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 Polynomials-and-rational-expressions/267733: What is the answer to this negative exponents problem ?1 solutions Answer 196444 by ankor@dixie-net.com(15649)   on 2010-02-09 19:52:27 (Show Source): You can put this solution on YOUR website! = ; the reciprocal of x and y, gets rid of the neg exponents
 Mixture_Word_Problems/267604: x-4 = -2/3(y-9) solve for y1 solutions Answer 196440 by ankor@dixie-net.com(15649)   on 2010-02-09 19:44:39 (Show Source): You can put this solution on YOUR website!x-4 = -2/3(y-9) solve for y : Assume the problem is: x - 4 = (y - 9) Multiply both sides by 3, results 3(x - 4) = -2(y - 9) : 3x - 12 = - 2y + 18 : 2y = -3x + 18 + 12 : 2y = -3x + 30 : Divide by 2 y = x + 15
 Quadratic_Equations/267481: x/(.900-2x)^2 = 4 How do I solve for x?1 solutions Answer 196433 by ankor@dixie-net.com(15649)   on 2010-02-09 19:28:15 (Show Source): You can put this solution on YOUR website!x/(.900-2x)^2 = 4 How do I solve for x? : Assume the problem is: = 4 FOIL = 4 : = 4 : x = 4(4x^2 - 3.6x + .81) : x = 16x^2 - 14.4x + 3.24 : 0 = 16x^2 - 14.4x - x + 3.24 : 16x^2 - 15.4x + 3.24 = 0 : Solve this using the quadratic formula Two solutions: x~.652 and x~.311 ; Check both of these in the original equation
 Travel_Word_Problems/267440: Going an average of 65 mph, Bob can travel 500 miles per day. How far can he travel in a day if he increases his average speed to 75 mph? Show (explain) how you can calculate your answer without calculating the time Bob spent on the road.1 solutions Answer 196398 by ankor@dixie-net.com(15649)   on 2010-02-09 17:58:37 (Show Source): You can put this solution on YOUR website!Going an average of 65 mph, Bob can travel 500 miles per day. How far can he travel in a day if he increases his average speed to 75 mph? Show (explain) how you can calculate your answer without calculating the time Bob spent on the road : Use a ratio equation, d = dist at 75 = Cross multiply 65d = 75 * 500 65d = 37500 d = d = 576.92 mi in a day
 Linear-systems/267425: i dont understand how to do this: 3x+2y=-6 x=y+31 solutions Answer 196396 by ankor@dixie-net.com(15649)   on 2010-02-09 17:51:29 (Show Source): You can put this solution on YOUR website!i don't understand how to do this: 3x + 2y =-6 x = y+3 : Since x = (y+3), why not substitute (y+3) for x in the 1st equation so you have: 3(y+3) + 2y = -6 : Multiply what's inside the brackets by 3 3y + 9 + 2y = -6 ; Subtract 9 from both sides, add the y's 3y + 2y = -6 - 9 5y = -15 : Divide both sides by 5 y = y = -3 : Remember that x = y + 3; substitute -3 for y x = (-3) + 3 x = 0 : : Check the solution by substituting for x and y in the 1st equation 3x + 2y =-6 3(0) + 2(-3) = -6 -6 = -6; confirms the solutions
 Linear_Equations_And_Systems_Word_Problems/267414: You inherit \$13,000 and decide to invest the money in two different investments, one paying 10% and the other paying 14%. After 6 months your investments are worth \$13,741. How much did you invest in each account?1 solutions Answer 196382 by ankor@dixie-net.com(15649)   on 2010-02-09 16:54:06 (Show Source): You can put this solution on YOUR website!You inherit \$13,000 and decide to invest the money in two different investments, one paying 10% and the other paying 14%. After 6 months your investments are worth \$13,741. How much did you invest in each account? : We know the interest earned = \$741; write a total interest equation Let x = amt invested at 14% then (13000-x) = amt invested at 10% : We assume the investment return % were per year, but this total is for 6 months We have to assume that after 1 yr the amt earned would be 2*741 = \$1482 Using that assumption: : .14x + .10(13000-x) = 1482 .14x + 1300 - .10x = 1482 .14x - .10x = 1482 - 1300 .04x = 182 x = x = \$4,550 invested at 14% and 13000 - 4550 = \$8,450 invested at 10% : : Check: .14(4550) + .10(8450) = 637 + 845 = 1482 per year then 781 for half a year
 Numbers_Word_Problems/267461: How to solve: The differences between the square of a positive number and ten times the number 11. Find the positive number. How to solve: The height of a parallelogram is 2cm longer than its base. Its area is 120cm2. Find the base and height of the parallelogram.1 solutions Answer 196379 by ankor@dixie-net.com(15649)   on 2010-02-09 16:32:51 (Show Source): You can put this solution on YOUR website!The differences between the square of a positive number and ten times the number is 11. Find the positive number. x^2 - 10x = 11 x^2 - 10x - 11 = 0; our old friend, the quadratic equation! Factors to (x-11)(x+1) = 0 The positive solution x = 11 Check: 11^2 - 10(11) = 11 : How to solve: The height of a parallelogram is 2cm longer than its base. Its area is 120cm2. Find the base and height of the parallelogram. : Area of a parallelogram; b * h = 120 "height is 2cm longer than its base." h = (b+2) Replace h with (b+2) in the area equation b * (b+2) = 120 b^2 + 2b = 120 b^2 + 2b - 120 = 0; what luck! Another quadratic equation! Factors to (b-10)(b+12) = 0 Positive solution b = 10 cm then h = 10+2 = 12 cm ; Check 10 * 12 = 120 sq/cm
 percentage/267426: I need help finding the regular price of an item before a tax was applied. "After a discount of 37%, the sale price for a book was \$32.09. What was the regular price. I've tried many different equations...I'm missing something here. x+.37x=32.09 ...I get 23.42. Please help...ty :)1 solutions Answer 196378 by ankor@dixie-net.com(15649)   on 2010-02-09 16:13:34 (Show Source): You can put this solution on YOUR website!"After a discount of 37%, the sale price for a book was \$32.09. What was the regular price. I've tried many different equations...I'm missing something here. x+.37x=32.09 ...I get 23.42 : The discount has to be subtracted from the regular price x - .37x = 32.09 : .63x = 32.09 x = x = \$50.94 is the regular price
 test/267581: A wave with a period of 0.008 second has a frequency of A. 12.5 Hz. B. 80 Hz. C. 125 Hz. D. 800 Hz. 1 solutions Answer 196377 by ankor@dixie-net.com(15649)   on 2010-02-09 16:07:31 (Show Source): You can put this solution on YOUR website!A wave with a period of 0.008 second has a frequency of = 125 Hz
 Travel_Word_Problems/267665: Lucas is 1/3 mile away from home bicycling at 20 miles per hour when his brother takes off on his bike to catch up. How fast must Lucas's brother go to catch him a mile from home.1 solutions Answer 196372 by ankor@dixie-net.com(15649)   on 2010-02-09 15:49:48 (Show Source): You can put this solution on YOUR website!Lucas is 1/3 mile away from home bicycling at 20 miles per hour when his brother takes off on his bike to catch up. How fast must Lucas's brother go to catch him a mile from home. : Briefly, bro has to travel 1 mi in the same time that L travels 2/3 of a mile : Let s = bro's speed to accomplish difficult feat : Write a time equation: Time = dist/speed : bro's time = L's time = : = : = Cross multiply s = 30 mph bro has pedal to catch L 1 mi from home ; : Check this by finding the times 1/30 = .033 hrs .667/20 = .033 hrs (about 2 min)
 Linear-equations/267601: one gallon of liquid occupies 231 cubic inches. Write a rule that expresses the number of gallons g(c) as a function of the number of cubic inches c.1 solutions Answer 196363 by ankor@dixie-net.com(15649)   on 2010-02-09 15:19:04 (Show Source): You can put this solution on YOUR website!one gallon of liquid occupies 231 cubic inches. Write a rule that expresses the number of gallons g(c) as a function of the number of cubic inches c. : g(c) =
 Exponential-and-logarithmic-functions/267560: At 2pm the number of bacteria in a colony was 100, by 4pm it was 4000. Write an exponential function to model the population y of bacteria x hours after 2pm. Please help1 solutions Answer 196361 by ankor@dixie-net.com(15649)   on 2010-02-09 15:16:35 (Show Source): You can put this solution on YOUR website!At 2pm the number of bacteria in a colony was 100, by 4pm it was 4000. Write an exponential function to model the population y of bacteria x hours after 2pm. : Ao*k^x = A where Ao is the initial amt k = constant factor x = time in hrs A = resulting amt ; Write an equation from the 1st statement, x = 2 hrs, find k 100 * k^2 = 4000 k^2 = k^2 = 40 k = k = 6.3246 : The equation y = 100(6.3246^x)
 Mixture_Word_Problems/267615: How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 50% antifreeze?1 solutions Answer 196354 by ankor@dixie-net.com(15649)   on 2010-02-09 15:04:53 (Show Source): You can put this solution on YOUR website!How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 50% antifreeze? : 1 gal of water, seems pretty obvious, but it you want an equation where x = amt of water : x = .5(x+1) x = .5x + .5 x - .5x = .5 .5x = .5 x = 1 gal
 Polynomials-and-rational-expressions/267535: Please help me solve: (a^2 - 10a + 21) / (a^2 - 11a + 28)1 solutions Answer 196351 by ankor@dixie-net.com(15649)   on 2010-02-09 14:57:02 (Show Source): You can put this solution on YOUR website!Please help me solve, this is not an equation, you can't solve it, just simplify it: Both numerator and denominator will factor : (a-7) will cancel so you end up with
 Geometry_Word_Problems/267524: Need help with the following: A box is being constructed by cutting 3-inch squares from the corners of a rectangualr sheet of metal that is 4 inches longer than it is wide. If the box is to have a volume of 135 cubic inches, find the dimensions of the metal sheet.1 solutions Answer 196347 by ankor@dixie-net.com(15649)   on 2010-02-09 14:48:29 (Show Source): You can put this solution on YOUR website!A box is being constructed by cutting 3-inch squares from the corners of a rectangular sheet of metal that is 4 inches longer than it is wide. If the box is to have a volume of 135 cubic inches, find the dimensions of the metal sheet. : Assume they mean an open box. : Cutting 3" squares from each corner make the box base dimensions 6" less than the metal sheet We know the height of the box = 3" therefore: Area of the base = = 45 sq/in : Let x = width of the metal then we can say: (x+4) = length of the metal : The base of the box dimensions: (x-6) by (x+4-6) The area (x-6)*(x-2) = 45 FOIL x^2 - 2x - 6x + 12 = 45 x^2 - 8x + 12 - 45 = 0 x^2 - 8x - 33 = 0 Factors to (x-11)(x+3) = 0 positive solution x = 11" is the width of the metal sheet then 11+4 = 15" is the length : : See if that's true (11-6) * (15-6) * 3 = 5 * 9 * 3 = 135 cu/in
 Travel_Word_Problems/267516: How far can a man drive out into the country at an average rate of 30 mph and return over the SAME road at the average of 50 mph, if he travels total time of 8 hours?1 solutions Answer 196339 by ankor@dixie-net.com(15649)   on 2010-02-09 14:25:15 (Show Source): You can put this solution on YOUR website!How far can a man drive out into the country at an average rate of 30 mph and return over the SAME road at the average of 50 mph, if he travels total time of 8 hours? : Let t = time driving at 50 mph then (8-t) = time driving at 30 mph : Write a distance equation, Dist = speed * time : Dist at 50 mph = dist at 30 mph 50t = 30(8-t) 50t = 240 - 30t 50t + 30t = 240 80t = 240 t = t = 3 hrs at 50 mph then 8 - 3 = 5 hrs at 30 mph : Find the dist at 50 mph 3 * 50 = 150 mile Check the dist at 30 mph, (should be the same) 5 * 30 = 150 miles : He can go 150 mi and satisfy the 8 hr requirement.
 Rectangles/267515: a rectangle has an area that is numerically twice its perimeter. if the length is twice the width, what are the dimensions?1 solutions Answer 196325 by ankor@dixie-net.com(15649)   on 2010-02-09 13:28:04 (Show Source): You can put this solution on YOUR website!a rectangle has an area that is numerically twice its perimeter. : L*W = 2(2L+2W) : If the length is twice the width, what are the dimensions? : Replace L with 2W (2W)*W = 2[2(2W) + 2W)] 2W^2 = 2(4W + 2W) 2W^2 = 2(6W) ; divide both sides by 2 W^2 = 6W W^2 - 6W = 0 : factor out W W(W - 6) = 0 : Two solutions W = 0, meaningless and W = 6 units is the width then 2(6) = 12 units is the length : : Is this true? 12*6 = 2(2(12) + 2(6)) 72 = 2(24 + 12),
 Travel_Word_Problems/267467: Two planes leave an airport 30 minutes apart. The first planes flies east and the second west. After 75 minutes the planes are 700 miles apart. How fast is each flying? I know that S X T = D. I know that the East plane flys for 1.25hrs at x speed so its distance is 1.25x. I know that the West plane flys for .75hrs at y speed so its distance is .75x. I know that if you add the two distances together you will get 700 miles. 1.25x + .75y = 700. I just don't know where to go next. Can you help?1 solutions Answer 196324 by ankor@dixie-net.com(15649)   on 2010-02-09 13:11:56 (Show Source): You can put this solution on YOUR website!Two planes leave an airport 30 minutes apart. The first planes flies east and the second west. After 75 minutes the planes are 700 miles apart. How fast is each flying? I know that S X T = D. I know that the East plane flys for 1.25hrs at x speed so its distance is 1.25x. I know that the West plane flys for .75hrs at y speed so its distance is .75x. I know that if you add the two distances together you will get 700 miles. 1.25x + .75y = 700. : The problem is there are many combinations of x & y that will work here Using your equation: .75y = -1.25x + 700 divide by .75 y = -1.67x + 933.33 you can choose a value for x, say 300 mph, and find y = 432.33 or: x = 500, y = 98.33 an integer solution: x=399, y=267 an infinite number of solutions
 Expressions-with-variables/267422: Here is a confusing question for me: The ratio of Aldo's cycling speed to Jose's cycling speed is 6:5. Jose leaves school at 3 P.M. and Aldo leaves at 3:10 P.M. By 3:30, Aldo is only 2 km behind Jose. How fast is each cycling?1 solutions Answer 196322 by ankor@dixie-net.com(15649)   on 2010-02-09 12:42:42 (Show Source): You can put this solution on YOUR website!The ratio of Aldo's cycling speed to Jose's cycling speed is 6:5. Let m = the multiplier then 6m = A's speed and 5m = J's speed : Jose leaves school at 3 P.M. and Aldo leaves at 3:10 P.M. By 3:30, J's travel time 30 min; hr A's travel time 20 min; hr : By 3:30, Aldo is only 2 km behind Jose. How fast is each cycling? ; Write a distance equation. Dist = time * speed J's dist - A's dist = 2 km (5m) - (6m) = 2 Multiply by 6 to get rid of the denominators, results 3(5m) - 2(6m) = 6(2) 15m - 12m = 12 3m = 12 m = 4 is the multiplier then 4(6) = 24 km/hr is A's speed and 4(5) = 20 km/hr is J's speed : : Check solution by finding the dist traveled by each J: .5(20) = 10 km A: .33(24)= 8 km --------------------- difference = 2 km
 Rectangles/267275: A box is 720 cubic centimeters. The height of the box is five centimeters and width is w centimeters. If the length of the box is four times the width, what will be the width in cnetimeters of the box? 1 solutions Answer 196320 by ankor@dixie-net.com(15649)   on 2010-02-09 12:23:33 (Show Source): You can put this solution on YOUR website!A box is 720 cubic centimeters. The height of the box is five centimeters and width is w centimeters. If the length of the box is four times the width, what will be the width in centimeters of the box? : The volume equation L * W * H = 750 : L * W * 5 = 750 : 5LW = 750 LW = LW = 150 : "the length of the box is four times the width" L = 4W : Replace L with 4W W*4W = 150 4W^2 = 150 W^2 = W^2 = 37.5 W = W = 6.1237 cm is the width : : See if that is true, check on a calc: 4(6.1237) * 6.1237 * 5 = 749.997 ~ 750
 Miscellaneous_Word_Problems/267398: A car traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossng, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing? 1 solutions Answer 196318 by ankor@dixie-net.com(15649)   on 2010-02-09 12:12:46 (Show Source): You can put this solution on YOUR website!A car traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing? : This is a pythag problem: a^2 + b^2 = b^2 Where: c = 50, a = 30 b = dist the train is from the crossing : 30^2 + b^2 = 50^2 900 + b^2 = 2500 b^2 = 2500 - 900 b^2 = 1600 b = b = 40 meters, is the train from the crossing
 Graphs/267219: what does it mean to draw a line with a slope of 51 solutions Answer 196288 by ankor@dixie-net.com(15649)   on 2010-02-09 09:50:37 (Show Source): You can put this solution on YOUR website!what does it mean to draw a line with a slope of 5 : Remember the definition of slope is "rise over run" : A slope of 5 is actually where rise = 5 and run = 1 : We can say for every 1 unit horizontally, we have 5 units vertially : an equation y = 5x would look like this : note when x (run) = 1, y (rise) = 5
 Exponents/267263: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coefficient of x^3. The coefficient of x is three times the coefficient of x^2. The remaining coefficient is 2 more than the coefficient of x^3. The sum of the coefficients is -4. Find the polynomial.1 solutions Answer 196282 by ankor@dixie-net.com(15649)   on 2010-02-09 09:43:02 (Show Source): You can put this solution on YOUR website!We will try to get every variable in terms of a : A polynomial in x has degree 3. ax^3 + bx^2 + cx + d : The coefficient of x^2 is 3 less than the coefficient of x^3. b = a - 3 : The coefficient of x is three times the coefficient of x^2. c = 3b Replace b with (a-3) c = 3(a-3) c = 3a - 9 : The remaining coefficient is 2 more than the coefficient of x^3. d = a + 2 : The sum of the coefficients is -4. Find the polynomial. a + b + c + d = -4 Substitute, solve for a a + (a-3) + (3a-9) + (a+2) = -4 6a - 10 = -4 6a = -4 + 10 6a = 6 a = 1 then b = 1 - 3 b = -2 and c = 3(1) - 9 c = -6 : d = 1 + 2 d = 3 : x^3 - 2x^2 - 6x + 3; is the polynomial
 Human-and-algebraic-language/267214: Translate the following sentence into an algebraic equation:"6 more than triple a number is 3 times the difference of a number & 2."1 solutions Answer 196278 by ankor@dixie-net.com(15649)   on 2010-02-09 09:25:07 (Show Source): You can put this solution on YOUR website!Translate the following sentence into an algebraic equation: "6 more than triple a number is 3 times the difference of a number & 2." : Just write what it says, the word "is" usually mean equal "=" 6 + 3x = 3*(x - 2) but we usually write this as 3x + 6 = 3(x-2)
 Quadratic_Equations/267189: Find x. 1 solutions Answer 196276 by ankor@dixie-net.com(15649)   on 2010-02-09 09:17:30 (Show Source): You can put this solution on YOUR website! Adding logs is the same as multiply FOIL : The exponent equiv of logs : x^2 - 4x - 5 = 27 : x^2 - 4x - 5 - 27 = 0 : x^2 - 4x - 32 = 0 Factor (x-8)(x+4) = 0 positive solution (cannot have a log of a neg number) x = 8 : See if this works Exponent equiv: 27 = 3^3
 Polynomials-and-rational-expressions/267181: Need help writing the polynomial withe exponents on x in descending order: 5x-2x to the fourth+3-5x to the second. thanks1 solutions Answer 196275 by ankor@dixie-net.com(15649)   on 2010-02-09 09:03:59 (Show Source): You can put this solution on YOUR website!Need help writing the polynomial withe exponents on x in descending order: 5x-2x to the fourth+3-5x to the second. thanks : Just put the highest exponent 1st and then in descending order
 Travel_Word_Problems/267173: A woman rides a bicycle at 12 miles per hour. What is her speed in yards per minute? If light can travel 186,000 miles per second, how many miles can it travel in one year? (Assume one year has 365.24 days.) 1 solutions Answer 196270 by ankor@dixie-net.com(15649)   on 2010-02-09 08:23:21 (Show Source): You can put this solution on YOUR website!a bicycle at 12 miles per hour. What is her speed in yards per minute? : There are 1760 yds in 1 mile : 12 mph is: = 352 yds/min : If light can travel 186,000 miles per second, how many miles can it travel in one year? (Assume one year has 365.24 days.) : 60 * 60 * 24 * 365.24 * 186,000 ~ 5.87 (10^12) which is 5,869,552,896,000 miles on my calc
 Mixture_Word_Problems/267282: A chemist wishes to mix some pure acid with some water to produce 16L of a solution that is 30% acid. How much pure acid and how much water should be mixed1 solutions Answer 196262 by ankor@dixie-net.com(15649)   on 2010-02-08 22:31:40 (Show Source): You can put this solution on YOUR website!A chemist wishes to mix some pure acid with some water to produce 16L of a solution that is 30% acid. How much pure acid and how much water should be mixed : let x = amt of pure acid : x = .30(16) x = 4.8 liters of pure acid then 16-4.8 = 11.2 liters of water : : Check: = .3 or 30% acid and: = .7 or 70% water
 Graphs/267223: what does it mean to draw a line with a slope of -1 over 41 solutions Answer 196259 by ankor@dixie-net.com(15649)   on 2010-02-08 21:55:11 (Show Source): You can put this solution on YOUR website!what does it mean to draw a line with a slope of -1 over 4 : One definition of slope is "Rise over Run" which means vertical over horizontal This slope is , so it drops 1 unit vertically for every 4 horizontal units If you graph x, it would look like this note that when x=4, y=-1
 Numbers_Word_Problems/267378: how do i solve and write two equations for the sum of two numbers is 30. the sum of the greater number and 3 times the lesser number is 54. Find both numbers?1 solutions Answer 196254 by ankor@dixie-net.com(15649)   on 2010-02-08 21:39:47 (Show Source): You can put this solution on YOUR website!how do i solve and write two equations: for the sum of two numbers is 30. x + y = 30 : the sum of the greater number and 3 times the lesser number is 54. x + 3y = 54 x + y = 30; subtract the 1st equation from the 2nd equation, eliminate x ------------ 2y = 24 y = 12 then x = 30 - 12 = 18 ; : Check solution in the statement "the sum of the greater number and 3 times the lesser number is 54." 18 + 3(12) = 54