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 Equations/555432: Solve for x. 4^5=2^(3x+2) 1024=2^(3x+2) This is the farthest I've been able to get, I'm not sure what to do next.1 solutions Answer 361934 by ankor@dixie-net.com(15624)   on 2012-01-11 16:03:46 (Show Source): You can put this solution on YOUR website!Solve for x. : : we know that 4^5 = 2^10, right" : therefore (exponents of the same number are equal) 3x + 2 = 10 3x = 10 - 2 3x = 8 x = : : See if this flies in the original problem Cancel the 3 We know already that
 Rational-functions/555361: I need to simplify by rationalizing each denominator. My equation is the square root of 11 all over 5 square root of 132. HELP please1 solutions Answer 361802 by ankor@dixie-net.com(15624)   on 2012-01-10 21:53:45 (Show Source): You can put this solution on YOUR website!the square root of 11 all over 5 square root of 132. : Multiply by the denominator radical over itself (same as multiplying by 1) Then seek out perfect squares inside the radical, cancel * = = = = = =
 Problems-with-consecutive-odd-even-integers/554989: 4 times a number and 5 times the same number added to 75 gives 156. Find the number. ?1 solutions Answer 361793 by ankor@dixie-net.com(15624)   on 2012-01-10 21:23:06 (Show Source): You can put this solution on YOUR website!4 times a number and 5 times the same number added to 75 gives 156. Find the number. ? : 4x + 5x + 75 = 156 9x + 75 = 156 Hey, you can do this yourself!
 Numbers_Word_Problems/555221: One number is 8 times another number. It is also 15 more than 3 three times the other number. Find the numbers and show all work. What do I do?1 solutions Answer 361792 by ankor@dixie-net.com(15624)   on 2012-01-10 21:20:11 (Show Source): You can put this solution on YOUR website!Here's what you do! : let x = "one number" let y = "another number : You write an equation for each statement: : "One number is 8 times another number." x = 8y : "It is also 15 more than 3 three times the other number." x = 3y + 15 : From the 1st statement, we know that x=8y, so replace x with 8y in the 2nd eq 8y = 3y + 15 8y - 3y = 15 5y = 15 y = 15/5 y = 3 : I'm going to leave something for you to do. You can find x using the 1st equation (x=8y), then check both solutions in the 2nd statement : How did you do on this? c
 Polynomials-and-rational-expressions/555264: Suzie’s flower shop estimates that supplies costs for one month will be given by the polynomial 2x2 – 7x – 4. She estimates that utilities costs for one month is given by 3x – 3. Find and simplify an expression that would estimate Suzie’s total costs for one month.1 solutions Answer 361788 by ankor@dixie-net.com(15624)   on 2012-01-10 21:06:32 (Show Source): You can put this solution on YOUR website!Suzie’s flower shop estimates that supplies costs for one month will be given by the polynomial 2x2 – 7x – 4. She estimates that utilities costs for one month is given by 3x – 3. Find and simplify an expression that would estimate Suzie’s total costs for one month. Total Cost = f(x) f(x) = (2x^2 - 7x - 4) + (3x - 3) Combine like terms f(x) = 2x^2 - 7x + 3x - 4 - 3 f(x) = 2x^2 - 4x - 7, cost for one month
 Systems-of-equations/554827: system of Equations and inequalities There are 2 triangles which I can't draw, imagine them between the letters and numbers. Could someone please help with this? Could you show all work and explain steps for me so I understand. The triangle on the left has a perimeter of 14. The triangle on the right has a perimeter of 21. What are x and y? 1st triangle has a y on each side and x at bottom the other triangle has 5/4y on each side and 3x at the bottom. 1 solutions Answer 361786 by ankor@dixie-net.com(15624)   on 2012-01-10 21:00:24 (Show Source): You can put this solution on YOUR website!The triangle on the left has a perimeter of 14. The triangle on the right has a perimeter of 21. What are x and y? 1st triangle has a y on each side and x at bottom the other triangle has 5/4y on each side and 3x at the bottom. : The way I understand this, the two triangles have two equal sides and writing a perimeter equation for each, I have: : Left triangle: x + 2y = 14 Right triangle: 3x + 2()y = 21 On the right triangle, let's get rid of the fraction, multiply each term by 4 4(3x) + 2(5y) = 4(21) 12x + 10y = 84 ; Back to the left triangle x + 2y = 14 x = (-2y + 14); put it in this form for substitution : Back to the right triangle 12x + 10y = 84 replace x with (-2y+14), find y 12(-2y+14) + 10y = 84 -24y + 168 + 10y = 84 -24y + 10y = 84 - 168 -14y = -84 Mult by -1 14y = 84 y = 84/14 y = 6 Find x x = -2(6) + 14 x = -12 + 14 x = 2 Summarize solutions, x=2, y=6 : Check this in the left equation x + 2y = 14 2 + 2(6) = 14 also in the right equation 3x + 2()y = 21 3(2) + 2()6 = 21 mult 5 by 6 6 + 2() = 21 Cancel the 2 into the 4 6 + = 6 + 15 = 21; confirms our solutions on this one too : did I succeed in explaining the step to you here? Any questions? C
 Age_Word_Problems/555447: My question is on linear systems : Angie is twice as old as Amelie. One year ago the sum of their ages was 10. How old is each now? I tried a couple different systems like 2y=x and x+y = 10 but I kept trying to work it out with others to but I can't get it. Please help me! Thank you!1 solutions Answer 361782 by ankor@dixie-net.com(15624)   on 2012-01-10 20:18:37 (Show Source): You can put this solution on YOUR website!Angie is twice as old as Amelie. One year ago the sum of their ages was 10. How old is each now? : Assume you had: x = Angie y = Amelie : "Angie is twice as old as Amelie." x = 2y : "One year ago the sum of their ages was 10." (x-1) + (y-1) = 10 x + y - 2 = 10 x + y = 10 + 2 x + y = 12 from the 1st equation, replace x with 2y 2y + y = 12 3y = 12 y = 12/3 y = 4 yrs is Amelie's present age, then obviously x = 2(4) = 8 yrs is Angies age ; : See if this checks out in the statement: " One year ago the sum of their ages was 10. " 8-1 + 4-1 = 10 How old is each now? 8 and 4
 Radicals/555157: please help me simplify this √18a3b6 1 solutions Answer 361767 by ankor@dixie-net.com(15624)   on 2012-01-10 19:04:19 (Show Source): You can put this solution on YOUR website!simplify this Factor this to reveal some perfect squares Extract those squares from the radical, leaving:
 Inverses/554919: The larger of two numbers is 10 less than twice the smaller. If half the larger is increased by 4 times the smaller, the result is 50. Please help .1 solutions Answer 361764 by ankor@dixie-net.com(15624)   on 2012-01-10 18:54:09 (Show Source): You can put this solution on YOUR website!The larger of two numbers is 10 less than twice the smaller. If half the larger is increased by 4 times the smaller, the result is 50. : Let x = the large number let y = the smaller : Write an equation for each statement: : "The larger of two numbers is 10 less than twice the smaller." x = 2y - 10 : "If half the larger is increased by 4 times the smaller, the result is 50." .5x + 4y = 50 From the 1st statement; replace x with (2y-10) .5(2y - 10) + 4y = 50 y - 5 + 4y = 50 5y = 50 + 5 5y = 55 y = 55/5 y = 11 find x x = 2y - 10 x = 2(11) - 10 x = 22 - 10 x = 12 : : Check our solution in the 2nd statement: " If half the larger is increased by 4 times the smaller, the result is 50." .5(12) + 4(11) = 6 + 44 = 50, confirms our solutions of x=12, y=11
 test/555089: Start at the begining . Leraning how to do algebra for the first time , can you teach me please?1 solutions Answer 361755 by ankor@dixie-net.com(15624)   on 2012-01-10 18:39:59 (Show Source): You can put this solution on YOUR website!Here's what you have to do on the site. : Carefully submit a problem that you are having difficulty with, you can include your efforts in solving it. Tutors like to see that you tried. : You can emphasis that you want step-by-step instructions. Give it a try. C
 Miscellaneous_Word_Problems/555141: The stopping distance D of a car after the brakes are applied varies directly as the square of the speed R. If a car traveling 40mph can stop in 90ft, how many feet will it take for the same car to stop traveling 90 mph? It will take ______ft. Please help with this word problem. Thank you. 1 solutions Answer 361727 by ankor@dixie-net.com(15624)   on 2012-01-10 17:11:13 (Show Source): You can put this solution on YOUR website!The stopping distance D of a car after the brakes are applied varies directly as the square of the speed R. If a car traveling 40mph can stop in 90ft, how many feet will it take for the same car to stop traveling 90 mph? : Find the constant of variation, k: k*R^2 = D R = 40, D = 90 k*40^2 = 90 1600k = 90 k = k = .05625 : D = .05625R^2; the equation At 90 mph D = .05625*90^2 D = 455.625 ft at 90 mph :
 Polynomials-and-rational-expressions/555156: There are approximately 5lbs of muscle for every 7lbs of body weight of a certain animal. For a 168-lb animal, how much of the weight is muscle? The are _____lbs of muscle.1 solutions Answer 361717 by ankor@dixie-net.com(15624)   on 2012-01-10 16:54:13 (Show Source): You can put this solution on YOUR website!There are approximately 5lbs of muscle for every 7lbs of body weight of a certain animal. For a 168-lb animal, how much of the weight is muscle? : Do this a proportion = 7m = 5 * 168 7m = 840 m = 840/7 m = 120 lbs are muscle in a 168 lb animal
 Linear_Equations_And_Systems_Word_Problems/554993: I live close to the local water park. I would like to go to the park throughout the summer but Im wondering what type of pass to purchase for the better deal. I have 2 options when it comes to purchasing a pass to the park. I can either buy an annual pass for \$100.00 that can be used as many times as I would like throughout the summer or I can purchase a daily pass each time for \$25.00. Depending on the amount of times I visit the park will depend on what would be the best to buy. I plan to visit the park at least 7 times. I need to create algebraic equations that represent the cost/yield and then I have to graph them.1 solutions Answer 361708 by ankor@dixie-net.com(15624)   on 2012-01-10 16:34:50 (Show Source): You can put this solution on YOUR website!I live close to the local water park. I would like to go to the park throughout the summer but Im wondering what type of pass to purchase for the better deal. I have 2 options when it comes to purchasing a pass to the park. I can either buy an annual pass for \$100.00 that can be used as many times as I would like throughout the summer or I can purchase a daily pass each time for \$25.00. Depending on the amount of times I visit the park will depend on what would be the best to buy. I plan to visit the park at least 7 times. I need to create algebraic equations that represent the cost/yield and then I have to graph them. : The annual pass: y = 100 (Red) The single pass: y = 25x : The graph: y axis is cost, x axis is no. of visits Obviously, if you visit 7 times, the annual would be best.
 Travel_Word_Problems/555102: With a strong wind at its back, a ship can make a 425 mile journey in 90 minutes less than it can without the breeze. If its average speed is increased by 15 mph with the aid of the wind, about how long did the joutney take with the breeze?1 solutions Answer 361702 by ankor@dixie-net.com(15624)   on 2012-01-10 16:11:40 (Show Source): You can put this solution on YOUR website!With a strong wind at its back, a ship can make a 425 mile journey in 90 minutes less than it can without the breeze. If its average speed is increased by 15 mph with the aid of the wind, about how long did the journey take with the breeze? : From the information given, we can find the speed of the boat in still water Let s = boat speed in still water : write a time equation, change 90 min to 1.5 hrs : no breeze time - with breeze time = 1.5 hrs - = 1.5 Multiply by s(s+15) 425(s+15) - 425s = 1.5s(s+15) 425s + 6375 - 425s = 1.5s^2 + 22.5s 6375 = 1.5s^2 + 22.5s A quadratic equation 1.5s^2 + 22.5s - 6375 = 0 Simplify divide by 1.5 s^2 + 15s - 4250 = 0 Use the quadratic formula to find the s I got a positive solution of s = 58.12 mph : " If its average speed is increased by 15 mph with the aid of the wind, about how long did the journey take with the breeze?" = 5.81 hrs : Check this by finding the time without the wind = 7.31 hrs : 7.31 - 5.81 = 1.5 hrs
 Rate-of-work-word-problems/555216: It takes 3 painters 4 hours to paint 1 classroom. How many hours does it take 1 painter to paint 2 classrooms of the same size as the first one? Assume all painters work at the same rate for the full time.1 solutions Answer 361686 by ankor@dixie-net.com(15624)   on 2012-01-10 15:21:18 (Show Source): You can put this solution on YOUR website!It takes 3 painters 4 hours to paint 1 classroom. How many hours does it take 1 painter to paint 2 classrooms of the same size as the first one? Assume all painters work at the same rate for the full time. : Find how many man-hrs required to paint 1 class-room 3 * 4 = 12 man-hrs to paint one classroom : "How many hours does it take 1 painter to paint 2 classrooms of the same size as the first one? : let h = no. of hrs for 1 painter to do it : 24 man-hrs to paint two classrooms, obviously. : 1h = 24 hrs for one man to paint two classrooms
 Radicals/554986: I need to simplify radical expression for 2 square root sign with a to the 4th power b to the fifth power1 solutions Answer 361683 by ankor@dixie-net.com(15624)   on 2012-01-10 15:14:36 (Show Source): You can put this solution on YOUR website!2 square root sign with a to the 4th power b to the fifth power factor inside the radical to reveal some perfect squares extract the square root of those perfect squares which is
 Travel_Word_Problems/555207: As part of a training program for the Boston Marathon, a runner wants to build endurance by running at a rate of 9 mph for 40 min. How far will the runner travel in that time period? (Enter your answer to three decimal places.)1 solutions Answer 361678 by ankor@dixie-net.com(15624)   on 2012-01-10 15:06:01 (Show Source): You can put this solution on YOUR website!a rate of 9 mph for 40 min. How far will the runner travel in that time period? : Change 40 min to hrs, multiply by 9 * 9 = 6 mi
 Graphs/555060: Good Morning, I am having a problem understanding and seeing how to graph the following inequality. Could someone show me the graph and explain it to me? Here is the inequality: 3x-2y<-6 Hope to hear from someone soon. Sincerely, T 1 solutions Answer 361676 by ankor@dixie-net.com(15624)   on 2012-01-10 15:03:07 (Show Source): You can put this solution on YOUR website!3x - 2y < -6 Put the equation in the point/slope format -2y < -3x - 6 Get rid all those negatives, mult by -1, this reverses the inequality sign 2y > 3x + 6 divide both sides by 2 y > x + y > 1.5x + 3, this is the equation we want to graph : Graph this for x=-3 and x=+3 y = 1.5(-3) + 3 y = -4.5 + 3 y = -1.5 and y = 1.5(3) + 3 y = 4.5 + 3 y = 7.5 : We graph points -3,-1.5 and 3,7.5 You want to shade the area above the line
 Travel_Word_Problems/555059: A plane can travel 350 km/h in still air. With the wind it flew 1000 km. In the same amount of time it could travel 750 km against the wind. Find the speed of the wind.1 solutions Answer 361666 by ankor@dixie-net.com(15624)   on 2012-01-10 14:20:59 (Show Source): You can put this solution on YOUR website!A plane can travel 350 km/h in still air. With the wind it flew 1000 km. In the same amount of time it could travel 750 km against the wind. Find the speed of the wind. : Let w = speed of the wind then (350-w) = effective speed against the wind and (350+w) = effective speeed with : Write a time equation: time = dist/speed : = Cross multiply 1000(350-w) = 750(350+w) simplify divide both sides by 250, results 4(350-w) = 3(350+w) 1400 - 4w = 1050 + 3w 1400 - 1050 = 7w + 4w 350 = 7w w = w = 50 mph is the speed of the wind : : Confirms this find the times of each trip 1000/400 = 2.5 hrs 750/300 = 2.5
 Numbers_Word_Problems/554877: The product of two consecutive even integers is 30 less than 15 times their sum. Find the two integers.1 solutions Answer 361665 by ankor@dixie-net.com(15624)   on 2012-01-10 14:09:31 (Show Source): You can put this solution on YOUR website!Two integers: x, (x+2) : The product of two consecutive even integers is 30 less than 15 times their sum. x(x+2) = 15[x + (x+2)] - 30 x^2 + 2x = 15(2x + 2) - 30 x^2 + 2x = 30x + 30 - 30 x^2 = 30x - 2x x^2 = 28x Divide both sides by x x = 28 and 30 are the two even integers : : see if that works 28(30) = 15[28+30] - 30 840 = 15(58) - 30 840 = 870 - 30; confirms our our solution
 Inequalities/555155: Please help me with this linear inequality 2k-3/4 < 3 I have tried to multiply both sides by 12 as a lowest common denominator and I am not getting the answer right. I need help how how to solve it. I cannot locate a problem like this one in my textbook. Thank you!1 solutions Answer 361664 by ankor@dixie-net.com(15624)   on 2012-01-10 13:48:51 (Show Source): You can put this solution on YOUR website!2k - 3/4 < 3 multiply both sides by 4, to get rid of the denominator 4(2k) - 3 < 4(3) 8k - 3 < 12 8k < 12 + 3 8k < 15 k < or k < 1.875
 Travel_Word_Problems/555072: If John can travel 130 miles in 2 hours, how far can he travel in 5 hours if he travels the same rate of speed1 solutions Answer 361661 by ankor@dixie-net.com(15624)   on 2012-01-10 13:43:42 (Show Source): You can put this solution on YOUR website!f John can travel 130 miles in 2 hours, how far can he travel in 5 hours if he travels the same rate of speed : Find his mph, multiply by 5 * 5 = 325 mi
 Expressions-with-variables/555134: im having trouble with the problem 0.3x-0.2(3-5x)= -0.5(x-6). ive looked at the examples in the book and i still dont understand. if anyone could please help that would be great!1 solutions Answer 361660 by ankor@dixie-net.com(15624)   on 2012-01-10 13:40:08 (Show Source): You can put this solution on YOUR website!0.3x - 0.2(3-5x) = -0.5(x - 6) Multiply what's inside the brackets: .3x - .6 + 1x = -.5x + 3 Combine like terms .3x + 1x + .5x = 3 + .6 1.8x = 3.6 x = x = 2 : : Check solution in original equation 0.3x - 0.2(3-5x) = -0.5(x - 6) replace x with 2 0.3(2)- 0.2(3-5(2)) = -0.5(2 - 6) .6 - .2(3-10) = -.5(-4) .6 - .2(-7) = +2 .6 + 1.4 = 2; confirms our solution
 logarithm/555048: what is the answer of the logarithm of 25 to the base 5 divided by the logarithm of 4 to the base 2?1 solutions Answer 361652 by ankor@dixie-net.com(15624)   on 2012-01-10 12:28:43 (Show Source): You can put this solution on YOUR website!what is the answer of the logarithm of 25 to the base 5 divided by the logarithm of 4 to the base 2? : Remember the exponent equiv of logs log5(25) = y 5^y = 25 y = 2 and log2(4) = y 2^y = 4 y = 2 : 2/2 = 1 is the answer
 Mixture_Word_Problems/554802: Hello tutor, I need help on this word problem, please help me. How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution? Thank You!!!!!!!!1 solutions Answer 361620 by ankor@dixie-net.com(15624)   on 2012-01-10 09:19:40 (Show Source): You can put this solution on YOUR website!How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 50% alcohol solution? : Let x = amt of 70% solution required : A typical mixture equation : .70x + .40(50) = .50(x+50) .70x + 20 = .50x + 25 .70x - .50x = 25 - 20 .20x = 5 x = x = 25 liters of 70% solution : : check this .7(25) + .4(50) = .5(25+50) 17.5 + 20 = 37.5
 Money_Word_Problems/554767: Hello, my algebra word problem is this "Use two variables and two equations to solve the problem. Part of \$9000 was invested at 10% interest and the rest at 12%. If the annual income from these investments was \$1020 how much was invested at rate?1 solutions Answer 361617 by ankor@dixie-net.com(15624)   on 2012-01-10 08:25:04 (Show Source): You can put this solution on YOUR website!Use two variables and two equations to solve the problem. Part of \$9000 was invested at 10% interest and the rest at 12%. If the annual income from these investments was \$1020 how much was invested at rate? : Let x = amt invested at 10% Let y = amt invested at 12% : The amt equation x + y = 9000 Rearrange for substitution x = (9000-y) : the interest equation .10x + .12y = 1020 substitute (9000-y) for x, solve for y .10(9000-y) + .12y = 1020 900 - .10y + .12y = 1020 .02y = 1020 - 900 .02y = 120 y = y = \$6000 invested at 12% : You should be able to find x, check your solutions in both equations
 Exponents/554600: What is the Least Common Multiple of and 1 solutions Answer 361554 by ankor@dixie-net.com(15624)   on 2012-01-09 21:20:52 (Show Source): You can put this solution on YOUR website!What is the Least Common Multiple of and
 Complex_Numbers/554885: Please help me solve this equation : √(-3/16) Thanks 1 solutions Answer 361552 by ankor@dixie-net.com(15624)   on 2012-01-09 21:18:50 (Show Source): You can put this solution on YOUR website!√(-3/16) It's not an equation we can solve, just simplify : : we know the square root of -1 = i, find square root of 1/4^2 *
 Exponents/554605: What is the Least Common Multiple of and 1 solutions Answer 361547 by ankor@dixie-net.com(15624)   on 2012-01-09 21:13:12 (Show Source):
 Unit_Conversion_Word_Problems/554576: A bicycle wheel has a diameter of 26 in. If the bicycle needs to travel 59 ft, how many revolutions of the wheel need to take place? Round to the nearest whole number. 1 solutions Answer 361493 by ankor@dixie-net.com(15624)   on 2012-01-09 19:36:34 (Show Source): You can put this solution on YOUR website!A bicycle wheel has a diameter of 26 in. If the bicycle needs to travel 59 ft, how many revolutions of the wheel need to take place? : Change ft to inches, divide by the circumference = 8.667 ~ 9 revolutions