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# Recent problems solved by 'bucky'

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 Miscellaneous_Word_Problems/84475: Three friends check into a single room in a motel and pay \$10 apiece. The room cost \$25 instead of \$30, so the clerk is sent to the room to give back \$5. The friends each take back \$1, and the clerk is given a \$2 for his trouble. Now each of the friends paid \$9, a total of \$27, and the clerk received \$2. What happened to the missing dollar?1 solutions Answer 60875 by bucky(2189)   on 2007-06-05 15:31:33 (Show Source): You can put this solution on YOUR website!Let's see if I understand this correctly. They each paid \$9 for a total of \$27. Of that amount \$2 went to the clerk and \$25 went for the room. What missing dollar? . This is an old, old puzzle that never fails to confuse people. You subtract the amount that is given to the clerk, not add it to the amount they paid (\$27) in an attempt to make it add up to \$30.
 Functions/84530: This question is from textbook College Agebra Find the real values of x such that f(x)=0 (directions). f(x)=3/x-1 + 4/x-2 - - I don't even know where to begin on this problem. the answer they gave is 10/7 and I'm really confused on that....1 solutions Answer 60873 by bucky(2189)   on 2007-06-05 14:18:52 (Show Source): You can put this solution on YOUR website!Just set f(x) equal to zero. When you do that the given equation becomes: . . Now get rid of the denominators by multiplying all terms (on both sides) of this equation by . When you do that multiplication you get: . . Note that the right side of the equation remains zero because 0 times anything is still zero. Note also that you can now cancel the terms in the denominator with the same term in the numerator. The result is: . . And the equation reduces to: . . Multiply out the terms to get: . 3x - 6 + 4x - 4 = 0 . Combine the x terms and the equation becomes: . 7x – 6 – 4 = 0 . Combine the -6 with the -4 and the equation further becomes: . 7x – 10 = 0 . Eliminate the -10 from the left side by adding +10 to both sides. This makes the equation: . 7x = 10 . Finally, solve for x by dividing both sides of the equation by 7 which is the multiplier of the x term. The division results in the answer: . . Hope this helps you understand the problem.
 Equations/84492: Factor completely. y^4 + 3y^3 – 5y^2 – 15y The answer I ended up with is y(y^2 – 5)(y + 3)1 solutions Answer 60870 by bucky(2189)   on 2007-06-05 13:46:37 (Show Source): You can put this solution on YOUR website!Your answer is correct for this one also. You're doing great!
 Equations/84489: Factor completely. 6b^4 – 18b^3 – 60b^2 The answer I ended up with is 6b^2(b + 2)(b – 5)1 solutions Answer 60869 by bucky(2189)   on 2007-06-05 13:44:13 (Show Source): You can put this solution on YOUR website!Your answer is correct! Keep it up!
 Polynomials-and-rational-expressions/84512: Factor completely: b^2-ab-6a^2 (a)(b+3a)(b-2a) (b)(b+6a)(b-a) (c)(b-3a)(b+2a) (d)(b-6a)(b+a) My answer is C am I right?1 solutions Answer 60861 by bucky(2189)   on 2007-06-05 13:25:41 (Show Source): You can put this solution on YOUR website!You are correct. When the factors of answer (c) are multiplied together the product is the original trinomial that you were given to factor. . Good job!
 Graphs/84499: How and what do I do?Please help me? Solve the system by graphing. 3x – y = 1 3x – y = 2 1 solutions Answer 60844 by bucky(2189)   on 2007-06-05 09:56:18 (Show Source): You can put this solution on YOUR website!Let me start by saying that these two equations have no common solution. You can tell that because when you graph them their graphs turn out to be parallel lines. In order for linear equations such as these to have a common solution, their graphs must cross at some point. . You can get points on each of the graphs easily. For the first equation: . 3x - y = 1 . one point could be found by setting x equal to zero. When you do that, the equation becomes - y = 1. Solve for y by multiplying both sides by -1 to get y = -1. This tells you that (0, -1) is a point on the graph. When you plot this point, you will find that it is on the y-axis. [by setting x = 0, the answer for y will be on the y-axis.] . Another point on the graph can be found by setting y = 0. When you do that the equation reduces to 3x = 1. Solve for x by dividing both sides by 3 and you get x = 1/3. In this case since x = 1/3 when y = 0, you know the point (1/3, 0) is on the graph. Note that when you plot this point you will find that it is on the x-axis. [by setting y equal to zero, the answer for x will be on the x-axis.] . Plot those two points (0, -1) and (1/3, 0) and extend a straight line that runs through them and you have the graph of the first equation. . You can get two points for the second equation in the same way. In the second equation: . 3x - y = 2 . You can set x equal to zero and solve for y to find that y = -2. So the point (0, -2) is on the graph of the second equation. . Then set y = 0 and solve for x to find that the point (2/3, 0) is also on the graph of the second equation. . Plot these two points and extend a straight line through them to complete the graph of this equation. . Your graphs should now look like this: . . Notice that the "brown" graph is for the first equation because it crosses the y-axis where y equals -1 and the "green" graph is for the second equation because it crosses the y-axis at -2. . Notice that the lines are parallel, so they will never cross. Therefore, there is no common solution for the two equations. . Hope this helps you to understand the process of finding a common solution (or lack of a common solution) by using the method of graphing.
 Equations/84487: Factor completely. b^2 – ab – 6a^2 I got (b – 3a)(b + 2a) Did I just maybe get it right?1 solutions Answer 60843 by bucky(2189)   on 2007-06-05 09:29:17 (Show Source): You can put this solution on YOUR website!Yes, you got it correct. . You can always check your answer by multiplying the two factors you got using the FOIL method. . FOIL stands for Firsts ... Outsides ... Insides ... Lasts and it applies to the arrangement of the terms in your answer. Your answer was: . (b – 3a)(b + 2a) . The two "Firsts" in each set of parentheses are both b. Multiplying them together gives you b*b which is b^2. . The two "Outsides" in this string are ... b from the first factor and +2a from the second factor. Multiplying b times +2a results in +2ab. . The two "Insides" are -3a from the first factor and b from the second factor. Multiplying these two gives you -3ab. . And finally, the two "Lasts" are -3a from the first set of parentheses and +2a from the second set. Multiplying -3a times +2a results in -6a^2. . Now add your four answers from the FOIL process: . b^2 + 2ab - 3ab - 6a^2 . The two middle terms (both containing ab) combine to give you -ab. Substitute this result in place of +2ab - 3ab and your product becomes: . b^2 - ab - 6a^2 . This is the same as the trinomial you were asked to factor. Therefore, you have factored it correctly. Had your FOIL multiplication given you a different answer you might have expected that your factors were wrong (or you made a mistake in the FOIL multiplication). . Hope this helps you to build confidence in what you are doing. Keep up the good work!
 Equations/84486: Factor completely. x^2 – 7x – 30 I got (x + 3)(x – 10) Did I just maybe get it right?1 solutions Answer 60842 by bucky(2189)   on 2007-06-05 08:58:06 (Show Source): You can put this solution on YOUR website!Yes, your answer is correct! In your factors: a) the +3 times the -10 gives you the -30 you need and . b) the +3 plus the -10 gives you the -7 for the x term that you also need . Good job!
 Polynomials-and-rational-expressions/84422: solve each by completing the square 2x^2+10x+11=01 solutions Answer 60826 by bucky(2189)   on 2007-06-04 19:59:51 (Show Source): You can put this solution on YOUR website!Given: . . Subtract 11 from both sides to get the constant on the right side of the equation. This results in the equation becoming: . . You want the multiplier (coefficient) of the term to be 1. To make that happen, divide every term on both sides of the equation by the multiplier of the which is 2. When you do that division the equation becomes: . . Next, divide the multiplier of the x term by 2. That is divide the 5 by 2 to get . Square that term to get . Now add to both sides of the equation. You get: . . The left side factors to: . . Multiply the by to get which now has a common denominator with the other term on the right side. Substitute this into the equation to get: . . The right side combines to give: . . Now take the square root of both sides to get: . . Note that when you take the square root of the right side, the square root is preceded by both a + and a - sign. This shows in the next step. Look carefully for the two signs between the two terms on the right side. . Subtract from both sides and also transform the square root of 3/4 into the square root of 3 divided by the square root of 4. When you do that you will get: . . The square root of 4 is 2 and when this is substituted the equation becomes: . . Hope this helps you to understand the process of completing the square to solve a quadratic equation.
 Exponential-and-logarithmic-functions/84434: Find an exponential Formula for f(-8) = 200 and f(30) = 580. Could you please explain to me what process I use to find the answer to this kind of problem? I wish to find the answer to the problem after understanding the process if I can. I don't wish for the answer, just an explanaton on how to find the answer if that is okay. I was able to figure out that I need to do something to show that there are 38 units between f(-8) and f(30) and I even found the answer using the calculator and lots of trial and error, but I simply can't figure out how to solve it properly. Please help.1 solutions Answer 60823 by bucky(2189)   on 2007-06-04 18:41:16 (Show Source): You can put this solution on YOUR website!Given f(-8) = 200 and f(30) = 580 . Find an exponential formula that fits these given data. . The formula you will need to find is of the form . So what you need to do is to solve for A and b using the given data and appropriate math processes. . Start with the given that y = 200 when x = -8. Plug these values into the formula to get: . . Take the natural logarithm of both sides: . . But the natural log of e is 1. Substitute that and you get: . . Solve this for ln(A) by adding 8*b to both sides to get: . . Next follow the identical process for the second data point in which y = 580 and x = 30. Using this data in the formula and solving for ln(A) results in: . . Now you can set the right sides of the two equations you have for ln(A) equal and solve for b. You should be solving: . . When you solve this you should find that b is somewhere around 0.028018703 or whatever you choose to round it to. . Now that you know b you can return to either of the two equations for the data points and solve for A. For example, return to: . . Substitute 200 for y, -8 for x, and 0.028018703 for b to get: . . Solve for A by dividing both sides by . . But a quantity in the denominator that has a negative exponent can be brought into the numerator with the same exponent only positive. This means that A becomes equal to: . . and by a calculator . Substituting this into the equation for A results in: . . Now put this value of A and also the known value of b into the equation and you should end up with something around: . . as the equation you are looking for. . Hope you can track your way through this. You can check by letting x = 30 and solving to see if y = 580. You should find that y computes to be 579.9999895 or so. Close enough to assume this works. Cheers and good luck!
 Equations/84352: Find the axis of symmetry. y = x^2 – x – 8 My answer that I got is x=1 Is that correct?1 solutions Answer 60766 by bucky(2189)   on 2007-06-04 10:24:29 (Show Source): You can put this solution on YOUR website!There are several ways that you can find the value of x that represents the axis of symmetry. . One of these ways is to get the quadratic equation in the form that you need to apply the quadratic formula. That form is: . . Then recognize that the axis of symmetry is determined by that term of the of the answer to the quadratic equation that is: . . In this case, by comparing the quadratic expression of the problem: . . with the standard quadratic form: . . you can see that a = 1, b = -1, and c = -8. Substitute the appropriate values here into: . . and you get: . . So the answer to this problem is that the equation for the line of symmetry is: . . Hope that this clarifies the significance of the first term in the quadratic formula: . . It is the axis of symmetry about which the answers are equally spaced in both the + and the - directions. .
 Inverses/84355: This question is from textbook Algebra 2 An incremental Development We need help. My daughter has been working on this problem all weekend and we still do not get the right answer. We are working on inverse variation as a ratio. The problem is : The ratio of acrobats in blue to acrobats in pink was 4 to 5. Those who wore blue numbered 1200 fewer than twice the number who wore pink. How many wore blue, and how many wore pink? All help is appreciated. Thank you!1 solutions Answer 60760 by bucky(2189)   on 2007-06-04 09:53:15 (Show Source): You can put this solution on YOUR website!First, let B represent the number of acrobats wearing blue. Also let P represent the number of acrobats wearing pink. . Two times the number of acrobats wearing pink is, therefore, 2*P . 1200 less that that is 2*P - 1200 and that is equal to the number of acrobats wearing blue. So we can write that B = 2*P - 1200 . So we can write the ratio of blue to pink acrobats as: . . But you were told in the problem that . Substitute this into the ratio equation to get: . . An easy way to work on this proportion (a fraction on the opposite sides of the equal sign) is to cross multiply ... that is multiply the numerator on the left side by the denominator on the right side and set this product equal to the product you get by multiplying the numerator on the right side by the denominator on the left side. For this problem that translates to multiplying 4 by P and setting that equal to multiplying (2*P - 1200) by 5. This gives you the equation: . . Multiply out the right side and the equation becomes: . . To get the P terms on the same side of the equation subtract 10P from both sides of the equation. This results in: . . Solve for P by dividing both sides of the equation by -6 which is the multiplier of P. When you do this division, the result is: . . You now know that there are 1000 acrobats in pink. Since the ratio of Blue to Pink is 4 to 5, you can write: . . Using the cross product process just as before results in: . . Dividing both sides by 5 results in: . . So there are 800 acrobats dressed in blue and 1000 acrobats dressed in pink. . Check ... twice the acrobats dressed in pink is 2000. Notice that the number dressed in blue is 2000 - 800 = 1200 less than that number. That checks. And the ratio of 800 acrobats in blue to 1000 in pink is and that reduces to so it also checks. . Hope this helps you to see how to work the problem.
 Equations/84347: Factor. 8m^4n – 16mn^4 I came up with 8mn(m^3 – 2n^3) Is it right?1 solutions Answer 60754 by bucky(2189)   on 2007-06-04 09:14:21 (Show Source): You can put this solution on YOUR website!If you meant the problem to be: . . Then your answer is correct! .
 Equations/84345: Multiply. (4m – 3n)(4m + 3n) I came up with 16m^2 – 9n^2 Is it right?1 solutions Answer 60752 by bucky(2189)   on 2007-06-04 08:55:49 (Show Source): You can put this solution on YOUR website!Your answer is correct. Good job!
 Inequalities/84349: where did the algebra word came from?1 solutions Answer 60751 by bucky(2189)   on 2007-06-04 08:52:04 (Show Source): You can put this solution on YOUR website!Go to the following website: . en.wikipedia.org/wiki/Algebra . and read the first sentence. It explains it ...
 Linear-systems/84336: This question is from textbook finite mathmatics Please help with solution and how obtained for this question. One printing shop charges \$5 plus \$0.02 per page and a second shop charges \$7 plus \$0.015 per page. If __________ pages are printed, the total cost is less for the first printing shop. A. less than 1500 B. less than 2100 C. less than 400 D. less than 9001 solutions Answer 60750 by bucky(2189)   on 2007-06-04 08:45:05 (Show Source): You can put this solution on YOUR website!Begin by writing the equations for the Cost (C) of each printer. The general form of these equations is based on multiplying the cost per page times the number of pages and adding to that the fixed cost that you pay regardless of the number of pages. . For the first printer, the equation for the Cost (C) and the number of pages (P) is: . C = (0.02*P) + 5 . For the second printer, the equation for the Cost (C) is: . C = (0.015*P) + 7 . The first printer is cheaper for a while. You can tell that because if you have 1 page printed, the cost at the first printer is \$5.02 and the cost at the second printer is \$7.015. However, as you increase the number of pages, the difference in the Cost between the two printers gets smaller and smaller until at some number of pages the Cost of the two printers is the same. After that number of pages, the Cost for printing more pages will be less at Printer 2. . You can find the point at which the number of pages make the Cost equal at the two printers. Do this by solving the two Cost equations simultaneously. . The two equations are: . C = (0.02*P) + 5 C = (0.015*P) + 7 . We are trying to find the number of pages (P) that will make the Costs equal. Notice that if C is the same in both equations then the right side of both equations must be equal also. So we can say: . (0.02*P) + 5 = (0.015*P) + 7 . To solve this requires collecting the terms that have P on one side of the equation and the numbers on the other side. You can start by subtracting (0.015*P) from both sides of the equation. This makes the equation become: . (0.02*P) - (0.015*P) + 5 = + 7 . Next subtract 5 from both sides. This results in: . (0.02*P) - (0.015*P) = + 2 . Then subtract the two terms on the left side to get: . 0.005*P = 2 . Finally, solve for P by dividing both sides by 0.005, the multiplier of P. The solution for P is: . P = 2/0.005 = 400 . So if you have 400 pages to print, the Cost should be equal at the two printers. Check this out. . The Cost at the first printer would be \$5.00 plus 2 cents a page for the 400 pages which is 800 cents or \$8.00. So the total cost is \$5 + \$8 = \$13. . The Cost at the second printer would be \$7.00 plus 1.5 cents a page for 400 pages which is 600 cents or \$6.00. That makes the the total Cost \$7 + \$6 = \$13. . Since the Cost is \$13 at each printer for 400 pages, you can draw the following conclusion: . For less than 400 pages, it will be cheaper to use the first printer. At 400 pages it doesn't matter which printer you use, the Cost will be the same. For any number of pages greater than 400, you will save money by using the second printer. . Answer C is the correct answer.
 Miscellaneous_Word_Problems/84151: Solve algebraically using one variable: The first digit in a four digit number is four more than the second and the second is three less than the third. The fourth digit is one less than the third and the sum of the four digits is 21. What is the number? (HINT: first decide which digit you should call 'x'.) 1 solutions Answer 60582 by bucky(2189)   on 2007-06-02 08:28:32 (Show Source): You can put this solution on YOUR website!Given: an unknown four-digit number. . Call the first digit x. Do this because the second digit is given in terms of the first. And the third digit is in terms of the second which is based on the first. And the third is based on the second which depends on the first. And the fourth is based on the third, which is based on the second, which depends on the first. Therefore, every one of the four digits is based on the first digit in some way. So if you can find the unknown first digit, you should be able to find all the other digits. . This first digit is 4 more than the second digit. This means that if you took 4 away from the first digit the answer would be the second digit. Therefore, you can write the second digit as x - 4 . The second digit is 3 less than the third. This means that if you add 3 to the second digit, the answer would be the third digit. Since the second digit is x - 4, adding 3 to it results in (x - 4) + 3 = x - 4 + 3 = x - 1. Therefore, the third digit is represented as x - 1. . Finally, the fourth digit is 1 less than the third. That means that if we subtract 1 from the third digit the result is the fourth digit. Since the third digit is x - 1, taking 1 away from it gives (x - 1) - 1 = x - 1 - 1 = x - 2. . Let's summarize to this point: . First digit = x Second digit = x - 4 Third digit = x - 1 Fourth digit = x - 2 . The problem says that the sum of these digits is 21. Write this in equation form: . x + (x - 4) + (x - 1) + (x - 2) = 21 . Since each set of parentheses is preceded by a plus sign, you can just remove the parentheses without any changes to the terms inside each set. (I just put the parentheses in the equation to separate each of the four numbers.) So remove the parentheses to get: . x + x - 4 + x - 1 + x - 2 = 21 . Adding all the x terms together reduces the equation to: . 4x - 4 - 1 - 2 = 21 . Now add the three negative numbers together to get: . 4x - 7 = 21 . Get rid of the -7 on the left side by adding +7 on the left. But if you do that you also have to add +7 to the right side to keep the equation in balance. Adding +7 to both sides makes the equation become: . 4x = 28 . Finally solve for x by dividing both sides of the equation by 4 which is the multiplier of the x. When you divide both sides of the equation by 4 it becomes: . x = 7 . Since x is the first digit of the 4 digits, you can now solve for the other three digits. . You know that the second digit is represented by x - 4. Substituting 7 for x, the second digit becomes 7 - 4 and the answer to that is 3. So the second digit is 3. . The third digit is represented by x - 1. Substituting 7 for x results in 7 - 1 which simplifies to 6. So the third digit is 6. . Finally the fourth digit is represented by x - 2. Substituting 7 for x gives you 7 - 2 which results in the fourth digit being 5. . The number is 7365. . Let's check it against the problem statement. . Is the first digit 4 more than the second digit? Yes, 7 is 4 more than 3. . Is the second digit 3 less than the third digit? Yes, 3 is 3 less than 6. . Is the fourth digit 1 less than the third digit? Yes, 5 is 1 less than 6. . Finally, is the sum of the 4 digits equal to 21? Yes, 7 + 3 + 6 + 5 = 21 . Everything checks, so the answer of 7365 is correct. . Hope this helps you to understand the problem a little better.
 Miscellaneous_Word_Problems/84063: If the basic charge for electricity is \$0.0683/kWh, how much will it cost per year to run a 60W porch light, 8 hrs/day, everyday? Please show all work. Thank you. It gets tricky somewhere bteween Joules (J) and kilowatt hours (kWh). Is this even an algebra problem or should I be asking the science tutors?1 solutions Answer 60508 by bucky(2189)   on 2007-06-01 10:46:05 (Show Source): You can put this solution on YOUR website!You don't have to get involved with joules or units other than those mentioned in the problem. . Look at the problem this way. In one hour the bulb consumes 60 watts times 1 hour which is the same as 60 watt*hours. To convert this to kw*hours, just divide by 1000. When you do this division you get: . 60 w*hr/1000 w/kw = 0.060 kw*hr . Units check: . . So for each hour it runs, the bulb uses up 0.060 kw*hr of energy. . How many hours does the bulb run per year? At 8 hours per day for 365 days in the year, the bulb runs 8 times 365 hours which is 2920 hours. . Units check: . . Then in a year the total consumption is 0.060 kw*hr for each hour times the 2920 hours in a year for an annual amount of: . kw*hr per year. . Units check: . . And at a cost of \$0.0683 for each kw*hr the annual cost to run the bulb will be: . \$0.0683 * 175.2 = \$11.96616 which rounds to \$11.97. . Units check - using D to represent dollars): . . Everything checks. Hope this helps you to see your way through this problem.
 Radicals/84041: what is 7 plus or minus the square root of 24 over 2? 1 solutions Answer 60500 by bucky(2189)   on 2007-06-01 07:56:37 (Show Source): You can put this solution on YOUR website!Presuming that you don't mean that only the square root of 24 is divided by 2, your problem is to find: . . This has two answers ... one answer involves the plus sign and the other answer involves the minus sign. In other words, the answers to your question are: . and . You can find using a calculator. You should find that . Substituting that number for in the two answers results in the two answers becoming: . and . In the first answer the two terms in the numerator add to give 11.898979486 so this answer becomes: . and dividing the 2 into the numerator of 11.898979486 results in that answer becoming: . . In the second answer the two terms of the numerator are subtracted. This subtraction (7 - 4.898979486) results in 2.101020514. Substituting this value for the numerator of the second answer, results in the second answer becoming: . . In summary, your original problem has two answers: . and . Hope this work helps you to understand how to evaluate expressions of the form that you have in this problem.
 Quadratic_Equations/83944: how do you solve quadratic equations and then also simplify the radical solution??? examle: 5(x.squared)- (x.squared)=42 help!!!1 solutions Answer 60392 by bucky(2189)   on 2007-05-31 09:57:00 (Show Source): You can put this solution on YOUR website!Given: . . If you want, you can solve this without using the quadratic formula. Notice that the left side of this equation simplifies to: . . So you can substitute for the left side of the equation you were given. This makes the given equation become: . . Then you can find by dividing both sides by 4 which is the multiplier of the term. This division of both sides by 4 reduces the equation to: . . and . Substituting for results in the equation becoming: . . and taking the square root of both sides gives you the two answers: . and . And since the square root of 10.5 is (from a calculator) 3.240370349, the two answers to this problem are: . and . But if you have to do the problem using the quadratic formula, you need to get the original problem into the standard quadratic form of: . . You still combine the two terms on the left side of the original equation to get: . . just as we did above. Next you need to get zero on the right side as the standard quadratic form calls for. Do this by subtracting 42 from both sides of the equation. That subtraction results in: . . This is in the standard quadratic form in which a = 4, b = 0 (because there is no term that contains just x), and c = -42. . The quadratic formula says that the answer to the problem is determined by the equation: . . Since b = 0 in this problem, the equation reduces to: . . Next substitute 4 for a and -42 for c to get: . . The term in the radical [that is -4*4*(-42)] multiplies out to be 672 so the problem becomes: . . The denominator of (2*4) becomes 8 which further simplifies the problem to: . . Since the square root of 672 is (by a calculator) 25.92296279 the answers to this problem become: . and . When you do the division, the two answers are: . and . And these are the same answers that we found earlier without using the quadratic formula. . Hope this discussion helps you to work your way through the problem.
 Complex_Numbers/83950: Perform the indicated operation. Write the result in the form a + bi Show work. (6 + 8i) - (-7 + i)1 solutions Answer 60391 by bucky(2189)   on 2007-05-31 09:14:37 (Show Source): You can put this solution on YOUR website!Given: . (6 + 8i) - (-7 + i) . The first set of parentheses is preceded by a plus sign (you can presume that because there is no sign actually shown). Parentheses that are preceded by a + sign (or by no sign) can be removed without any change to the terms they contain. This changes the given problem to: . 6 + 8i - (-7 + i) . Notice that the remaining set of parentheses is preceded by a minus sign. The rule is that you can remove these parentheses if you change the signs of the terms inside the parentheses. Following this rule leads to the given expression now becoming: . 6 + 8i + 7 - i . Now you deal with the "regular" integer terms separately from the terms containing "i". In other words you can combine the +6 and +7 to get +13. Then you add the 8i and the -i to get +7i. . The answer to your problem is the combination of these two terms and it is: . 13 + 7i. . Hope this helps you to work your way through this problem and helps you understand how the process works. .
 Graphs/83878: What is the slope and y intercept of the line? -2y = 3x - 15 1 solutions Answer 60355 by bucky(2189)   on 2007-05-30 21:11:24 (Show Source): You can put this solution on YOUR website!Given: . -2y = 3x - 15 . You can easily find the slope and the y-axis intercept if you can get the given equation in the form: . y = mx + b . In this form the slope is "m" and the y-axis intercept is "b" . To get the given equation into slope intercept form, you need to solve for +y. In this case the left side will become +y if you divide all terms on both sides of the given equation by -2. The process is as follows: . -2y = 3x - 15 <--- given equation . (-2y/-2) = (3x/-2) - (15/-2) <--- shows division of all terms by -2 . y = -(3/2)x - (-15/2) <--- notice that - (-15/2) = + 15/2 . y = -(3/2)x + (15/2) <--- given equation in slope intercept form . By comparing this equation with the slope intercept form, you can see that "m" (the multiplier of the "x") is -3/2 and "b" the y-axis intercept is +15/2. That's the answer to the problem. As an aid to seeing that this is correct, here's a graph of the original equation in the problem: . . Notice that the slope is negative and the value of y where the graph crosses the y-axis is about +7.5 or +15/2. . Hope this helps you to understand the problem a little more.
 absolute-value/83887: What is the absolute value of 0?1 solutions Answer 60343 by bucky(2189)   on 2007-05-30 20:47:30 (Show Source): You can put this solution on YOUR website!By convention: . .