show Source): You can put this solution on YOUR website! See this solution at the following link: http://www.algebra.com/algebra/homework/Percentage-and-ratio-word-problems/Percentage-and-ratio-word-problems.faq.question.252266.html

Geometry_proofs/252317: i need help with the following proof. Ive put it into a link can someone explain it please? http://www2.edmastery.com/li/itemAssets/nnds_li%20-%20production%5Cdmeyer%5C16.bmp 1 solutions Answer 184172 by jim_thompson5910(28598)   on 2009-12-26 15:30:10 (Show Source): You can put this solution on YOUR website! When you have and you want to solve for 'x', the next step would be to add 84 to both sides to get which then becomes . The property that you are using here is the addition property of equality. So the answer is C)

Quadratic_Equations/252256: 3x squared + 12x = -2 I can find the square sign on my computer so I just wrote out 3x squared 1 solutions Answer 184089 by jim_thompson5910(28598)   on 2009-12-25 17:41:03 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add 2 to both sides. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Square to get . Multiply to get Subtract from to get Multiply and to get . Simplify the square root (note: If you need help with simplifying square roots, check out this solver) or Break up the expression. or Reduce. So the solutions are or which approximate to or

Matrices-and-determiminant/252267: Can cramer's rule be used for: if so what would I use for the middle equation for the coefficient of y and what would the constant be...??? x+y+z=2 2x=z x-2y+2z=1 1 solutions Answer 184086 by jim_thompson5910(28598)   on 2009-12-25 17:35:33 (Show Source): You can put this solution on YOUR website! Since can be rewritten as , this means that the middle coefficient for 'y' of the 2nd row is 0. Let me know if you need help with any more parts of the problem.

Systems-of-equations/252265: Hello I have a problem that is nonlinear and cramer's rule or Gaussian elimination can't be used for. I'm trying to use substitution and factoring for this one but I'm coming up with the right thing... And I know its something that I'm missing I just can't see it.... it seems like the simplier the problem, I make mistakes. Could you please assist me with solving this problem .. Thanks y=x^2-4x+7 y=x+1 1 solutions Answer 184085 by jim_thompson5910(28598)   on 2009-12-25 17:33:48 (Show Source): You can put this solution on YOUR website! Start with the first equation. Plug in Get everything to one side. Combine like terms. Factor the right side. or Use the zero product property. or Solve for 'x' in each equation. Now for each 'x', plug them into to find the corresponding 'y' values. So when , then which gives the first ordered pair (3,4) and when , then which gives the second ordered pair (2,3)

Functions/252222: In A = xy - (1 - z/4)r^2, solve for r in terms of the other variables, r a positive number. 1 solutions Answer 184047 by jim_thompson5910(28598)   on 2009-12-25 00:59:26 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract xy from both sides. Divide both sides by . Reduce. Take the square root of both sides. Note: Since 'r' is positive, we don't have to worry about the negative square root. So the answer is Note: if the original problem was , then the answer is which simplifies to