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

 Equations/650306: Hi, I am able to answer the first part of the question, but am confused with how to describe the line in terms of it's relationship to the x and y axes. Please can you help me understand? Thank you. Write the equation of the line that passes through (-4,5) with slope equal to zero. y-5=0(x-(-4)) y-5=0 y=5 Describe this line in terms of its relationship to the x and y axes.1 solutions Answer 407449 by bucky(2189)   on 2012-09-13 13:24:59 (Show Source): You can put this solution on YOUR website!You correctly solved the first part of the problem. Your answer tells you that this equation: . y - 5 = 0(x - (-4)) . will always be true if y = +5 because when you substitute +5 for y this equation becomes: . 0 = 0(x - (-4)) . which reduces to: . 0 = 0 . Notice that it does not matter what value you assign to x. x could be -100, +50, or any other value you choose. As long as y is +5, the slope of the graph of this equation will be zero. . How does this translate to a graph? Any time that you are told that a line has a slope of zero, you can immediately say that it's graph is a horizontal line because its value of y never changes as you move to the right along the x-axis. . In this problem, you calculated that the unchanging value of y is +5. Therefore, you can describe the graph as being horizontal (parallel to the x-axis) and crossing the y-axis at +5. In picture form: . . The horizontal red line above the x-axis is the graph of a line having a zero slope and a y value of +5. Note that on the x-axis at the point where x equals -4, the corresponding value of y as shown by the graph is +5, so the two original constraints (a zero slope graph having the x,y point (-4,5) on the line) are both satisfied. . Hope this helps.
 Triangles/633396: What is the area of a right triangle with a hypotenuse measuring 5 inches and a base measuring 4 inches? 1 solutions Answer 399514 by bucky(2189)   on 2012-08-03 07:53:07 (Show Source): You can put this solution on YOUR website!This is a very common size for a right triangle. If a right triangle has a hypotenuse of 5 and one of its legs is 4, then the other leg is 3. Other than knowing this, you can find the unknown leg by using the Pythagorean theorem. It says that the square of the hypotenuse (in this case 5) equals the sum of the squares of the two legs. One of the legs in this case is known to be 4 and the other leg is unknown. Call this unknown leg A. So we can write: . . Square the two numbers and this equation becomes: . . Subtract 16 from both sides of the equation to reduce it to: . . Solve for A by taking the square root of both sides and you have: . . So now you know all three sides are 3, 4, and 5 in which the hypotenuse (or longest side) is 5. . This means that the base (given in the problem) is 4 and the perpendicular to it (the altitude in a right triangle) is the leg that you found to be 3. . The area of a triangle is 1/2 times the base times the altitude. So the area of this triangle is: . . Find the area by multiplying the three numbers on the right side to get: . . And don't forget to add the units of square inches since the problem said that the two given sides in the triangle had units of inches. . Hope this helps you to understand the problem. .
 Travel_Word_Problems/632549: How long would it take me to go 18 miles at 72 mph? 1 solutions Answer 398933 by bucky(2189)   on 2012-07-31 13:02:50 (Show Source): You can put this solution on YOUR website!The equation that applies to this problem is: . Distance = Speed * Time . The first thing to do is to ensure that the units are consistent. In this problem the distance you are given is in "miles" and the speed also involves "miles". This means that you do not have to make any changes or conversionss to get the units to agree. Then since the speed involves "hours", the answer for the time will also have the unit "hours". . Just substitute 18 for the distance in the equation and 72 for the speed to get: . 18 = 72*Time . Solve for Time by dividing both sides of this equation by 72: . 18/72 = (72/72)* Time . The 72/72 is just 1. This reduces the equation to: . 18/72 = Time . The fraction on the left side of this equation can be reduced by either dividing 72 into 18 to get 0.25 (which is equal to 1/4) or by replacing 72 by its equivalent value of 18*4. In the latter case this makes the equation become: . 18/(18*4) = Time . Then cancel the 18 in the numerator with the 18 in the denominator and this reduces the equation to: . 1/4 = Time . And the units is hours. So the answer is: . Time = 1/4 hours . or in an equivalent form: . Time = 0.25 hours . At a speed of 72 mph, you go 18 miles in a-quarter of an hour (which is 15 minutes). . Hope this helps you to understand the problem a little better. .
 Linear-equations/631699: eveluate the expression for the given values or x and y x=2 y=3 5xy1 solutions Answer 397766 by bucky(2189)   on 2012-07-25 06:56:57 (Show Source): You can put this solution on YOUR website!The expression you are given is 5xy, and this means 5 times x times y. . To evaluate the expression for x = 2 and y = 3, just substitute 2 for x and 3 for y in the expression. When you make those substitutions you get: . 5 times 2 times 3 . 5 times 2 is 10 and then you multiply that by 3 to get the answer 30. . So you can say that when x 2 and y = 3, then 5xy = 30 . Hope this helps you to understand this problem.
 Equations/631609: Solve sysyem of three equations 3x+4y+z=14 2y+7z=24 -2y+3z=5 please show all work1 solutions Answer 397764 by bucky(2189)   on 2012-07-25 06:45:19 (Show Source): You can put this solution on YOUR website!Given the following three equations to solve simultaneously: . (A) 3x + 4y + z = 14 (B) .. + 2y + 7z = 24 (C) .. - 2y + 3z = 5 . Begin by adding equations B and C vertically. Note that the + 2y and the - 2y cancel each other out. The + 7z and the + 3z add to give + 10z and on the other side of the equal sign the 24 and 5 add up to 29. So the result of adding these two equations is the new equation: . 10z = 29 . Solve this new equation for z by dividing both sides by 10 to get: . z = 29/10 = 2.9 . Since you now know that z = 2.9, you can return to either equation B or equation C and, after substituting 2.9 for z, you can solve for y. Go to equation B and substitute 2.9 for z to get: . 2y + 7*2.9 = 24 . Multiply out the 7 times 2.9 to get 20.3 and the equation becomes: . 2y + 20.3 = 24 . Subtract 20.3 from both sides of this equation and you are left with: . 2y = 3.7 . Solve for y by dividing both sides of this equation by 2 to get: . y = 3.7/2 = 1.85 . Now you know that z = 2.9 and y = 1.85. Equation A is the only equation that has a term containing x. So you next go to equation A and substitute 2.9 for z and 1.85 for y to get: . 3x + 4(1.85) + 2.9 = 14 . Multiply the 4 times 1.85 and the equation becomes: . 3x + 7.4 + 2.9 = 14 . Add the two numbers on the left side: . 3x + 10.3 = 14 . Subtract 10.3 from both sides: . 3x = 3.7 . Solve for x by dividing both sides by 3 to get: . x = 3.7/3 = 1.23333333... . So the values of x, y, and z that satisfy all three of the given equations simultaneously are x = 1.23333333..., y = 1.85, and z = 2.9 . Hope this helps you to understand the problem a little better. Check my work to ensure that it has no errors. You can also practice a little by using 2.9 for z and substituting that value into equation C. Then solve for y and see if you again get 1.85 for y just as you did by substituting 2.9 into equation B above.
 Polynomials-and-rational-expressions/622641: Please help! Divide. 1 solutions Answer 391497 by bucky(2189)   on 2012-06-21 02:15:33 (Show Source): You can put this solution on YOUR website!Given to divide: . . Note that this is one great big fraction. The numerator is: . . and the denominator is: . . So you are dividing the numerator by the denominator. Remember the rule for dividing by a fraction ... namely that you can divide by a fraction by inverting the fractional divisor and then multiplying that inverted fraction by the number you are dividing into. . When you invert the denominator you get: . . Now multiply that inverted fraction times the numerator and you have: . . Note that the denominator of the first fraction is and it will divide into the numerator of the second fraction to give just 2. This reduces the problem to: . . Next note that the denominator of the second fraction can be factored by 9 to give: . . Then the numerator of the first fraction can be factored by 3 to result in: . . So you have a (y+4) factor in the numerator and a (y+4) factor in the denominator. These cancel out and you are left with: . . which after multiplication gives: . . and 6 divided by 9 is equal to . and that is the answer to this problem. . I hope this helps you to see your way through this problem .
 Quadratic_Equations/622630: Solve the equation by factorisation method x^2+(x+2)^2=650 I attempted the question but I am stuck at this step x^2+x^2+4-650=0 2x^2-646=01 solutions Answer 391487 by bucky(2189)   on 2012-06-21 01:31:23 (Show Source): You can put this solution on YOUR website!Given to solve by factoring: . . First, square the terms in the parentheses by multiplying: . . When you do this multiplication you get: . . Substitute this into the original problem in place of and the problem then becomes: . . Combine the two x-squared terms to get: . . Subtract 650 from both sides and you have: . . You can simplify this a little by dividing both sides (all terms) by 2 to get: . . Now you can do the factoring process. The negative sign on the 323 tells you that you will have one positive factor and one negative factor whose product gives you negative 323. The coefficient of the x term is +2. This tells you that the positive factor must be bigger than the negative factor by 2. . Now you can make some educated guesses. If the two factors were +20 and -18, their product would be (you can do this in your head) -360. You need two numbers whose product is -323, so you are pretty close, but the factors you guessed are a little too big because they give a product of -360. How about trying +18 and -16. The product of these two numbers is -288 and since this is smaller that -323, you need two bigger numbers. If you now try +19 and -17, you will find that their product is -323, just as you need it to be. So you know that the product of the two factors is: . . and if you set these equal to zero as above you have: . . Notice that this equation will be true if either of the factors equals zero. So you can set both factors equal to zero and solve for x to get: . . and solve for x to get x = -19 . Then: . . and solve for x to get x = +17 . Those are the two solutions for x in the equation: . . You can check the solutions by first substituting -19 for x and you have: . . When you square -19 you get +361. and when you add -19 and +2 in the parentheses you get -17. Then square that and you have get +289. Substituting these values into the equation gives: . . And if you add the terms on the left side you find that the equation balances, so x = -19 works. . You can do the same kind of analysis for the second answer. Go back to the original equation and substitute +17 for x and you find that it also checks out. . Hope this helps you see where you went slightly off track and lets you see how the answers can be found. .
 Radicals/614338: Solve. sq.root(x^2 - 9) = 41 solutions Answer 386988 by bucky(2189)   on 2012-05-27 07:41:59 (Show Source): You can put this solution on YOUR website!Given to solve: . . Square both sides to get: . . add 9 to both sides to get rid of the -9 on the left side: . . Take the square root of both sides to get the two answers: . and . You can check these two answers by returning to the original equation of: . . and first substituting +5 for x to get: . . Square the 5 and this equation becomes: . . Do the subtraction on the left side to get: . . 4 is the square root of 16, so this equation reduces to: . . And since this is true, we know that if x = +5, the equation works and therefore +5 is a solution. . Next, return to the original equation of: . . and this time substitute -5 for x to get: . . Square the -5 to again get +25 and this equation becomes: . . Just like last time do the subtraction on the left side to get: . . Again, 4 is the square root of 16, so this equation reduces to: . . And since this is true, we know that if x = -5, the equation works and therefore -5 is also a solution. . Hope this helps you to understand the problem a little more and you can see how to solve and check a problem such as this one. .
 test/614778: How to work out equation 4(m-3)=m+6 ?1 solutions Answer 386708 by bucky(2189)   on 2012-05-25 08:48:21 (Show Source): You can put this solution on YOUR website!The general idea of solving linear equations such as this one is to do what is necessary to get the unknown variable on the left side of the equal sign and the numbers on the right side. Looking at the problem you are given should tell you that you have to do a little work to do that. . First, note that on the left side you have a distributed multiplication, so you need to multiply that out. Do this multiplication by multiplying the 4 times each of the terms in the parentheses. 4 times m is 4m and 4 times -3 is -12. So after the multiplication, the equation becomes: . 4m - 12 = m + 6 . Now we are ready to collect all the terms containing m on the left side of the equal sign and all the numbers on the right side. Remember that whatever we do to one side of an equation we must also do to the other side to keep the equality unchanged. . Let's get rid of the m on the right side by subtracting m on the right side. But if we do that we must also subtract an m from the left side. This subtraction results in: . 4m - m - 12 = m - m + 6 . On the left side the 4m - m results in 3m and on the right side the m - m results in zero, meaning that the m is gone on the right side. So our equation is then: . 3m - 12 = 6 . Now let's get rid of the -12 on the left side. We can do that by adding +12 to the left side, but then we must also add +12 to the right side: . 3m - 12 + 12 = 6 + 12 . On the left side the -12 and the + 12 add to zero, so the -12 has disappeared from the left side. On the right side the 6 + 12 adds to 18. What's left is: . 3m = 18 . Finally, our goal is to solve for m. On the left side we have 3m and we can make that just m if we divide the left side by 3. But to do that we must also divide the right side by 3. This is shown as follows: . 3m/3 = 18/3 . And when we do these divisions we get the answer: . m = 6 . That's the answer to the problem. We can check it by returning to the original problem and substituting 6 for m as follows: . 4(m - 3) = m + 6 . Now let m be 6: . 4(6 - 3) = 6 + 6 . Do the subtraction in the parentheses of 6 - 3 which gives 3: . 4(3) = 6 + 6 . Multiply out the left side (4 times 3 is 12) and do the addition on the right side ( 6 + 6 = 12). This results in: . 12 = 12 . And since the left side and right side are both 12 when m is 6, we know we have solved the problem correctly. . When m equals 6 the equation is equal on both sides. . Hope this helps you to have a little better understanding of what can be done to solve equations such as this. .
 Linear-systems/614383: A company produces a product which it sells for \$55 per unit.each unit cost the firm \$23 in variable expenses,and fixed costs on an annual basis are \$400,000. if x equals the number of units produced and sold during the year: (a) formulate the linear total cost function. (b)formulate the linear total revenue function. (c)formulate the linear profit function. 1 solutions Answer 386539 by bucky(2189)   on 2012-05-24 08:51:31 (Show Source): You can put this solution on YOUR website!Let's define: . For part (a) the annual linear total cost function as C(x) For part (b) the annual linear total revenue function as R(x) and For part (c) the annual linear profit function as P(x) . In part a, the cost of production will increase by \$23 for each unit that is produced. So to find the cost for the units produced, you just multiply the cost per unit times the number of units that are made. That is \$23 times x or just 23x. But the total cost also includes the annual fixed costs of \$400,000 probably consisting of taxes on the property, average annual building maintenance costs, average annual utility costs, and other similar costs that are incurred whether or not you produce any products. The total annual costs are the sum of these two. So we write the annual cost function in dollars as follows: . C(x) = 23x + 400,000 . That's the answer to part (a) . For part (b) the total annual revenue function is the entire amount of money that the company receives for selling units of the product during the year. Since the selling price is is \$55 per unit, and the company sells x units during the year, the total revenue for the year is \$55 times x. We can express this as follows: . R(x) = 55x . and that's the answer to part (b) . But all the revenue is not profit. The profit is found by subtracting from the income (total revenue) the cost of production. In other words the annual profits is calculated from: . P(x) = R(x) - C(x) . But we now know what R(x) and C(x) are and we can substitute those relationships into this equation as follows: . P(x) = 55x - (23x + 400,000) . Since the parentheses are preceded by a minus sign, we can remove them if we change the signs of each of the terms within the parentheses. This makes the equation become: . P(x) = 55x - 23x - 400,000 . We can then combine the 55x and -23x to get 32x and the equation is then: . P(x) = 32x - 400,000 . And that's the answer to part (c) . Just as an interesting exercise, we weren't asked but we might want to find how many units the company has to sell each year, just to break even. By breaking even we mean that the company neither loses nor makes any money for the year. At this point the profit would be zero. So we can go to the profit equation and set P(x) equal to zero. The equation then becomes: . 0 = 32x - 400,000 . Subtract 32x from both sides and you have: . -32x = -400,000 . Solve for x by dividing both sides by -32 and you get: . x = -400,000/-32 = 12,500 . This means that unless the company sells 12,500 units in a year, it will lose money. Selling more than 12,500 units will make the company profitable. Hope this helps you to understand the problem and how it can be worked.
 �t�e�s�t/612381: which of the following is equal to 5.93 x 10 exponent negative -2 a 0.0593 b 0.00593 c 593 d 5930 e 59300 i need to solce it but i dont know1 solutions Answer 385387 by bucky(2189)   on 2012-05-18 06:47:16 (Show Source): You can put this solution on YOUR website!The fact that the exponent on the 10 is NEGATIVE tells you to move the decimal point to the LEFT. The fact that the exponent is 2 tells you to move the decimal point two places. So combined, this means that the decimal point gets moved two places to the left. . So start with 5.93 . After you move the decimal point to the left one place you would have 0.593. Then you have to move the decimal point to the left again so that you have moved it a total of 2 places to the left. When you do that you have 0.0593. . And that's the answer ... answer (a) in your answer list. . In summary, when the exponent on the 10 is negative, move the decimal point that many places to the left. If the exponent on the 10 is positive, move the decimal point that many places to the right. . Hope this helps to clear things up for you. .
 sets-and-operations/612378: I invested 50 000 more in teachers' cooperation than in home owners' cooperative. If my total investments in the two cooperatives is 110 000, how much is my investment in each?1 solutions Answer 385386 by bucky(2189)   on 2012-05-18 06:32:10 (Show Source): You can put this solution on YOUR website!Let x represent the unknown amount invested in the home owners' cooperative. . Since 50 000 more is invested in the teachers' cooperative, we can write that the investment in the teachers' cooperative is x + 50 000 , The sum of these two investments is: . x + x + 50 000 and adding the two x terms results in a total of 2x + 50 000 . But the problem tells you that the sum of the two investments is 110 000. Therefore, we can write the equation: . 2x + 50 000 = 110 000 . To solve this for x we can first eliminate the 50 000 on the left side by subtracting 50 000 from both sides to get: . 2x = 60 000 . Now we can solve for x by dividing both sides of this equation by 2 to get: . x = 30 000 . Since we chose x to represent the amount invested in the home owners' cooperative, we know that we have 30 000 in it. And since 50 000 more was invested in the teachers' cooperative we know that we have invested 30 000 plus 50 000 for a total of 80 000 in the teachers cooperative. . And as a check, the total of 30 000 in the home owners' cooperative plus the 80 000 in the teachers' cooperative does add up to the total 110 000 that we have invested all together. . I hope this helps you to understand the problem and how you can solve it. .
 Functions/612203: If the the function is C(g)= 3.03 (g) What is C(2)? What is C(a)? How do you solve this?1 solutions Answer 385316 by bucky(2189)   on 2012-05-17 19:29:32 (Show Source): You can put this solution on YOUR website!All these two problems are telling you to do is to replace the variable in the function with the quantity in the parentheses. . So for C(2) just replace g with 2. . Start with C(g) = 3.03(g) . For the first problem replace every g with 2. When you do that you get the equation: . C(2) = 3.03(2) . Multiply out the right side by multiplying 3.03 times 2 and the result is: . C(2) = 6.06 .... that's the first answer. . For the second problem, follow the same process, but replace every g with "a" . Again start with C(g) = 3.03(g) . Replace every g with a to get: . C(a) = 3.03(a) . And that's the answer to the second problem you were given. . Pretty easy once you understand what the problem is asking you to do. . Hope this helps.