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 Polynomials-and-rational-expressions/229231: I'm stuck on a problem. directions tell me to factor the polynomial. x^3 + 1 I would be very grateful for any help that you may give me. Thank you, Mike1 solutions Answer 169980 by ankor@dixie-net.com(15656)   on 2009-10-20 15:42:46 (Show Source): You can put this solution on YOUR website!factor the polynomial. x^3 + 1 : You should recognize this as "the sum of cubes", which factors as (a^3 + b^3) = (a + b) (a^2 - ab + b^2) : In this problem a = x, and b = 1 (1^3 = 1) x^3 + 1 = (x + 1) (x^2 - x + 1) : : You can prove this to yourself: let x = 2 2^3 + 1 = 8 + 1 = 9 and (2 + 1) (2^2 - 2 + 1) 3 * (4 - 2 + 1) 3 * 3 = 9 also
 Polynomials-and-rational-expressions/229227: If a rock is thrown upward at a speed of 64 ft/sec and over the edge of a cliff 80 feet above a river, its heights h after t seconds is given by the equation . After how many seconds will it hit the water (h=0)? Solve by factoring the polynomial, using the Zero Factor Property, then solving the linear equations.1 solutions Answer 169979 by ankor@dixie-net.com(15656)   on 2009-10-20 15:33:31 (Show Source): You can put this solution on YOUR website! After how many seconds will it hit the water (h=0)? : = 0 normal form = 0 Factor out -16, simplifies and changes the signs -16(t^2 - 4t - 5) = 0 Factors to -16(t - 5)(t + 1) = 0 The positive solution t - 5 = 0 t = +5 sec to hit the water ; : prove this to yourself h = 80 + 320 - 16(25) h = 400 - 400 h = 0
 Functions/229228: if x+y=1, and x-y=1, then y = ?1 solutions Answer 169978 by ankor@dixie-net.com(15656)   on 2009-10-20 15:22:16 (Show Source): You can put this solution on YOUR website!Obviously y has to = 0, however prove it with elimination : x + y = 1 x - y = 1, -------------Subtraction eliminates x and gives us y 0 + 2y = 0 y = 0
 Angles/229211: Please explain the steps this confuses me. I understand what supplementary means and complementary whats confusing me is how to get an equation out of this: angle AFB is 2 times its supplement. Find angle A's complement. 1 solutions Answer 169977 by ankor@dixie-net.com(15656)   on 2009-10-20 14:58:14 (Show Source): You can put this solution on YOUR website!When two angles are complimentary, they add up to 90 For example, an angle of 35 degrees, it's complement is: 90-35 = 55 degrees just like When two angles are supplementary, they add up to 180 The supplement of 35 degrees, 180 - 35 = 145 degrees : Angle AFB is 2 times its supplement. : Let angle AFB = x x = 2(180 - x) x = 360 - 2x x + 2x = 360 3x = 360 x = 360/3 x = 120 degrees is angle AFB : Find angle A's complement. I am not sure what they mean by "angle A" here! Anyway: 90 - A = Angle A's complement
 Miscellaneous_Word_Problems/228828: Anyone have any idea of how to solve this: The volume of a cube with the side length x is V(x)=x^3. Find the rate of change of volume with respect to the side length if the surface area is 54cm^2.1 solutions Answer 169974 by ankor@dixie-net.com(15656)   on 2009-10-20 14:43:59 (Show Source): You can put this solution on YOUR website!The volume of a cube with the side length x is V(x)=x^3. Find the rate of change of volume with respect to the side length if the surface area is 54cm^2. : We know the surface area of a cube = 6x^2 (total area of the six sides) 6x^2 = 54 x^2 = x^2 = 9 x = 3 : Vol = x^2 V = 3^3 V = 27 cu/cm : We can say the relationship = = (where x = 1 side) : : See if this is true Let v = 125 cu/cm x^3 = 125 x = x = 5 cm : Find the surface area SA = 6(5^2) SA = 6(25) SA = 150 : =
 Geometry_Word_Problems/229192: Given the volume of a box equals 72 cubic inches, the height of the box equals the width of the box, and the length is five more than the width, find the height of the box.1 solutions Answer 169968 by ankor@dixie-net.com(15656)   on 2009-10-20 13:26:23 (Show Source): You can put this solution on YOUR website!Given the volume of a box equals 72 cubic inches, the height of the box equals the width of the box, and the length is five more than the width, find the height of the box. : Let x = the width and the height and 5x = the length : Volume = L * W * H = 72 cu/in : 5x * x * x = 72 5x^3 = 72 x^3 = x^3 = 14,4 x = x ~ 2.4329 inches is the height ; : Check solution on a calc: enter 2.4329 * 2.4329 * 5(2.4329) = 72.00
 Unit_Conversion_Word_Problems/229149: The average distance between the earth and the sun is 93 million miles. Using the velocity of light, find an approximate value for the amount of time it takes a light ray to travel from the sun to the earth. Please help and thank you.1 solutions Answer 169965 by ankor@dixie-net.com(15656)   on 2009-10-20 12:58:02 (Show Source): You can put this solution on YOUR website!The average distance between the earth and the sun is 93 million miles. Using the velocity of light, find an approximate value for the amount of time it takes a light ray to travel from the sun to the earth. : Using accepted value for the speed of light, 186,000 mi/sec : = 500 sec which is 8 min 20 sec
 Complex_Numbers/229103: Express in a+bi form 3-6i/-4i1 solutions Answer 169928 by ankor@dixie-net.com(15656)   on 2009-10-20 08:26:11 (Show Source): You can put this solution on YOUR website! multiply * = = = We can write it like this and reduce the fraction + = + Write it: 1.5 + .75i
 test/228995: this is long division; (-30+6y^3-28y+y^2)divided by (2y-5)1 solutions Answer 169878 by ankor@dixie-net.com(15656)   on 2009-10-19 21:57:54 (Show Source): You can put this solution on YOUR website!Do it a lot like ordinary long division; (-30+6y^3-28y+y^2) divided by (2y-5) Put it the degrees in descending order (use.... to keep things lined up : ..........................3y^2 + 8y + 6 .............--------------------- (2y-5)|6y^3 + y^2 - 28y - 30; choose a value, that, when mult by the divisor = the 1st term ..............6y^3 - 15y^2 ...........--------------- ...........................16y^2 - 28y ...........................16y^2 - 40y ...........................------------ .........................................12y - 30 .........................................12y - 30 ........------------------------------------------ ................................................0 remainder : Study this carefully and it will make sense to you.
 Unit_Conversion_Word_Problems/228962: Hi all I have been doing pretty good lately Until Now!! I need help with writing the problem in a simplified radical form. Assume that all variables represent positive real numbers. And I have no idea how to write the v------- type thing. Except it is a solid line and not quite a v at the begining. Does anyone no what I am talking about? Square root symbol maybe? These are under the line of the 'square root symbol" there is nothing on the left side of the symbol. And the 11 and the 2 are 'to the power numbers.' 12t11 u2 I have no idea if anyone will even understand this but if you do please help me. Thank you very much!! 1 solutions Answer 169869 by ankor@dixie-net.com(15656)   on 2009-10-19 21:39:34 (Show Source): You can put this solution on YOUR website!Assume you mean: : Factor to reveal perfect squares : Extract these square roots from the radical
 Equations/228973: 6x-7= 2x=29 My teach helped me to understand this. I got an answer of x=9. My teacher actually did the work for me and I have a test tomorrow. I don't want to fail! I still don't understand it. Please help my by tomorrow! Thanks!~1 solutions Answer 169853 by ankor@dixie-net.com(15656)   on 2009-10-19 21:23:13 (Show Source): You can put this solution on YOUR website!6x - 7 = 2x + 29 : We want to perform operations on both sides of the equation to get the variable (x) on one side by itself, usually the left side ; Add 7 to both sides 6x - 7 + 7 = 2x + 29 + 7 so we have 6x = 2x + 36 : Subtract 2x from both sides 6x - 2x = 2x - 2x + 36 we have 4x = 36 : Divide both sides by 4 = we have x = 9 ; ; Confirm your answer by replacing x with 9 in the original problem 6x - 7 = 2x + 29 6(9) - 7 = 2(9) + 29 54 - 7 = 18 + 29 47 = 47; confirms our solution
 Mixture_Word_Problems/228894: Dan is 1/6 his father's age. In 4 years, Dan will be 1/4 his fathers age. what is Dan's age?1 solutions Answer 169813 by ankor@dixie-net.com(15656)   on 2009-10-19 20:00:54 (Show Source): You can put this solution on YOUR website!Dan is 1/6 his father's age. d = f or f = 6d : In 4 years, Dan will be 1/4 his fathers age. d + 4 = (f+4) : what is Dan's age? : Replace f with 6d in the last equation d + 4 = (6d + 4) Multiply both sides by 4 4(d + 4) = 6d + 4 : 4d + 16 = 6d + 4 : 16 - 4 = 6d - 4d : 12 = 2d : d = 6 yrs is Dan's age ; : Check solution: f = 6(6) = 36 "In 4 years, Dan will be 1/4 his fathers age." 6 + 4 = 1/4 * 36 + 4
 Polynomials-and-rational-expressions/228908: How would you factor: 4u^4v^2+4u^2v+11 solutions Answer 169812 by ankor@dixie-net.com(15656)   on 2009-10-19 19:51:43 (Show Source): You can put this solution on YOUR website!How would you factor: Factor it like a quadratic equation
 Linear_Algebra/228736: What is 2x-y+z=14 -x+2y-4z=5 x+4y-6z=-1 This is solve the system using the elimination method get the x,y, and z please help this is hard.1 solutions Answer 169791 by ankor@dixie-net.com(15656)   on 2009-10-19 18:51:16 (Show Source): You can put this solution on YOUR website!2x - y + z = 14 -x+ 2y -4z = 5 x + 4y -6z =-1 : You're right this is a pain! : Add the 2nd and 3rd equations, to eliminate x -x+ 2y -4z = 5 x + 4y -6z =-1 -----------------adding eliminates x 0 + 6y - 10z = 4 Simplify, divide by 2 3y - 5z = 2 : Multiply the 2nd equation by 2 and add to the 1st equation 2x - y + z = 14 -2x+ 4y -8z = 10 -----------------addition eliminates x again 0 + 3y - 7z = 24 : Two 2 unknown equation to deal with now : Subtract 3y - 5z = 2 from the above equation 3y - 7z = 24 3y - 5z = 2 ---------------subtraction eliminates y, find z 0 - 2z = 22 -2z = 22 z = z = -11 : find y using the equation 3y - 5z = 2 3y - 5(-11) = 2 3y + 55 = 2 3y = 2 - 55 3y = -53 y = y = -17.667 : Find x using the 1st equation 2x - y + z = 14 2x - (-17) - 11 = 14 2x + 17 - 11 = 14 2x + 6 = 14 2x = 14 - 6.667; go to decimals here 2x = 7.333 x = 3.667 ; : It's kind of disgusting they give you a problem that doesn't have integer solutions. I checked this using the matrix feature on my TI83, so I think it's right
 Linear-systems/228772: Hello, Im in Gr.10. Solving Problems dealing with linear systems: (I need to make an equation then solve) 1) A school athletic council sold 835 tickets to the championship football game for a total of \$5792. Students pay \$4 and nonstudents pay \$8. How many nonstudents attended the game?1 solutions Answer 169751 by ankor@dixie-net.com(15656)   on 2009-10-19 16:18:01 (Show Source): You can put this solution on YOUR website!1) A school athletic council sold 835 tickets to the championship football game for a total of \$5792. Students pay \$4 and nonstudents pay \$8. How many nonstudents attended the game? : Let x = no. of non-students Total ticket were given as 835, therefore (835-x) = no. of students : The total\$ equation 8x + 4(835-x) = 5792 8x + 3340 - 4x = 5972; multiply what's inside the brackets 8x - 4x = 5972 - 3340 4x = 2632 x = ; divide both sides by 4 x = 658 non-students ; ; Check our solution 835 - 658 = 177 students 8(658) + 4(177) = 5264 + 708 = 5972; confirms our solution : : Did this make sense to you?
 Rate-of-work-word-problems/228633: In testing the rate at which a polluted stream flows, a boat that travels 5.5mi/hr in still water took 5 hrs to go down stream and 8 hrs to go upstream, between 2 points. what is the rate of flow of the stream1 solutions Answer 169750 by ankor@dixie-net.com(15656)   on 2009-10-19 16:07:03 (Show Source): You can put this solution on YOUR website!a boat that travels 5.5mi/hr in still water took 5 hrs to go down stream and 8 hrs to go upstream, between 2 points. what is the rate of flow of the stream : Let r = rate of flow of the stream then (5.5 + r) = boat speed down stream and (5.5 - r) = boat speed up stream : Write a distance equation, distance is the same for both trips Dist = speed * time : dist down = dist up 5(5.5 + r) = 8(5.5 - r) : 27.5 + 5r = 44 - 8r : 5r + 8r = 44 - 27.5 : 13r = 16.5 r = r ~ 1.27 mi/hr (flow of the stream) ; ; See if this is true; find the dist of each (should be equal) 5(5.5 + 1.27) = 33.8 mi 8(5.5 - 1.27) = 33.8 mi
 Numbers_Word_Problems/228746: I am thibking of a three digit number. It is an odd multiple of three, and the product of its digits is 24. It is larger than 15 squared. What are the five numbers I could be thinking of?1 solutions Answer 169745 by ankor@dixie-net.com(15656)   on 2009-10-19 15:46:55 (Show Source): You can put this solution on YOUR website!I am thinking of a three digit number. It is an odd multiple of three, and the product of its digits is 24. It is larger than 15 squared. What are the five numbers I could be thinking of? ; The three digits whose product is 24 2 * 2 * 6 = 24; all even 2 * 3 * 4 = 24 1 * 3 * 8 = 24 : Odd multiple of three, last digit has to be odd Greater than 225 (15^2) : 243, 423, 381, 831, 813 would be the 5 numbers
 Numbers_Word_Problems/228547: What is the consecutive number of which 4 over 7 of the sum of first and second equals the third numbers decrease by 1?1 solutions Answer 169738 by ankor@dixie-net.com(15656)   on 2009-10-19 15:01:52 (Show Source): You can put this solution on YOUR website!What is the consecutive number of which 4 over 7 of the sum of first and second equals the third numbers decrease by 1? : Three consecutive numbers: x, (x+1), (x+2) : (x + (x+1)) = (x+2) - 1 (2x+1) = (x + 1) Multiply both sides by 7 4(2x + 1) = 7(x + 1) : 8x + 4 = 7x + 7 8x - 7x = 7 - 4 x = 3 ; Numbers are: 3, 4, 5 ; : See if that works in the statement: "4/7 of the sum of first and second equals the third numbers decrease by 1" (3+4) = (5) - 1 (7) = 4 4 = 4
 Rectangles/228677: The length of a rectangle is three less than twice its width. If the length is increased by 3 and the width is decreased by 1, a new rectangle is formed whose area is 5 more than the original rectangle. Find: a) The dimensions of the original rectangle. b) The area of the new rectangle. 1 solutions Answer 169730 by ankor@dixie-net.com(15656)   on 2009-10-19 14:46:57 (Show Source): You can put this solution on YOUR website!The length of a rectangle is three less than twice its width. If the length is increased by 3 and the width is decreased by 1, a new rectangle is formed whose area is 5 more than the original rectangle. Find: a) The dimensions of the original rectangle. Let x = the width then (2x-3) = the length and A = x(2x-3) A = 2x^2 - 3x; area of original ; b) The area of the new rectangle. (x-1) = the width of the new rectangle and (2x-3) + 3 = 2x; length of the new rectangle and A = 2x(x-1) A = 2x^2 - 2x; area of new : "new rectangle is formed whose area is 5 more than the original rectangle. New area - old area = 5 2x^2 - 2x - (2x^2 - 3x) = 5 2x^2 - 2x - 2x^2 + 3x = 5 2x^2 - 2x^2 - 2x + 3x = 5 x = 5 units, original width then 2(5) - 3 = 7 units, original length and 5 - 1 = 4 units, new width then 2(5) = 10 units, new length ; ; Check solution using the area statement new area - original area 10*4 - 7*5 = 5
 Numbers_Word_Problems/228697: Find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 7 times the third.1 solutions Answer 169706 by ankor@dixie-net.com(15656)   on 2009-10-19 13:41:31 (Show Source): You can put this solution on YOUR website!Three positive consecutive integers: x, (x+1), (x+2) : Find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 7 times the third. : x(x+2) - (x+1) = 7(x+2) + 1 : x^2 + 2x - x - 1 = 7x + 14 + 1 : x^2 + x - 1 = 7x + 15 : Combine like terms on the left: x^2 + x - 7x - 1 - 15 = 0 : x^2 - 6x - 16 = 0; our old friend, the quadratic equation! Factors to (x - 8)(x + 2) = 0 We only want the positive solution in this problem x = 8, is the 1st integer, then 9, 10; obviously. ; : Check our solution in the statement: "the product of the first and third, minus the second, is 1 more than 7 times the third. " 8*10 - 9 = 7*10 + 1 80 - 9 = 70 + 1; confirms our solution
 Mixture_Word_Problems/228403: A mixture of 10% acid and 90% water is added to 5 liters of pure acid. the final mixture is 40% water . How many liters of water are in the final mixture? thanks1 solutions Answer 169703 by ankor@dixie-net.com(15656)   on 2009-10-19 13:30:08 (Show Source): You can put this solution on YOUR website!A mixture of 10% acid and 90% water is added to 5 liters of pure acid. The final mixture is 40% water. How many liters of water are in the final mixture? : Let x = amt of acid/water mixture added ; Write an amt of water equation .90x = .40(x + 5) .90x = .40x + 2 .9x - .4x = 2 .5x = 2 x = x = 4 liters of 90% water mixture added to the 5 liters of pure acid : Find the amt of water in the final mixture w = .4(4+5) w = .4(9) w = 3.6 liters is water in the final mixture
 Square-cubic-other-roots/228591: Can someone please please help me with these questions. I am preparing for a quiz on Monday. 1) z sqrt 80zu^2 - u sqrt 5z^3 2) sqrt z +16 = sqrt 7z+12 3) sqrt -6w+16=w 4) sqrt 10+8 / -5 sqrt 10+1 Thank you in advance1 solutions Answer 169700 by ankor@dixie-net.com(15656)   on 2009-10-19 12:44:38 (Show Source): You can put this solution on YOUR website!1) Factor to reveal the perfect squares extract the squares and combine like terms = ; ; 2) Square both sides: z + 16 = 7z + 12 16 - 12 = 7z - z 4 = 6z z = = ; ; 3) square both sides -6w + 16 = w^2 0 = w^2 + 6w - 16 Factors to: (w+8)(w-2) = 0 Two solutions w = -8 w = +2; Check both solutions in the original equation (only one is valid) : : 4) = = =
 Numbers_Word_Problems/228598: The sum of the digits of a three-digit number is 18. The ten's digit is 2 more than the unit's digit. If the digits are reversed, the resulting number is 396 less than the original number. Find the original number.1 solutions Answer 169668 by ankor@dixie-net.com(15656)   on 2009-10-19 09:50:15 (Show Source): You can put this solution on YOUR website!The sum of the digits of a three-digit number is 18. The ten's digit is 2 more than the unit's digit. If the digits are reversed, the resulting number is 396 less than the original number. Find the original number. : Three digits, x & y & z the number: 100x + 10y + z : "The sum of the digits of a three-digit number is 18." x + Y + z = 18 : " The ten's digit is 2 more than the unit's digit. y = z + 2 : "If the digits are reversed, the resulting number is 396 less than the original number." original number - 396 = reversed number 100x + 10y + z - 396 = 100z + 10y + x Group like terms and combine 100x - x + 10y - 10y = 100z - z + 396 99x = 99z + 396 Simplify, divide equation by 99 x = z + 4 : Find the original number. : Using the equation x + y + z = 18, replace y and x (z+4) + (z + 2) + z = 18 3z + 6 = 18 3z = 18 - 6 3z = 12 z = 4 : I'll let you find x and y using the equations derived from the statements Construct the number using 100x + 10y + z, check in last statement Any questions, ankor@att.net
 Geometry_Word_Problems/228492: a clock with a diameter of 23 feet. minute hand is 14ft., hour hand is 9 ft. how much farther does minute hand travel than hr. hand in 24 hours.1 solutions Answer 169662 by ankor@dixie-net.com(15656)   on 2009-10-19 08:31:04 (Show Source): You can put this solution on YOUR website!a clock with a diameter of 23 feet. minute hand is 14ft., hour hand is 9 ft. how much farther does minute hand travel than hr. hand in 24 hours. : Assuming this is a 12 hr clock, I guess they mean how far the tip of each hand travels. : 24 times the circumference of the large hand - 2 times the circumference of the small hand : radius of small hand, 9; long hand 15 : 24() - 2()
 Triangles/228364: What is the area of the largest triangle that can be inscribed in the semicircle shown? One side of the triangle is the 10 unit diameter of the semicircle. Be sure to justify your answer as being the largest area possible.1 solutions Answer 169565 by ankor@dixie-net.com(15656)   on 2009-10-18 20:33:26 (Show Source): You can put this solution on YOUR website!What is the area of the largest triangle that can be inscribed in the semicircle shown? One side of the triangle is the 10 unit diameter of the semicircle. Be sure to justify your answer as being the largest area possible. : This would be an isocoles triangle, the base is the diameter (10) and the height is the radius (5) A = .5*10*5 A = 25 sq units