Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

Recent problems solved by 'bucky'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189, >>Next

 Miscellaneous_Word_Problems/88039: could you help to solve this problem and show in a equation . One number is 8 more than another. If the sum of the smaller number and twice the larger number is 46, find the two numbers. 1 solutions Answer 63930 by bucky(2189)   on 2007-07-11 18:54:30 (Show Source): You can put this solution on YOUR website!When you read the problem, it becomes apparent that you need to find a small number and a larger number. For ease of understanding and identification, call the Small number S and the Larger number L. . The first sentence tells you that one number is 8 more than another. If it is 8 more, then this means that it is L. So you should get the idea that if you take 8 away from L then you should have S. You can write this as: . L - 8 = S . or by adding 8 to both sides, it may be clearer to you as S + 8 = L. Either one is OK to use. . The second sentence tells you that the sum of the Small number (S) and twice the Larger number (2*L) equals 46. Writing this in equation form gives you: . S + 2L = 46 <- call this the second equation . Then, from the first equations you can either use the fact that S = L - 8 or that L = S + 8 and substitute into the second equation. For ease, let's use S = L - 8 and so we can replace S in the second equation with L - 8 to get: . L - 8 + 2L = 46 . Next you can get rid of the -8 on the left side by adding 8 to both sides. When you do this addition you get: . L + 2L = 54 . Add the terms on the left side and the equation reduces to: . 3L = 54 . Finally divide both sides by 3 to reduce the equation and solve for L: . L = 54/3 = 18 . Now you know that L = 18 you can solve for S. You know that L is 8 larger than the smaller number S. So you can subtract 8 from L and you have S. Therefore, L - 8 = 18 - 8 = 10. Therefore, S is 10. . So the two numbers are 10 and 18. . Obviously the larger number is 8 more than the smaller number. Then check further by adding the smaller number to twice the larger. If you do you get 10 + 2*18 and this becomes 10 + 36 and this equals 46, just as the problem says it should. . Hope this helps you to understand the problem and how to solve it. .
 Functions/87832: I have a question that states: find f(-2) for the function f(x)=2^4x-11 solutions Answer 63815 by bucky(2189)   on 2007-07-11 01:21:39 (Show Source): You can put this solution on YOUR website!I'm not sure whether you meant the problem to be find f(-2) given that . <=== first case . or . <=== second case . In either case, the way you work this problem is to substitute -2 for x and calculate the answer. . In the first case, substituting -2 for x results in: . . In the second case, substituting -2 for x results in: . . [Note that in these two problems and ] . Hope this helps you to see your way through the problem. Just remember that when you write f(-2) it means substitute -2 for the variable on the right side. So f(5) would mean substitute +5 for the variable, and so forth.
 Radicals/87805: This question is from textbook algebra structure and method I'm supposed to express this in simplest radical form. (square root of 2 minus 3)(square root of 2 plus 3) I'm not sure how you are supposed to do that or is it in simplest form already?1 solutions Answer 63707 by bucky(2189)   on 2007-07-10 08:26:54 (Show Source): You can put this solution on YOUR website!Given: . . Note that this product is covered by the rule for the product of the sum and difference of two quantities. This rule is: . . If you actually do the multiplication of (a - b) times (a + b) you will see why this rule is true. . Anyhow, if you let and then, according to the rule, the product will be or . . But squaring the square root of 2 results in an answer of 2 and squaring 3 results in 9. . So according to the rule, the answer is: . . The answer is -7 and notice that the radicals are gone completely. .
 Radicals/87806: This question is from textbook algebra structure and method We are suppose to express this in simplest radical form. 3square root of 2 plus square of 50. Please help!1 solutions Answer 63705 by bucky(2189)   on 2007-07-10 08:04:06 (Show Source): You can put this solution on YOUR website!I suspect that you meant to say the square root of 50 instead of the square of 50. So you meant for the problem to be: . . Note that 50 is 25*2. So you can substitute 25*2 for 50 and the problem becomes: . . By the rules of square roots you can split into to convert the problem to: . . But the square root of 25 is 5 and substituting 5 for the square root of 25 changes the problem to: . . Then you can factor out the square root of 2 to make the problem: . . and replace 3+5 by 8 makes it: . . and we conventionally write this as: . . Hope this helps you to understand the problem and some of the steps you can take to simplify radicals. . If you really meant the problem to be: . . then please post the problem again because that is a whole different problem from the one I worked above.
 Length-and-distance/87808: A bottle when empty weighs 115g and 1.22kg when filled with water. About how many mL of water does it contain if 1mL of water weighs approximately 1g?1 solutions Answer 63701 by bucky(2189)   on 2007-07-10 07:32:23 (Show Source): You can put this solution on YOUR website!You need to work in consistent units. Note that the weight of the bottle is given in grams and the combined weight of the bottle and water is given in kilograms. Convert the weight of the combined water & bottle from kilograms to grams. Do this by multiplying 1000 times the weight in kilograms to find that the combination weighs: . 1.22 kg * 1000 = 1220 grams . Next you can subtract the weight of the bottle (115 grams) from the weight of the bottle-water combination to find the weight of only the water as follows: . Weight of Water = 1220 gms - 115 gms = 1105 gms . And since each gram is 1 ml of water, there must be 1105 ml of water. . Hope this helps you to see your way through this problem. .
 Miscellaneous_Word_Problems/87653: Please i need help on this problem: Assuming that on a blueprint 1/4 inches equals 12 inches, the actual length in feet of a steel bar represented on the blueprint by a line 3 3/8 inches long is... A. 3 3/8 B. 6 3/4 C. 12 1/2 D. 13 1/21 solutions Answer 63699 by bucky(2189)   on 2007-07-10 07:17:38 (Show Source): You can put this solution on YOUR website!The problem tells you that each 1/4 inch on the drawing equals 12 inches in "real world" dimensions. And since 12 inches is 1 foot, you can say that each 1/4 inch on the drawing represents 1 foot in actual size. . In the explanations below, you will see 3 3/8 written as 3+3/8 in some places. These are equivalent ways of writing the mixed number. . If you measure 3 3/8 inches on the drawing, how many 1/4 inches is that? Since each inch contains 4 quarter inches, the three inches is 4*3 or 12 quarter inches. You still have the 3/8 inches, and 3/8 of an inch contains one 1/4 plus half of another or 1.5 quarters. So the total number of 1/4 inches is 12 + 1.5 = 13.5 quarters and since each of those quarters represents a foot, the total number of feet is 13.5 feet. . If this explanation is a little confusing, there are a couple of other ways you can look at it. You can find the number of quarters in 3 3/8 by dividing 3 3/8 by 1/4. Convert the 3 3/8 to an improper fraction by multiply 8 times the whole number 3 and adding the additional 3 from the numerator to get 3 3/8 = (24+3)/8 = 27/8. To divide this by 1/4, invert the 1/4 to get 4/1 and multiply that by the 27/8. The result is: . (27*4)/(8*1) = 118/8 = 13 4/8 = 13 1/2. This again tells you that the drawing measurement of 3 3/8 contains 13 1/2 quarter inches and since each quarter inch represents 1 foot, the drawing dimension represents 13 1/2 feet. . Or you could set up the proportion of one-quarter inch is to 1 foot as 3 3/8 inches is to X feet which translates to the equation: . . Solve this equation by cross multiplying ... multiplying the numerator of the left side times the denominator of the right side and setting that product equal to the numerator of the right side times the denominator of the left side. When you do that you get: . . If you multiply both sides of this equation by 4 to eliminate the denominator on the left side, you get: . . The distributed multiplication on the right side leads to: . . Again the answer is 13 1/2 feet. . Hope one or more of these methods makes sense to you.
 Age_Word_Problems/87803: Herny's father is now twice as old as Henry. Sixteen years ago, he was four times as old. How old is each now?? 1 solution1 solutions Answer 63698 by bucky(2189)   on 2007-07-10 06:27:49 (Show Source): You can put this solution on YOUR website!Let F represent the current age of Henry's father. And Let H represent Henry's current age. . Currently the father is twice as old as Henry. Therefore, if you double Henry's current age, the result equals the father's age. In equation form this is: . F = 2*H . Sixteen years ago, the father's age was his current age less 16 which is F - 16. The same with Henry. Sixteen years ago Henry was his current age less 16 or H - 16. And at that time the father's age (F - 16) was equal to 4 times Henry's age [4 times (H - 16)]. In equation form this is: . F - 16 = 4*(H - 16) . Simplify this by multiplying out the right side to get: . F - 16 = 4H - 64 . Then get rid of the -16 on the left side by adding 16 to both sides. When you add 16 to both sides you get: . F = 4H - 48 . Now from the first equation we wrote, F = 2H. So we can substitute 2H in place of F in the equation and with this substitution the equation . F = 4H - 48 . becomes: . 2H = 4H - 48 . Next let's get rid of the 4H on the right side by subtracting 4H from both sides. When you subtract 4H from both sides, the equation becomes: . -2H = -48 . Divide both sides by -2 which is the multiplier of H and you get: . H = -48/-2 = 24 . This tells us that Henry is currently 24 years old. And since we know that his father is presently twice as old as he is, Henry's father must currently be 48 years old. . Let's check that. Sixteen years ago, Henry's father was 48 - 16 = 32 years old and also 16 years ago, Henry was 24 - 16 = 8 years old. So 16 years ago the father's age (32) was 4 times Henry's age (8). That works! So the answer to the problem is that Henry is currently 24 years old and his father is currently 48 years old. . Hope this helps you to understand the problem and a process that you can use to solve it.
 Quadratic_Equations/86764: Please help...my original problem is: 2(x-5)^2 = 3. I think the answer is: x= 10 (plus/minus) sq.rt.6 / 2....am I on the right track? Thank you for your help! 1 solutions Answer 63217 by bucky(2189)   on 2007-07-05 07:52:26 (Show Source): You can put this solution on YOUR website!If you are saying that the answer is: . . You are correct.
 Expressions-with-variables/87230: 4. George is 12 years older than Jeannie. The sum of their ages in 5 years will be 50. How old is Jeannie now? a. Define the variables. b. Write an expression for the age of George in terms of Jeannie's age. c. Write an equation for the sum of their ages in 5 years from now. d. Solve the equation for the age of Jeannie now. 1 solutions Answer 63181 by bucky(2189)   on 2007-07-04 09:43:38 (Show Source): You can put this solution on YOUR website!George is 12 years older than Jeannie. The sum of their ages in 5 years will be 50. How old is Jeannie now? a. Define the variables. . Just to help us remember what is what, let's use G to represent George's current age and J to represent Jeannie's current age. . b. Write an expression for the age of George in terms of Jeannie's age. . The problem tells you that George is 12 years older than Jeannie. That means if you subtract 12 from George's age, the answer should be Jeannie's age. In equation form this would be: . G - 12 = J . Solve for G by adding 12 to both sides to get: . G = J + 12 . c. Write an equation for the sum of their ages in 5 years from now. . Five years from now George's age will be G + 5 and Jeannie's age will be J + 5. The problem tells you that the sum of these ages will be 50. In equation form this would be: . G + 5 + J + 5 = 50 . By adding the two 5s on the left side this simplifies to: . G + J + 10 = 50 . And subtracting 10 from both sides further simplifies this equation to: . G + J = 40 . d. Solve the equation for the age of Jeannie now. . Start with the equation from part c: . G + J = 40 . But way back in part b it is known that G = J + 12. Substitute the right side of this equation in place of G and get: . J + 12 + J = 40 . Add the two Js and the equation becomes: . 2J + 12 = 40 . Subtract 12 from both sides results in: . 2J = 28 . Divide both sides by 2 to solve for J and you get: . J = 28/2 = 14 . This tells us that Jeannie is 14 years old at present. . That means that George, who is 12 years older, is 26 at present. . Five years from now, Jeannie will be 14 + 5 or 19 years old. And George will be 26 + 5 or 31 years old. The sum of their ages will be 19 + 31 which is 50, just as the problem said it should be. . Hope this helps you to understand the problem.
 Linear_Equations_And_Systems_Word_Problems/87216: Your maximum exercise heart rate M is given by the formula M = 0.85(220-a), where "a" is your age. What is the age of someone who has a maximum exercise heart rate of 133?1 solutions Answer 63179 by bucky(2189)   on 2007-07-04 09:19:48 (Show Source): You can put this solution on YOUR website!Given: . M = 0.85(220 - a) . and also given that M = 133 . Find "a" . Method: . Substitute 133 for M in the equation to get: . 133 = 0.85(220 - a) . Multiply 0.85 times each of the quantities in the parentheses: . 133 = 0.85*220 - 0.85*a . Note that 0.85 times 220 is 187. When you do that multiplication, the equation becomes: . 133 = 187 - 0.85a . Next you need to get the term containing "a" by itself on one side of the equation, and everything else on the other side. Let's begin by adding 0.85a to BOTH sides of the equation. When you do, the addition of 0.85a to the right side cancels the -0.85a on the right side. This makes the equation become: . 133 + 0.85a = 187 . Subtract 133 from both sides to get rid of it on the left side. When you subtract 133 the equation becomes: . 0.85a = 187 - 133 . The subtraction on the right side results in: . 0.85a = 54 . Divide both sides by the multiplier of "a" to solve for "a". When you do that the equation becomes: . a = 54/0.85 . and the right side is: . a = 63.5294 . which tells you that at the age of 63.5 years the maximum rate of heart exercise is 133. . You can check this by substituting 63.5 into the original equation to find that: . M = 0.85(220 - 63.5) . Subtract the two numbers in parentheses to get: . M = 0.85(156.5) . do the multiplication and the result is: . M = 133.025 . The slight difference is due to rounding off the number of years. So the answer we got in this checking work is equal to the heart rate specified by the problem ... 133. . Hope this helps you to understand how to work the problem.
 logarithm/86947: Solve for x in (125)^x=625 I'm completely lost on this1 solutions Answer 62899 by bucky(2189)   on 2007-06-30 08:05:01 (Show Source): You can put this solution on YOUR website!Anytime you see an equation that has a variable in the exponent, one of the first things you should think of is "logarithms" . You are given: . . Take the logarithm of both sides of this equation. You can use base 10 or base e, which is "ln" or natural logarithms. These can be worked on a normal scientific calculator so either is a good choice. Let's choose base 10. Taking the Log base 10 of both sides of the equation results in: . . To simplify things a little, let's use a calculator to find . Enter 625 on the calculator and press the "log" key. You should get 2.795880017. Substituting this value results in the equation becoming: . . Next we'll use another property of logarithms. If you are finding the logarithm of a quantity that has an exponent, an equivalent form is to multiply the logarithm by the exponent. In other words, is equivalent to so let's substitute that into our equation to get: . . Now use a calculator to find . Enter 125 and press the "log" key to get . Substitute this into the equation and you now have: . . Finally divide both sides by 2.096910013 and the answer becomes: . and this is . Hope this helps you with your understanding of logarithms.
 logarithm/86948: Solve for the approximate value of x: In x=3 Is it 3?1 solutions Answer 62898 by bucky(2189)   on 2007-06-30 07:36:40 (Show Source): You can put this solution on YOUR website!By "In" I believe you mean "ln" which is the notation for natural logarithms. Natural logarithms have the base e which is the symbol for a number that is approximately 2.718281828 ... . This is a problem in which you can use a translation from logarithmic form to the equivalent exponential form. This translation is done according to the following rule: . is equivalent to the exponential form . In your problem, the "ln" tells you that you are using a logarithm with the base e. Therefore, your problem can be written: . . and by comparing this to the translation rule you can tell that b = e, C = 3, and A = x. Substitute these values into the exponential form and you get an exponential form of: . . So you now know that and since e is approximately 2.718281828 you can get an approximate value for x by using the equation: . . You can then use a calculator to cube 2.718281828 and you will get: . . as a pretty close approximation of the value of x. . Remember that translation form. It's a fundamental definition for logarithms and it comes in quite handy for solving lots of logarithmic problems. .
 logarithm/86946: log base5 x=30 The value of x is? is it 15?1 solutions Answer 62897 by bucky(2189)   on 2007-06-30 07:13:44 (Show Source): You can put this solution on YOUR website!Given: . . Solve for x . You can convert this problem to exponential form to solve it. The conversion between logarithmic and exponential form is done according to the following relationship: . is equivalent to the exponential form . Remember this relationship. It's quite useful in solving logarithmic problems. . If you compare what you are given to the log form you can see that b = 5, C = 30, and A = x. . Now substitute these values into the exponential form and you get: . . So and that is a pretty big number. You can use a calculator to find that is approximately . These are answers that you are looking for. Let's work a similar problem with smaller numbers just for practice. Suppose the problem had been: . . You solve for x by converting this log form to exponential form. In this case b = 5, C = 3, and A = x. Substituting these values into the exponential form results in: . . and 5 cubed is 5*5*5 = 125. So for this problem, x would be 125, and you can now write: . . Hope this helps you to understand the problem a little better .
 expressions/86907: Tutor: Can you help me simplify this expression? 9(x-7)(x+7)/3(x-7) Thank you1 solutions Answer 62868 by bucky(2189)   on 2007-06-29 20:02:42 (Show Source): You can put this solution on YOUR website!Given: . . The first thing you can do is to divide the 3 in the denominator into the 9 in the numerator. The result of this division in that you are left with a 3 in the numerator. [You can also replace the 9 with 3*3 and then cancel the 3 in the denominator with one of the 3s in the numerator. The result is the same ... a 3 left in the numerator.] The problem is now simplified to: . . Next you can cancel the (x-7) in the denominator with the (x-7) in the numerator. This cancellation is as follows: . . And the simplification asked for by the problem is what is now leftover, and is: . . If you want to, you can perform the distributed multiplication by 3 to get: . . Either answer [3(x + 7) or 3x + 21] is correct. . Hope this helps you to understand the problem. .
 Radicals/86825: Divide the following: (18 + the square root of 567) /9 Thanks1 solutions Answer 62832 by bucky(2189)   on 2007-06-29 10:06:52 (Show Source): You can put this solution on YOUR website!Divide the following: . . You can split this into two terms as follows: . . The term of 18 divided by 9 is equal to 2. This simplifies the problem to: . . Note that the denominator of 9 is equal to . If we replace the 9 with this radical the problem now becomes: . . By the rules of radicals we can put both terms under the same radical sign to convert the problem to: . . and note that 81 goes into 567 exactly 7 times. So replace 567/81 by 7 and the problem simplifies to: . . Let's check with a calculator. First, the original problem: . Square root of 567 = 23.8117618 . Add 18 to this and you get 41.8117618 . Divide this total by 9 and the result is 4.645751311 . Next let's use a calculator to check our answer. . The square root of 7 is 2.645751311 and if you add 2 to that you get 4.645751311. . The two answers agree, so we have a correct solution to the problem. The original problem simplifies to . Hope this helps you to understand the original problem a little better. .
 Miscellaneous_Word_Problems/86822: a 30 year old can purchase a one year life insurance policy for 20,000 at a cost of 25.00. The probability of a person dying at age 30 is 0.0002. What is the company's expected profit per policy?1 solutions Answer 62811 by bucky(2189)   on 2007-06-28 21:39:54 (Show Source): You can put this solution on YOUR website!Here's an approach to this problem. . If the number of policies sold is 10,000, the probability is that of this pool of policies 0.0002 is the probability of death. Multiply the 10,000 by 0.0002 and you get that 2 deaths will occur. . At \$25 per policy, 10,000 policies will bring in a total of \$250,000 (which comes from \$25 * 10,000). . But the company will statistically have to pay for two policies, and since the payoff will be \$20,000 per policy for a total payoff of \$40,000. . Therefore, the "profit" on \$250,000 of income to the company will be \$250,000 less the \$40,000 payoff which is \$210,000. . Dividing this profit by the 10,000 policies that generate it will give the "per policy profit". . . Therefore, you can say that of the \$25 the company collects for a policy, the policy will typically return \$21 as "profit". . Hope this helps you to understand the problem and a way that you can analyze it to get an answer.
 Quadratic_Equations/86790: simplify: square root of 721 solutions Answer 62810 by bucky(2189)   on 2007-06-28 21:12:01 (Show Source): You can put this solution on YOUR website!How about doing it this way: . . Then by the rules of square roots, you can use the rule that: . . So you can write: . . But . Substituting 6 for in the right side of the simplification equation you get: . . So the answer to this problem is simplifies to . Hope this helps you understand the simplification process for radicals.
 Quadratic_Equations/86811: Simplify: square root of 5001 solutions Answer 62806 by bucky(2189)   on 2007-06-28 21:01:00 (Show Source): You can put this solution on YOUR website!Since 500 is an even number you know that it is divisible by 2. Therefore, you can write it as . But 250 is also even and divisible by 2. So 250 can be replaced by 125 * 2. Therefore, you can replace 500 by 125*2*2 which is equivalent to . Then . So if you substitute for 125 you get: . . Taking the square root of all three terms in this multiplication string results in: . . So the simplified form of is . Had you recognized it earlier, you could have written: . . much quicker, but not as much practice as the long way. . Hope this helps you to see how square root problems such as this one can be simplified. .
 Points-lines-and-rays/86732: please help me solve this problem: what is the slope of the line 3x+2y=6 ?1 solutions Answer 62753 by bucky(2189)   on 2007-06-28 07:27:34 (Show Source): You can put this solution on YOUR website!An easy way to find the slope is to work the equation into the slope-intercept form which is given by the equation: . y = mx + b . In this form m is the slope and b is the value on the y-axis where the graph crosses the axis. . So take the given equation 3x + 2y = 6 and solve it for y. . First step, subtract 3x from both sides to get: . 2y = -3x + 6 . Then divide both sides (all terms) by 2 to solve for y. When you do that division you get: . y = (-3/2)x + 3 . By comparing this with the slope intercept form, you can see that m, the slope, is -3/2 and you can tell that the graph crosses the y-axis at the value y = +3. . Hope this helps you understand the problem.
 Linear-equations/86726: This question is from textbook Find the slope and y-intercept of the line 2x - 3y = 6 Write the equation of the line with given slope and y-intercept. How would they be graphed using slope and y-intercept. slope 5; y-intercept: (0, -2) Slope -2; y-intercept: (0,4) slope - 3/4; y-intercept: (0,8) 1 solutions Answer 62752 by bucky(2189)   on 2007-06-28 07:19:12 (Show Source): You can put this solution on YOUR website!The form of the equation that you need for this problem is called the slope-intercept form. It is given by the equation: . y = mx + b . where m is the slope of the graph of the equation and b is the y-intercept, that is, the value on the y-axis where the graph crosses. . The first part of the problem gives you the equation: . 2x - 3y = 6 . and asks you to find the slope and the y-intercept of the graph. The easiest way to do that is to rearrange the equation into the slope intercept form. Once you do that you know that the slope (m) is the multiplier of the x and the constant is the y-intercept . So we need to solve the given equation for y. The first step is to isolate the y term on one side of the equation and have everything else on the other side. So let's begin by subtracting 2x from both sides of the equation. When you do that the equation becomes: . -3y = -2x + 6 . Next solve for y by dividing all terms on both sides of the equation by -3, the multiplier of the y term. When you do that division the equation becomes: . -3y/3 = -2x/-3 + 6/-3 . and this simplifies to: . y = (2/3)*x - 2 . Now by comparing this equation with the slope-intercept form you can tell that the slope (the multiplier of x represented by m) is (2/3) and the y-intercept (the constant represented by b) is -2. Those are the answers to the first part of this problem. . The remainder of the problem can be done just by substituting values into the slope-intercept equation form. . The first of the three givens tells you that the slope is 5 and the y-intercept is (0, -2). The intercept point on the y-axis is, therefore, -2. The slope intercept equation form becomes: . y = 5x - 2 . You can graph this by marking the point -2 on the y-axis. You know that the graph goes through this point. Put your pencil on that point. Move in horizontally to the right 1 unit. Stop. Then move it vertically upward 5 units. Stop and mark that point. This is a second point on the graph. Now you can run a straight line through the two points and you have the graph. Another way you can find points is to just assume values for x, plug them into the equation, and solve for y. The point (x, y) will then be on the graph. For example, assume x = 2. Then the equation for y tells you that y = 5(2)-2 = 10 - 2 = 8. So the point (2,8) is on the graph. When you get done, the graph should look like: . . You can do the remaining two problems the same way. For the second one you are given that the slope is -2 and the intercept is (0,4). That means the slope intercept equation is: . y = -2x + 4 . Since the graph crosses the y axis at +4 you can mark that point on the y-axis. Start your pencil on that location. Go horizontally to the right 1 unit and at that location go down -2 units because the slope is -2. (You should be at (1,2)). That is a second point on the graph. Since you now have two points on the graph you can draw a line through these points and that is the graph you need. Again you can also find additional points by assuming values for x and solving for corresponding values of y. Then plot the (x,y) points. When you get done the graph should look like: . . The final problem gives you a slope of -3/4 and a y-intercept of 8. The equation for this is: . y = -(3/4)x + 8 . Mark +8 on the y-axis. Then go horizontally to the right from that point 1 unit followed by going vertically down 3/4 of a unit. Mark that point. (or you can go horizontally to the right 4 units from the point on the y-axis and then go vertically down 3 units). You can also substitute values for x into the equation and find corresponding values of y to give you more points on the graph. When you get done, your graph should look like: . . Hope this helps you to understand the slope-intercept form a little better.
 Travel_Word_Problems/86400: This question is from textbook prealgebra Solve: A ski lift has a seat suspended from a wire above. Three skiers with masses of 70 kilograms, 82 kilograms, and 20 kilograms are riding the lift. The seat itself has a mass of 17 kilograms. What is the total force exerted on the wire above?1 solutions Answer 62751 by bucky(2189)   on 2007-06-28 06:25:06 (Show Source): You can put this solution on YOUR website!Force is defined as mass times acceleration. And in SI units, mass is in units of kilograms and a generally accepted figure for the force of gravity is 9.8 meters per second^2. . In this problem, the total mass acting on the wire is 70 + 82 + 20 + 17 = 189 kilograms. . Substituting this and the acceleration due to gravity into the Force equation results in: . F = m*a = 189 * 9.8 = 1852.2 kg/m/sec^2 . and since a Newton is equal to a kg/m/sec^2, the answer is . 1852.2 Newtons . Hope this helps you to understand the relationship between mass (kilograms) and Force (Newtons).
 Polynomials-and-rational-expressions/86529: aimplify 3 over 4 over 4 over 5 A)16 over 15 B) 15 over 16 C)5 over 3 D)3 over 51 solutions Answer 62750 by bucky(2189)   on 2007-06-28 05:52:58 (Show Source): You can put this solution on YOUR website!Given: . divided by . To divide by a fraction you can invert that divisor and multiply it times the dividend. Therefore, this division problem converts to the multiplication of the dividend by the inverted divisor which is now ... . . Just multiply the terms in the two numerators to get the resulting numerator, and also multiply the terms in the two denominators to get the resulting denominator. This makes the problem become: . . So the correct answer is B ... .
 Polynomials-and-rational-expressions/86530: divide 2x-6 over 21 divided by 5x-15 over 121 solutions Answer 62747 by bucky(2189)   on 2007-06-28 04:38:46 (Show Source): You can put this solution on YOUR website!Given: . . Divide it by: . . Recall the "arithmetic" rule about fractions. If you are dividing by a fraction you can invert the divisor and multiply it by the dividend. In this case it means you can take and multiply it by the inversion of to get the answer to this problem. After the inversion, the original division problem is converted to the following multiplication problem: . . Before it gets too complicated, let's do some factoring. Note that: . factors to and factors to and factors to and factors to . Substitute all these factored forms into the appropriate places in the multiplication problem and it becomes: . . Cancel all the terms that appear in the numerator with a corresponding appearance in the denominator as follows: . . The remaining factors in the numerator are 4 and 2. They multiply out to 8. And the remaining factors in the denominator are 7 and 5 and they multiply out to 35. This makes the answer: . and there are no more common factors in the numerator and the denominator. So this cannot be reduced further and the answer to the original problem is . Hope this helps you to understand the division process in this problem. .
 Exponents-negative-and-fractional/86680: add or subtract as indicated. x/x+4-36/x^2-x-201 solutions Answer 62746 by bucky(2189)   on 2007-06-28 03:23:58 (Show Source): You can put this solution on YOUR website!Given: . . Subtract . Notice first that factors into . Substitute the factored form into the problem, and the problem becomes: . . Next, create a common denominator in the two terms by multiplying the first term by which is equivalent to multiplying by 1 because the numerator of this multiplier is the same as the denominator. This multiplication makes the problem become: . . and this simplifies to: . . The numerator of the first term multiplies out to . Substituting this into the polynomial makes it become: . . Now since the two terms have the same denominator, they can be combined by just subtracting the two numerators and putting that result over the common denominator. This results in: . . Now notice that the numerator factors into . Substitute this for the numerator and the result is: . . Cancel the like terms in the numerator and denominator: . . and this reduces to the form: . . This is the answer you are looking for. Hope this helps you to understand the problem and how to work it through to an answer. .
 Quadratic_Equations/86672: square root of 144 + 3[8+7(2-3)]= I can't seem to get the right answer which is 151 solutions Answer 62682 by bucky(2189)   on 2007-06-27 14:57:12 (Show Source): You can put this solution on YOUR website!Given: . . Find y . First you can do . Substitute this and the equation becomes: . . Now start with the most nested (the interior) set of parentheses. These are the parentheses that contain 2 - 3. Since 2 - 3 = -1 we can substitute this and the equation becomes: . . Then multiply 7 times the -1 and get -7. Substitute -7 for 7(-1) and the equation then becomes: . . Then subtract 7 from 8 to get +1. Substitute +1 for the parentheses and you have: . . Multiply 3 times +1 and the equation is reduced to: . . and the answer (y) is equal to 12 + 3 and this is +15 . Hope this explains where the answer came from.
 Functions/86661: Help I can't seem to understan algebra no matter how hard I try. Please help me learn to figure out this problem 5x + 41 = -4 Incorrect 1 solutions Answer 62680 by bucky(2189)   on 2007-06-27 14:35:19 (Show Source): You can put this solution on YOUR website!Given: . 5x + 41 = -4 . The problem asks you to solve for x. . The first basic rule is whatever you do to one side of this equation (add, subtract, multiply, divide, square, square root ... and so on), you must also do to the other side or else you "upset" the balance of the equation. . The process of solving equations like this one involves four steps ... . (1) get the term or terms containing the unknown alone on one side of the equal sign. (2) get all the number terms on the other side of the equal sign (3) combine the like terms on their sides (4) divide by the multiplier of x . Let's apply the process one step at a time: . First we need to get all the terms containing "x" on one side. Hmmm. There is only one term containing "x" and it's on the left side. So we're OK there. . Next we need to get rid of the +41 on the left side so the "x" term is left by itself on the left side. Do that by subtracting 41 from the left side. But when you do that, don't forget the rule. If you subtract 41 from the left side, you must also subtract 41 from the right side. This subtraction is: . 5x + 41 - 41 = -4 - 41 . On the left side the +41 and the -41 cancel each other. As a result, the equation becomes: . 5x = -4 - 41 . On the right side the -4 and the -41 are like terms that combine to give -45. So the equation is now reduced to: . 5x = -45 . Now you do the last step. You see that 5 times the unknown equals - 45. To find 1 times the unknown (1x or just x) you divide both sides by the multiplier of x which is 5. Dividing both sides by 5 (remember the rule ... divide one side by 5 and you must also divide the other side by 5) and you get: . 5x/5 = -45/5 . and this simplifies to just: . x = -9 . You can check this answer by going back to the original given equation and substituting -9 for x to see if the equation balances. The original equation was: . 5x + 41 = -4 . Substitute -9 for x and you get: . 5*(-9) + 41 = - 4 . Do the multiplication 5*(-45) and the equation becomes: . -45 + 41 = -4 . The terms on the left side (-45 and + 41) combine to give you -4 and this makes the equation: . -4 = -4 . And since both sides are equal, the equation balances and the answer of x = -9 is correct. . Hope this helps you with your understanding of how to do equations of this sort.