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 'Earlsdon'

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 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299, >>Next

 Graphs/24796: I haven't taken algebra in 4 years I just need help refreshing. The problem says to find the center and the radius of the graph of the circle. 9x^2+9y^2-6y-17=01 solutions Answer 13237 by Earlsdon(6294)   on 2006-01-18 15:39:04 (Show Source): You can put this solution on YOUR website!First, you need to put your equation into the standard form for a circle with centre at (h, k) and radius r. To accomplish this, you will need to "complete the square" in the y-terms. The x-term is already squared so it does not need to be changed. Here are the steps: 1) Add 17 to both sides of the equation. 2) Divide through by 9. 3) Complete the square in the y-terms by adding the square of half the y-coefficient (that's ) to both sides of the equation. 4) Simplify and factor the y-group. 5) Rewrite the x-term as 6) Compare this with the standard form: 7) You can see that the centre: (h, k) is (0, 1/3) and the radius, r, is
 Complex_Numbers/24681: I AM SUPOSED TO USE i for this but the teacher did not explain how x^2=-16 8x^2=-2 x^2=-30 please help thank you for your time1 solutions Answer 13162 by Earlsdon(6294)   on 2006-01-17 18:11:36 (Show Source): You can put this solution on YOUR website!Your teacher must have explained to you that i (for imaginary) is the symbol used to represent, so: Take the square root of both sides. x = + or - Simplify. x = +or- x = +or- x = +or-4i The other problems are handled in a similar fashion.
 Linear-systems/24598: Would someone please tell me if this is correct?! Thank You! 9x^2-4y^2 Is this Prime Factorized???1 solutions Answer 13110 by Earlsdon(6294)   on 2006-01-16 21:22:36 (Show Source): You can put this solution on YOUR website!No, it isn't! Factor: Notice that this the difference of two squares and it can be factored.
 Polynomials-and-rational-expressions/24601: How do you factor an expression when the last constant is more than one number greater than the middle constant? as in 16m(sq)-24mn+9n(sq)1 solutions Answer 13100 by Earlsdon(6294)   on 2006-01-16 20:39:16 (Show Source): You can put this solution on YOUR website!You can start by trying this: Factor: Notice that the first term and the last term are perfect squares, so try taking the square root of these as factors: Use FOIL to check: = The answer is:
 Bodies-in-space/24616: find the surface area of a cone with a radius of 3 inches and a slant height of 5 inches.1 solutions Answer 13098 by Earlsdon(6294)   on 2006-01-16 20:14:52 (Show Source): You can put this solution on YOUR website!The surface area of a right circular cone is given by: Where: R is the radius and s is the slant height. square inches. If you use , then, square inches. If you include the area of the base, then you add: Total surface area: If , then, square inches.
 Quadratic_Equations/24543: suppose you throw a basebal straight up at a velocity of 64 ft per second.A funtion can be created by expressing distance above the ground, s , as a function of time, t. this function is (< 16 represents 1/2 g,gravitational pull in ft per second^2. v0is the inital velocity in ft per second so is intial distance above ground in ft. if you are stading on the ground , then s0= zero. what is the function descibing this problem? how high above the ground will the ball be after one sec? how long will it take to hit the ground? what is the maximum height and time attained by the ball? 1 solutions Answer 13085 by Earlsdon(6294)   on 2006-01-16 15:30:34 (Show Source): You can put this solution on YOUR website!Hmmm...I think I have answered this one previously. Anyway, here it is again. The equation is correct: This is the function describing the problem. In words, the height (s) is a quadratic function of time (t) with initial velocity of 64 ft/sec and an initial height of zero. After 1 second (t=1), the height of the baseball will be: The height will be 48 feet after 1 second. Find when the baseball will hit the ground (s=0) by setting the function s(t) = 0 and solving for t. Factor out a t. Divide both sides by t. Subtract 64 from both sides. Divide both sides by -16 The baseball will return to ground in 4 seconds. The maximum height and time is found by finding the location of the vertex of this parabola. Since the parabola opens downward, the vertex will be at the maximum point of the vertex and will represent the maximum height attained by the baseball. The x-coordinate (or, in this problem, the t-coordinate) is given by: The a and b come from the standard form of the quadratic equation: In this case, a = -16, b = 64, and c = 0 The maximum height of the baseball will be attained in 2 seconds. To find this maximum eight, substitute t=2 into the original function and solve for s. The maximum height attained by the baseball is 64 feet.
 Linear-systems/24552: Solve for x in the expression: - ( 1/x ) – 5 = 0; Show your recheck. I'm not sure what to do with the -(1/x)?1 solutions Answer 13082 by Earlsdon(6294)   on 2006-01-16 14:56:45 (Show Source): You can put this solution on YOUR website!First of all, this is an "equation" rather than an "expression". Remember, equations have equal signs while expressions do not. On to your problem! Solve: First, add 5 to both sides of the equation. Now multiply both sides by x. Finally, divide both sides by 5. Check: Substitute -1/5 for x in the original equation. Simplify.
 Functions/24562: Given that g(x)=3x^2-2x+1, find each of the following: g(0) g(3) g(1-t) g(-1) g(-x) I haven't been in Algebra in 13 years. The teacher suggested that I go back to basic, but I am determined to pass this class. I appreciate any help you can provide.1 solutions Answer 13080 by Earlsdon(6294)   on 2006-01-16 14:44:35 (Show Source): You can put this solution on YOUR website!If you are given: and are asked to find g(0), you simply replace every x in the original function with 0, thus: Simplify. ...it's just that easy. One more Simplify.
 Polynomials-and-rational-expressions/24564: Factoring Polynomials. I had a horrible Algebra II teacher last year and learned almost nothing that i was supposed to because of it. I dont think I am very good at factoring. This is for College Algebra. I am dually enrolled in high school and a community college. The directions say to factor out, relative to the integers, all factors common to all terms. The problem is.. 2w(y-2z)-y(y-2Z) I went ahead and simplified the problem, believing that to be the right thing to do. I got..2wy-4wz-y^2+2yz The answer is..(2w-x)(y-2z) Thank you so much. I absolutely must learn this stuff. Any correct explanation will be taken to heart.1 solutions Answer 13078 by Earlsdon(6294)   on 2006-01-16 14:28:42 (Show Source): You can put this solution on YOUR website!Well, your answer is almost correct...except for a small typo. You have an x in the answer when there is no x in the original expression. Here are the steps: Factor: It is not neccesary to simplify as you did because, if you look at the expression, you will see that each term has a common factor of (y-2z) and this, of course, can be factored out. ...and there you have it!
 Quadratic_Equations/24566: Please show me step by step how to solve the following quadratic equation: (x-6)^2 = 10 Thanks1 solutions Answer 13077 by Earlsdon(6294)   on 2006-01-16 14:17:47 (Show Source): You can put this solution on YOUR website!Since the equation is already in factored form, you can start by taking the square root of both sides. Take the square root of both sides. with a + or - in front of the sq.rt. sign. Next, add 6 to both sides.
 Equations/24560: I am having difficulty with 2 step equations reading the wording and then translating it to numbers. question: The difference of 8 and the quotient of a number and 6 is 9. this is what I tried x divided by 8 +6=9 and my answer was x=24 am I correct thanks in advance Dave H. 1 solutions Answer 13076 by Earlsdon(6294)   on 2006-01-16 13:58:13 (Show Source): You can put this solution on YOUR website!Let's try again. The difference (means subtraction) of 8 and the quotient (means divide) of a number (x) and 6 (x/6) is (=) 9. In algebrese: Subtract 8 from both sides of the equation. Multiply both sides by -6. Check: =
 Quadratic-relations-and-conic-sections/24555: what is the center of the circle x^2 + 4x + y^2 + 2y - 9 = 0?1 solutions Answer 13072 by Earlsdon(6294)   on 2006-01-16 12:00:15 (Show Source): You can put this solution on YOUR website!Find the centre of the circle: First get your equation into the standard form for a circle. You can do this by "completing the square" in the x-terms and in the y-terms. Complete the square in the x- and y-terms by adding the square of half the x-, y-coefficients to both sides of the equation. Factor and Simplify. Add 9 to both sides. Now compare this with the standard form for a circle with centre at (h, k). You can see that the centre of the circle is at (-2, -1)
 Triangles/24532: PLEASE HELP WITH THIS TOO! In a certain triangle, the first angle measures 9 degrees less than the second angle. The third angle measures 3 degrees more than the second angle. Find the measures of all three angles. I can solve this if I have the degrees of two sides, but this doesn't give any. I thought I should let x=second angle, x-9=first angle, and x+3=third angle but I didn't know where to go from there(or if that was the way to start) THIS IS DUE BY 01/17/06. THANKS FOR YOUR TIME!1 solutions Answer 13053 by Earlsdon(6294)   on 2006-01-15 23:24:18 (Show Source): You can put this solution on YOUR website!Let the first angle be A, the second angle be B and the third angle be C. From the problem description, you can write: A = B-9 C = B+3 And you already know (or should know) that for any plane triangle: A+B+C = 180 degrees. So, in A+B+C = 180, substitute for A and C the first two equations: (B-9) + B + (B+3) = 180 Simplify and solve for B. 3B - 6 = 180 Add 6 to both sides of the equation. 3B = 186 Divide both sides by 3. B = 62 A = B-9 A = 62-9 = 53 C = B+3 C = 62+3 = 65. The three angles are: A = 53 degrees. B = 62 degrees. C = 65 degrees.
 Mixture_Word_Problems/24528: I set up a table for this question, but the numbers I got were too big to be right. Here is the problem: A candy mix is being prepared by mixing candy that is worth \$12 per pound with candy that is worth \$15 per pound. The candy store wants to have 120 pounds of this mixture which will sell for \$13.75 per pound. How many pounds of each type of candy should be used? Find the number of pounds @\$12 and @\$15. I made a table with x and y representing the # of lbs. With 120lbs. as the total. 12 and 15 as the price per pound and 13.75 for the total price per pound. In the third boxes of my table I wrote 12x, 15x, and 120(13.75)=1650. Then I wrote the equation: 12x+15y=1650 (here is where I get lost) I then did: 12(120-y)+y=1650 = 1440-12y+y=1650 = 1440-11y=1650 I subtracted 1440 from both sides to isolate the variable and came up with: -11y=210 then I divided -11y and 210 by -11= y= -19.09 and then I solved for x by: 120-19.09= 100.91 x=100.91!!!! I KNOW THIS IS TOTALLY WRONG, BUT THERE IS NOT ANYTHING IN MY TEXT BOOK TO SHOW ME HOW TO SOLVE THIS PROBLEM!!!! PLEASE HELP!! THIS HOMEWORK IS DUE BY 01/17/06 HELP WILL BE GREATLY APPRECIATED! :)1 solutions Answer 13052 by Earlsdon(6294)   on 2006-01-15 23:11:27 (Show Source): You can put this solution on YOUR website!Try this: Let x = the required number of pounds at \$12.00 a pound (12x), then (120-x) = the number of pounds at \$15.00 a pound 15(120-x). The sum of these are to equal 120 pounds at \$13.75 a pound (120(13.75). Let's set up the equation to find x. Simplify and solve for x. Combine like-terms. Add 3x to both sides of the equation. Subtract 1650 from both sides. Now divide both sides by 3. The candy store will have to mix 50 pounds of \$12.00 candy with 120-50= 70 pounds of \$15.00 candy to obtain 120 pounds of \$13.75 candy.
 Quadratic_Equations/24521: Please show me how to solve this problem by completing the square. 1 solutions Answer 13051 by Earlsdon(6294)   on 2006-01-15 22:54:55 (Show Source): You can put this solution on YOUR website!Well, it looks like you were on the right track! Solve by completing the square: First divide through by 3. Now subtract 5/3 from both sides of the equation. Complete the square in the x-terms by adding the square of half the x-coefficient to both sides. Factor the left side and simplify. Take the square root of both sides. Add 3 to both sides.
 Linear-systems/24526: I am having trouble with this problem. SOLVE THIS SYSTEM OF EQUATIONS, WHEN POSSIBLE... x+y+z=4 x-y+2z=8 2x+y-z=3 I used the elimination method and broke this down into two equations with only two variables. I try to eliminate another variable, but cannot do it! HELP PLEASE!!1 solutions Answer 13050 by Earlsdon(6294)   on 2006-01-15 22:33:57 (Show Source): You can put this solution on YOUR website!Solve: 1) 2) 3) Add equations 1) and 2) to get: 4) Add equations 2) and 3) to get: 5) Multiply equation 5) by 3 to get: 6) Now subtract equation 4) from equation 6) to get: 7) Divide both sides by 7. Substitute this into equation 5) and solve for z. Subtract 9 from both sides. Finally, substitute x=3 and z=2 into equation 1) and solve for y. Subtract 5 from both sides. Solution: x = 3 y = -1 z = 2 Check by substituting these values into the three equations, 1), 2), and 3)
 Angles/24499: what is a complementary angles 1 solutions Answer 13048 by Earlsdon(6294)   on 2006-01-15 20:02:04 (Show Source): You can put this solution on YOUR website!The sum of two complementary angles equals 90 degrees.
 Percentage-and-ratio-word-problems/24500: I am struggling with this problem. Please help. Sam Barns worked as a waiter. He earned \$15,000 which he wants to invest. He invested a certian amount in a savings account that pays 5% simple intrest. He invested the balance in another account that pays 3.5% simple interest. The total amount on interest earned is \$600. How much did Sam invest at 5% and 3.5%. Thamks for any help you can give. 1 solutions Answer 13047 by Earlsdon(6294)   on 2006-01-15 19:59:17 (Show Source): You can put this solution on YOUR website!Let x = the amount Sam invested at 5%, then (\$15,000-x) = the amount invested at 3.5%. Change the percentages to their decimal equivalents and set up the equation to solve for x. Simplify and solve for x. Combine like-terms. Subtract 525 from both sides of the equation. Divide both sides by 0.015 Sam invested \$5,000 at 5% interest and \$15,000 - \$5,000 = \$10,000 at 3.5% interest.
 Rational-functions/24503: I can't get this problem, I have worked on it but i just cant get it. Simply each rational expression: 9x(squared)-15x+25 divided by 27x(cubed)+125 thanks for your help1 solutions Answer 13046 by Earlsdon(6294)   on 2006-01-15 19:44:06 (Show Source): You can put this solution on YOUR website!Simplify: Factor the denominator. This is the sum of two cubes. Cancel the like-terms in the top & bottom. This is the answer.
 Equations/24350: If possible I need help with the following problems. Thank you for your help. (5-6y)(3y²-y-7) and Office Space: The length of a professors office is x feet, and the width is x+4 feet. Write the polynomial that represents the area. Find the area if x=10ft 1 solutions Answer 13022 by Earlsdon(6294)   on 2006-01-14 21:43:27 (Show Source): You can put this solution on YOUR website!1) Multiply: = = 2) A = L*W But Length is x feet and Width = (x+4) feet, so: This is the polynomial. If x = 10 ft., then: sq.ft. This is the area.
 Linear_Algebra/24399: What is the factor of the number 6734?1 solutions Answer 13014 by Earlsdon(6294)   on 2006-01-14 14:45:21 (Show Source): You can put this solution on YOUR website!The number 6734 has many factors, including,: 1, 2, 7, 13, 14, 37, 182, 481, 518, 962, 3367, 6734 Which one do you want?
 Graphs/24437: I have an elimination question I hope some one could help me? x/2+2y=9 2x-y=18 thank you also if you have time could you help me with this graph Solve the following systems of equations by graphing: y=x^2-4 and y=x-2 this would be greatly appreciated.1 solutions Answer 13013 by Earlsdon(6294)   on 2006-01-14 14:05:18 (Show Source): You can put this solution on YOUR website!1) Solve by elimination: 1) Multiply this equation by 4 to get equation 1a) 2) 1a) Now subtract equation 2) from equation 1a)to eliminate x. ---------------- Divide both sides of the equation by 9. Now substitute this value of y into either of the two original equations and solve for x. Take the second equation. Add 2 to both sides. Divide both sides by 2. The solution is: (10, 2) Here's the graphical solution:
 Graphs/24435: I understand how to do these but for sme reason this one is giving me a problem could you please help? Use sustitution to solve: 2x+y=7 5x-2y=4 thank you1 solutions Answer 13012 by Earlsdon(6294)   on 2006-01-14 13:29:59 (Show Source): You can put this solution on YOUR website!Solve by substitution: 1) Write this in terms of y: 1a) and substitute into equation 2) then solve for x. 2) Simplify and solve for x. Add 14 to both sides of the equation. Divide both sides by 9. Now substitute this value of x into equation 1a) and solve for y. The solution is: (2, 3) Here's the graphical solution: Red line is: Green line is:
 Graphs/24428: this is my question: Determine whether the system has one solution,no solution, or many solutions: y=2/3x 2x-y=-4 could somebody please explain how to get the answer? Thank you.1 solutions Answer 13010 by Earlsdon(6294)   on 2006-01-14 11:17:40 (Show Source): You can put this solution on YOUR website!The first equation is ambiguous! Is it or ??? Let's assume that it is the first case. You can solve questions like this by graphing or algebraically. Let's look at the graphic solution: The red line is The green line is This is the 2nd equation written in terms of y. Now solve algebraically by substitution: 1) Substitute this equation for y in the second equation. 2) 2) Simplify and solve for x. Multiply both sides by the multiplicative inverse of 4/3 (that's 3/4) Now substitute this value of x into either one of the two original equations and solve for y. Take the first equation, There is only one solution, it is: (-3, -2) Compare this with the intersection point of the two lines on the graph. Now assume that the first equation is: and let's look at the graph: As you can see, there would be two solutions (points of intersection) in this case.
 Polynomials-and-rational-expressions/24416: The polynomial equation x(x^2+4)(x^2-x-6)=0. Has how many real roots? We are very rusty on our Algebra skills, and we are reviewing for a math placement exam, b/c we are returning back to college. Thanks, K 1 solutions Answer 12993 by Earlsdon(6294)   on 2006-01-13 20:45:17 (Show Source): You can put this solution on YOUR website!You can apply the zero product principle to this problem: If then either or or both. and/or and/or One of the real roots is x = 0 If then and x = +or- so these two roots are: x = 2i and x = -2i These are not real roots If then so and These two roots are real. The real roots are: x = 0 x = -2 x = 3
 Numbers_Word_Problems/24246: The sum of the squares of two consecutive positive even integers is 340. What are the integers? The answer should be in this form: 6 and 71 solutions Answer 12891 by Earlsdon(6294)   on 2006-01-11 22:04:11 (Show Source): You can put this solution on YOUR website!Let the first positive even integer = x, then the next consecutive positive even integer = (x+2) Simplify the left side. Subtract 340 from both sides of the equation. Factor a 2 from the left side. Factor the parentheses. Apply the zero product principle. and/or If then This is the first postive even integer. If then Discard this solution as you want positive integers only. The two integers are: 12 and 14 Check: = 340
 Expressions-with-variables/24171: what is 7a-2=1 what is a? 1 solutions Answer 12854 by Earlsdon(6294)   on 2006-01-11 11:03:07 (Show Source): You can put this solution on YOUR website!Solve for a: Add 2 to both sides of the equation. Divide both sides by 7.
 Mixture_Word_Problems/24135: How many pounds of coffee beans selling for \$2.00 per pound should be mixed with 6 pounds of coffee beans selling for \$2.80 per pound to obtain a mixture selling for \$2.48 per pound.1 solutions Answer 12821 by Earlsdon(6294)   on 2006-01-10 21:59:45 (Show Source): You can put this solution on YOUR website!Let x = the number of lbs of coffee selling for \$2.00/lb. You want to mix x lbs of \$2.00 coffee beans with 6 lbs of \$2.80 coffee beans to obtain a mixture of (6+x) lbs of \$2.48 coffee beans. Let's set up the appropriate equation to solve this mystery: Simplify and solve for x. Subtract 2x from both sides of the equation. Subtract 14.88 from both sides. Finally, divide both sides by 0.48 You will need to mix 4 lbs of the \$2.00 coffee beans with 6 lbs of the \$2.80 coffee beans to obtain 10 lbs of \$2.48 coffee bean mixture.
 Travel_Word_Problems/24123: Trying to help daughter with this problem and am at wits end.I guess I need a refresher algebra course if I'm going to survive this year. On a family trip, your father started out driving an average of 55 mph for 4 hours.Your mother, who was getting impatient, decided she would drive the rest of the way.She drove an aveage of 60 mph.How many hours did your mother drive? How many hours was the total trip if the average speed between both drivers was 58 mph. Any help would be appreciated!!1 solutions Answer 12820 by Earlsdon(6294)   on 2006-01-10 21:42:09 (Show Source): You can put this solution on YOUR website!For this problem, you'll need to apply the concept of weighted averages. Let x = the number of hours driven by mother. We can find the weighted average of father's speed plus mother's speed as follows: The weighted average speed is given as: 58 mph. 58 mph = (father's distance + mother's distance)/total trip time. Father's distance is: 55 mph(4 hrs) Mother's distance is: 60 mph(x hrs) The total trip time is (father's driving time) 4 hours plus (mother's driving time) x hours or (4+x) hours. Now you can write the equation for the weighted average speed for the trip which is given as 58 mph. Simplify and solve for x. Multiply both sides by (4+x) Simplify. Subtract 58x from both sides. Subtract 220 from both sides. Divide both sides by 2. So, mother's driving time is 6 hours. Father's diving time is 4 hhours. The total trip time is 6 hrs + 4 hrs = 10 hours. Check: Father's distance is 55 mph(4 hours) = 220 miles. Mother's distance is 60 mph(6 hours) = 360 miles. Total distance is 220 miles + 360 miles = 580 miles. Total distance driven = weighted average speed (58 mph) X total driving time (10 hours). Total distance driven = 58 mph X 10 hours = 580 miles.
 Graphs/24077: Explain how the constant of variation and the slope are related in a direct variation equation. Please help I'm stuck and need help.1 solutions Answer 12818 by Earlsdon(6294)   on 2006-01-10 20:59:52 (Show Source): You can put this solution on YOUR website!Compare the slope-intercept form of a linear equation with an equation for direct variation. Slope-intercept form: m is the slope of the line. Direct variation: y varies diectly as x. k is the constant of variation. Do you see the similarity? Let's compare the two equations using numbers: Slope-intercept: The slope (m) is 4 and the y-intercept (b) is 3. Direct variation: To find the value of k, you'll need to know the values of y and x. Let's say that y = 8 when x = 2, so that k = y/x = 8/2 = 4. So you can write: Now let's graph these two lines and compare them. The red line is: The green line is: Conclusion: The constant of variation in a direct-variation equation is the slope of the line when the equation is graphed.