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Quadratic_Equations/549931: X^2-13x-12=0 what is x? 1 solutions Answer 358209 by nerdybill(7003)   on 2011-12-22 22:09:47 (Show Source): You can put this solution on YOUR website! X^2-13x-12=0 Since you can't factor, you can apply the "quadratic formula" to get: x = {13.87, -0.87} . Details of quadratic follows: Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=217 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 13.8654599313281, -0.865459931328117. Here's your graph:

Miscellaneous_Word_Problems/549902: Working together, Pat, Lindsay, and Robin can dig a drainage ditch in 2 hours. Working alone, Robin can do it in 6 hours, while Pat can do it 2 1/4 hours faster than Lindsay. How long will it take Lindsay to dig the ditch by herself? 1 solutions Answer 358206 by nerdybill(7003)   on 2011-12-22 22:08:00 (Show Source): You can put this solution on YOUR website! Working together, Pat, Lindsay, and Robin can dig a drainage ditch in 2 hours. Working alone, Robin can do it in 6 hours, while Pat can do it 2 1/4 hours faster than Lindsay. How long will it take Lindsay to dig the ditch by herself? . Let x = time (hours) it takes Lindsay then x - 2.25 = time it takes Pat . 2(1/6 + 1/x + 1/(x-2.25)) = 1 multiplying both sides by 6x(x-2.25): 2(x(x-2.25) + 6(x-2.25) + 6x) = 6x(x-2.25) 2(x^2-2.25x + 6x-13.5 + 6x) = 6x^2-13.5 2(x^2+9.75x-13.5) = 6x^2-13.5 2x^2+19.5x-27 = 6x^2-13.5 19.5x-27 = 4x^2-13.5 -27 = 4x^2-19.5x-13.5 0 = 4x^2-19.5x+13.5 applying the quadratic formula we get: x = {4.04, 0.84} toss out the .84 solution (extraneous) leaving: x = 4 hours (Lindsay's time) . Details of quadratic follows: Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=164.25 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4.03950070224704, 0.835499297752963. Here's your graph:

Average/549570: inverse h(x)=9x-4 1 solutions Answer 357859 by nerdybill(7003)   on 2011-12-21 11:22:43 (Show Source): You can put this solution on YOUR website! h(x)=9x-4 replace h(x) with a y: y=9x-4 switch x's and y's: x=9y-4 solve for y: x=9y-4 x+4=9y x/9 + 4/9= y . Therefore the inverse of: h(x)=9x-4 is h^(-1)(x)=x/9 + 4/9

test/549558: what is the new answer if you round $88.8888 to the nearest cent?? 1 solutions Answer 357857 by nerdybill(7003)   on 2011-12-21 11:06:28 (Show Source): You can put this solution on YOUR website! what is the new answer if you round $88.8888 to the nearest cent?? it would be: $88.89

Miscellaneous_Word_Problems/549569: Valley View College has 15% more students this year then 5 years ago. Total students enrolled is 2415. How many were enrolled 5 years ago? 1 solutions Answer 357856 by nerdybill(7003)   on 2011-12-21 11:04:56 (Show Source): You can put this solution on YOUR website! Valley View College has 15% more students this year then 5 years ago. Total students enrolled is 2415. How many were enrolled 5 years ago? . Let x = number enrolled 5 years ago then x + .15x = 2415 x(1 + .15) = 2415 x(1.15) = 2415 x = 2415/1.15 x = 2100

Mixture_Word_Problems/549564: lilly and wilma working together can complete a job in 1 and 1/3 hours. if it takes lilly working alone 2 hours less than wilma to do the job, find the time inquired by each woman working alone. 1 solutions Answer 357855 by nerdybill(7003)   on 2011-12-21 11:02:58 (Show Source): You can put this solution on YOUR website! lilly and wilma working together can complete a job in 1 and 1/3 hours. if it takes lilly working alone 2 hours less than wilma to do the job, find the time inquired by each woman working alone. . 1 and 1/3 hours = 1 + 1/3 = 3/3 + 1/3 = 4/3 hours . Let x = time (hours) it takes Wilma to do the job then x-2 = time (hours) it takes Lilly to do the job . (4/3)(1/x + 1/(x-2)) = 1 multiplying both sides by 3: 4(1/x + 1/(x-2)) = 3 multiplying both sides by x(x-2): 4((x-2) + x) = 3x(x-2) 4(2x-2) = 3x^2-6x 8x-8 = 3x^2-6x -8 = 3x^2-14x 0 = 3x^2-14x+8 0 = 3x^2-12x-2x+8 0 = (3x^2-12x)-(2x-8) 0 = 3x(x-4)-2(x-4) 0 = (x-4)(3x-2) x = {2/3, 4} We can toss out the 2/3 (extraneous) because it doesn't make sense leaving x = 4 hours (Wilma) . Lilly: x-2 = 4-2 = 2 hours

Travel_Word_Problems/549520: Does a race car driving around a track at 240 km/h have a constant velocity? 1 solutions Answer 357817 by nerdybill(7003)   on 2011-12-21 08:00:20 (Show Source): You can put this solution on YOUR website! Does a race car driving around a track at 240 km/h have a constant velocity? NO "Velocity" is a vector measurement of the rate AND direction of motion. Since the car has to turn to stay on the track, the "direction" of motion will change.

logarithm/549397: I'm completely done with my assignment, But i'm on my last question and it's a critical thinking question. It says, 2(log 2x - log y)-(log 3 + 2log 5). I got told the answer is: log 4x^2/75y^2 but i don't know how to work it out and explain my work. It's a difficult question and if you could help me that would be great. Thanks for your help. 1 solutions Answer 357712 by nerdybill(7003)   on 2011-12-20 17:52:23 (Show Source): You can put this solution on YOUR website! I'm completely done with my assignment, But i'm on my last question and it's a critical thinking question. It says, 2(log 2x - log y)-(log 3 + 2log 5). I got told the answer is: log 4x^2/75y^2 but i don't know how to work it out and explain my work. It's a difficult question and if you could help me that would be great. Thanks for your help. You need to apply "log rules": 2(log 2x - log y)-(log 3 + 2log 5) distribute the 2 and remove parentheses: 2log 2x - 2log y-log 3 - 2log 5 multiplier of a log can be thought of as an exponent: log(2x)^2 - logy^2 - log(3) - log 5^2 subtraction can be thought of as division: log(4x^2) - logy^2 - log(3) - log 25 log(4x^2)/y^2 - log(3) - log 25 log(4x^2)/3y^2 - log 25 log(4x^2)/(75y^2)

Square-cubic-other-roots/549333: Perform the indicated operations and simplify: . 1 solutions Answer 357655 by nerdybill(7003)   on 2011-12-20 12:27:30 (Show Source): You can put this solution on YOUR website!

logarithm/548913: how do i solve: log (base 2) 8^x = -3 1 solutions Answer 357275 by nerdybill(7003)   on 2011-12-18 21:50:48 (Show Source): You can put this solution on YOUR website! log (base 2) 8^x = -3 we can rewrite as: log (base 2) (8)^x = -3 log (base 2) (2^3)^x = -3 log (base 2) 2^(3x) = -3 3x = -3 x = -1

Exponents/548787: What would be the answers to this question, 9m^3=81m Im pretty sure I need three different answers for it. 1 solutions Answer 357209 by nerdybill(7003)   on 2011-12-18 17:35:23 (Show Source): You can put this solution on YOUR website! 9m^3=81m move terms to one side: 9m^3 - 81m = 0 factor left: 9m(m^2 - 9) = 0 9m(m^2 - 3^2) = 0 9m(m-3)(m+3) = 0 solution: m = {-3, 0, 3}

Quadratic_Equations/548620: REPRESENT THE GIVEN SITUATION IN THE FORM OF QUADRATIC EQUATION- THE HYPOTENUSE OF A RIGHT TRIANGLE IS 1M LESS THAN TWICE THE SHORTEST SIDE.IF THE THIRD SIDE IS 1M MORE THAN THE SHORTEST SIDE. 1 solutions Answer 357124 by nerdybill(7003)   on 2011-12-18 11:21:29 (Show Source): You can put this solution on YOUR website! REPRESENT THE GIVEN SITUATION IN THE FORM OF QUADRATIC EQUATION- THE HYPOTENUSE OF A RIGHT TRIANGLE IS 1M LESS THAN TWICE THE SHORTEST SIDE.IF THE THIRD SIDE IS 1M MORE THAN THE SHORTEST SIDE. . Let x = length of shortest side then 2x-1 = hypotenuse x+1 = third side . applying Pythagorean theorem: x^2 + (x+1)^2 = (2x-1)^2 x^2 + (x+1)(x+1) = (2x-1)(2x-1) x^2 + x^2+2x+1 = 4x^2-4x+1 2x^2+2x+1 = 4x^2-4x+1 2x+1 = 2x^2-4x+1 1 = 2x^2-6x+1 0 = 2x^2-6x 0 = x^2-3x (this is what they're looking for)

logarithm/548631: 15. A can of soda at 90° F. is placed in a refrigerator that maintains a constant temperature of 36° F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by T(t) = 36 + 54 e^(– 0.058) t Find the temperature of the soda 12 minutes after it is placed in the refrigerator. (Round to the nearest degree.) 1 solutions Answer 357123 by nerdybill(7003)   on 2011-12-18 11:17:04 (Show Source): You can put this solution on YOUR website! T(t) = 36 + 54 e^(– 0.058) t I believe you meant the 't' to be part of the exponent: T(t) = 36 + 54 e^(– 0.058t) . substitute 12 for t and solve: T(12) = 36 + 54 e^(– 0.058*12) T(12) = 36 + 54 e^(– 0.696) T(12) = 36 + 54(.4986) T(12) = 36 + 29.9 T(12) = 62.9 rounding: T(12) = 63 degrees

Polynomials-and-rational-expressions/548331: Factor completely: 6a^2b-12a^3b^2+36ab 1 solutions Answer 356906 by nerdybill(7003)   on 2011-12-16 19:04:33 (Show Source): You can put this solution on YOUR website! 6a^2b-12a^3b^2+36ab factor out a 6: 6(a^2b-2a^3b^2+6ab) factor out an 'a': 6a(ab-2a^2b^2+6b) factor out an 'b': 6ab(a-2a^2b+6)

Quadratic_Equations/548218: Write a quadratic function in standard form with zeros 6 and -8? 1 solutions Answer 356796 by nerdybill(7003)   on 2011-12-16 09:28:08 (Show Source): You can put this solution on YOUR website! Write a quadratic function in standard form with zeros 6 and -8? A zero at 6 means a factor of (x-6) A zero at -8 means a factor of (x+8) . the function must then be: (x-6)(x+8) x^2+8x-6x-48 x^2+2x-48

Mixture_Word_Problems/548187: A container has 6 liters of a 40% solution of alcohol in it. How much pure alcohol should be added to raise it to a 60% solution. I have a test today and i dont understand mixture problems very well and i was hoping you could be my lifesaver and help me learn this before i have to go to school :) 1 solutions Answer 356765 by nerdybill(7003)   on 2011-12-16 06:27:50 (Show Source): You can put this solution on YOUR website! A container has 6 liters of a 40% solution of alcohol in it. How much pure alcohol should be added to raise it to a 60% solution. . Let x = amount (liters) of pure (100%) alcohol then "amt added" + "amt of alcohol at star" = "new percentage" x + .40(6) = .60(x+6) x + 2.4 = .60x+3.6 .40x + 2.4 = 3.6 .40x = 1.4 x = 1.4/.40 x = 3.5 liters

Rational-functions/548030: who do i solve x^2+9x+8=0 1 solutions Answer 356680 by nerdybill(7003)   on 2011-12-15 19:27:30 (Show Source): You can put this solution on YOUR website! x^2+9x+8=0 factoring the left side: (x+1)(x+8) = 0 x = {-1, -8}

Rectangles/547972: Hey, Im stuck on this one question for HOMEWORK, so I would like if this would be answered ASAP. the question is: The length of a rectangle is ten less than three times its width. If the width is increased by five and the length is increased by two, then the perimeter of the new rectangle is 90cm. Find the dimensions of the original rectangle. 1 solutions Answer 356667 by nerdybill(7003)   on 2011-12-15 18:11:21 (Show Source): You can put this solution on YOUR website! The length of a rectangle is ten less than three times its width. If the width is increased by five and the length is increased by two, then the perimeter of the new rectangle is 90cm. Find the dimensions of the original rectangle. . Let x = width then 3x-10 = length . width increased by 5: x+5 length increased by 2: 3x-10+2 = 3x-8 . 2(x+5 + 3x-8) = 90 2(4x+5-8) = 90 2(4x-3) = 90 4x-3 = 45 4x = 48 x = 14 cm (width) . Length: 3x-10 = 3(14)-10 = 42-10 = 32 cm . Dimensions: 14 cm by 32 cm

Polynomials-and-rational-expressions/547661: Factor: 30x^2y+5xy-10y 1 solutions Answer 356467 by nerdybill(7003)   on 2011-12-15 00:40:07 (Show Source): You can put this solution on YOUR website! 30x^2y+5xy-10y 5(6x^2y+xy-2y) 5y(6x^2+x-2) 5y(6x^2-3x+4x-2) 5y(6x^2-3x)+(4x-2) 5y[3x(2x-1)+2(2x-1)] 5y(2x-1)(3x+2)

Rate-of-work-word-problems/547216: Ben can paint a fence in 3 hours and Billy takes 4 hours. How long will it take them to painting together 1 solutions Answer 356293 by nerdybill(7003)   on 2011-12-14 11:59:58 (Show Source): You can put this solution on YOUR website! Ben can paint a fence in 3 hours and Billy takes 4 hours. How long will it take them to painting together . Let x = time (hours) it takes for both then x(1/3 + 1/4) = 1 multiplying both sides by 12: x(4 + 3) = 12 x(7) = 12 x = 12/7 x = 1.71 hours or x = 1 hour and 43 minutes

Triangles/547097: The shorter leg of a right triangle is 17cm less than the longer leg.. If the hypotenuse is 25ch long,find the perimeter of the triangle 1 solutions Answer 356234 by nerdybill(7003)   on 2011-12-14 07:43:07 (Show Source): You can put this solution on YOUR website! The shorter leg of a right triangle is 17cm less than the longer leg.. If the hypotenuse is 25ch long,find the perimeter of the triangle Let x = longer leg then x-17 = shorter leg . Applying Pythagorean theorem: x^2 + (x-17)^2 = 25^2 x^2 + (x-17)(x-17) = 25^2 x^2 + x^2-34x+289 = 625 2x^2-34x+289 = 625 2x^2-34x-336 = 0 x^2-17x-168 = 0 (x+7)(x-24) = 0 x = {-7, 24} throw out the negative solution leaving: x = 24 cm (longer leg) . shorter leg: x-17 = 24-17 = 7 cm . perimeter = 24+7+25 = 56 cm

logarithm/547117: log (2+x)-log (x-4)=log 3 1 solutions Answer 356232 by nerdybill(7003)   on 2011-12-14 07:34:34 (Show Source): You can put this solution on YOUR website! log (2+x)-log (x-4)=log 3 log (2+x)/(x-4)=log 3 (2+x)/(x-4) = 3 (2+x) = 3(x-4) 2+x = 3x-12 2 = 2x-12 14 = 2x 7 = x

Equations/546722: Please help me solve: What is the slope-intercept form of the line passing through the point (-8,-3) and parallelt to the line 5x+6y=-9 1 solutions Answer 356076 by nerdybill(7003)   on 2011-12-13 15:43:53 (Show Source): You can put this solution on YOUR website! What is the slope-intercept form of the line passing through the point (-8,-3) and parallelt to the line 5x+6y=-9 First, determine slope of: 5x+6y=-9 by rearranging into "slope-intercept" form of y = mx + b . 5x+6y=-9 6y = -5x-9 y = (-5/6)x - (9/6) y = (-5/6)x - 3/2 slope is (-5/6) . plug slope and point (-8, -3) into "point-slope" form: y - y1 = m(x - x1) y - (-3) = (-5/6)(x - (-8)) y + 3 = (-5/6)(x + 8) y + 3 = (-5/6)x + (-5/6)8 y + 3 = (-5/6)x - 40/6 y + 3 = (-5/6)x - 20/3 y = (-5/6)x - 20/3 - 3 y = (-5/6)x - 20/3 - 9/3 y = (-5/6)x - 29/3 (this is what they're looking for)

Functions/546501: what is the domain of a rational function when the denominator cannot be zero.i.e, (x^3+1)/(x^2+2x) 1 solutions Answer 356031 by nerdybill(7003)   on 2011-12-13 09:26:01 (Show Source): You can put this solution on YOUR website! what is the domain of a rational function when the denominator cannot be zero.i.e, (x^3+1)/(x^2+2x) . Find values that would make the denominator zero: x^2+2x = 0 x(x+2) = 0 x = {-2, 0} (values that x can't take) . Therefore, the domain is ALL numbers except {-2, 0} . You can specify this by: (-oo, -2) U (-2, 0) U (0, +oo) where oo represents infinity

Numbers_Word_Problems/546527: Six times a number decreased by ten is eight. Find the number. 1 solutions Answer 356027 by nerdybill(7003)   on 2011-12-13 09:20:23 (Show Source): You can put this solution on YOUR website! Six times a number decreased by ten is eight. Find the number. . Let x = the number then 6x - 10 = 8 6x = 18 x = 18/3 x = 6

Angles/546518: The measure of one complementary angle is six times as large as the measure of the second angle. What is the measure of each angle? 1 solutions Answer 356026 by nerdybill(7003)   on 2011-12-13 09:19:04 (Show Source): You can put this solution on YOUR website! The measure of one complementary angle is six times as large as the measure of the second angle. What is the measure of each angle? If two angles are complementary, the sum must be 90 degrees . Let x = smaller angle then 6x = larger angle . x + 6x = 90 7x = 90 x = 90/7 degrees (smaller angle) 0r, approximately 12.86 degrees . Larger angle: 6x = 6(90/7) = 540/7 degrees (larger angle) 0r, approximately 77.14 degrees

Polynomials-and-rational-expressions/546529: The map scale for Figure A is 1½ inches represents 315 miles. If the cities of Briar Patch and Sharpstown measure 2¾ inches apart (as the crow flies) on the map, how far would this be on the earth’s surface? Let m represent the number of miles between the two cities. Round to the nearest tenth of a mile if necessary. 1 solutions Answer 356025 by nerdybill(7003)   on 2011-12-13 09:14:10 (Show Source): You can put this solution on YOUR website! The map scale for Figure A is 1½ inches represents 315 miles. If the cities of Briar Patch and Sharpstown measure 2¾ inches apart (as the crow flies) on the map, how far would this be on the earth’s surface? Let m represent the number of miles between the two cities. Round to the nearest tenth of a mile if necessary. . From::"The map scale for Figure A is 1½ inches represents 315 miles." that's 315 miles per 1.5 inches or 315/1.5 miles/inch . m = 2.75(315/1.5) m = 2.75(210) m = 577.5 miles

Triangles/546524: the two perpendicular sides of a triangle are 4 and 8. what is the length of the third side 1 solutions Answer 356024 by nerdybill(7003)   on 2011-12-13 09:10:09 (Show Source): You can put this solution on YOUR website! the two perpendicular sides of a triangle are 4 and 8. what is the length of the third side Since "two sides are perpendicular", it must be a "right triangle" -- you can now apply Pythagorean theorem: Let x = third side then (exact answer) OR (approximate answer)

Inverses/546519: 3x+7x-5=15 what is x alone? 1 solutions Answer 356022 by nerdybill(7003)   on 2011-12-13 09:04:25 (Show Source): You can put this solution on YOUR website! 3x+7x-5=15 add 5 to both sides: 3x+7x-5 +5 = 15 +5 3x+7x = 20 10x = 20 divide both sides by 10: x = 2

Systems-of-equations/546395: A chemist wants to make 40 liters of 22.5% acid solution. She is going to make it by mixing a 10% acid and a 30% acid solution. How many liters of each will she need? 1 solutions Answer 355962 by nerdybill(7003)   on 2011-12-12 22:46:36 (Show Source): You can put this solution on YOUR website! A chemist wants to make 40 liters of 22.5% acid solution. She is going to make it by mixing a 10% acid and a 30% acid solution. How many liters of each will she need? . Let x = amount (liters) of 10% acid then 40-x = amount (liters) of 30% acid . .10x + .30(40-x) = .225(40) .10x + 12-.30x = 9 12-.20x = 9 12 = 9+.20x 3 = .20x 3/.20 = x 15 liters = x (amount of 10% acid) . Amount of 30% acid: 40-x = 40-15 = 25 liters

Travel_Word_Problems/545499: MOTION PROBLEMS Can you please help me solve this problem: An airplane flew for 4 hours with a 20-km/h tail wind. The return flight against the same wind took 5 hours. Find the speed of the plane in still air. 1 solutions Answer 355603 by nerdybill(7003)   on 2011-12-11 17:29:43 (Show Source): You can put this solution on YOUR website! An airplane flew for 4 hours with a 20-km/h tail wind. The return flight against the same wind took 5 hours. Find the speed of the plane in still air. . Let x = speed of plane in still air then from distance formula: 4(x+20) = 5(x-20) 4x+80 = 5x-100 80 = x-100 180 km/hr = x