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 Triangles/218267: hi, im having a bit of trouble with some homework... as usual! th question is: How do you construct a triangle given the length of the hypotenuse and one of the shorter sides? even if you can't answer it then i apreciate you trying! thanks!:)1 solutions Answer 164389 by ankor@dixie-net.com(15649)   on 2009-09-28 12:41:00 (Show Source): You can put this solution on YOUR website!How do you construct a triangle given the length of the hypotenuse and one of the shorter sides? : You should know the Pythagorean theorem: a^2 + b^2 = c^2 where: a and b are the two sides and c is the hypotenuse : A simple example let a = the unknown side let b = 4 let c = 5 : Substitute for b & c and in the equaiton a^2 + 4^2 = 5^2 : a^2 + 16 = 25 : a^2 = 25 - 16; subtracted 16 from both sides : a^2 = 9 : a = a = 3 is the unknown side : Draw the two legs of right triangle and join them, that's it!
 Geometry_Word_Problems/218034: Dalton has a closed rectangular box with a square base at least 10 inches long have a surface area of 900 square inches. what dimensions will give the box a maximum volume?1 solutions Answer 164363 by ankor@dixie-net.com(15649)   on 2009-09-28 09:56:49 (Show Source): You can put this solution on YOUR website!Dalton has a closed rectangular box with a square base at least 10 inches long have a surface area of 900 square inches. what dimensions will give the box a maximum volume? ; Let x = the side of the square base Actually the maximum is when the box is a perfect cube, therefore let x = the height of the box also : Surface area equation, find h: 6x^2 = 900 simplify divide by 6 x^2 = 150 x = x = 12.247" : Max vol: 12.247 by 12.247 by 12.247, and 12.247^3 = 1836.9 cu/in : You can prove this: let the height = h, : Surface area equation, find h: 2x^2 + 4xh = 900 simplify divide by 2 x^2 + 2xh = 450 2xh = -x^2 + 450 h = : Volume equation V = x^2 * h Replace h V = x^2() V = x() V = x() Graph this equation y=V : Shows max volume when x is a little over 12"; vol is about 1800 cu/in
 Numbers_Word_Problems/217899: tripling the greater of 2 consectutive even integers gives the same result as subtracting 10 from the lesser even integer. What are the integers?1 solutions Answer 164265 by ankor@dixie-net.com(15649)   on 2009-09-27 20:14:23 (Show Source): You can put this solution on YOUR website!tripling the greater of 2 consecutive even integers gives the same result as subtracting 10 from the lesser even integer. What are the integers? : Obviously the solution here will be negative : Let the integers be x, (x+2) : 3(x+2) = x - 10 3x + 6 = x - 10 3x - x = -10 - 6 2x = -16 x = -8 ; The integers: -8, -6 ; ; Check this (-6 is greater than -8) 3(-6) = -8 - 10
 Travel_Word_Problems/217822: On the first part of a 317-mile trip, a salesperson average 58 miles per hour. The salesperson averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. The total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speeds. 1 solutions Answer 164261 by ankor@dixie-net.com(15649)   on 2009-09-27 20:00:48 (Show Source): You can put this solution on YOUR website!On the first part of a 317-mile trip, a salesperson average 58 miles per hour. The salesperson averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. The total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speeds. ; Convert 5 hr 45 min to 5.75 hr : Let t = travel time at 58 mph then (5.75-t) = travel time at 52 mph : Write a distance equation: Dist = speed * time : Dist at 58mph + dist at 52mph = 317 mi : 58t + 52(5.75-t) = 317 58t + 299 - 52t = 317 58t - 52t = 317 - 299 6t = 18 t = 3 hrs at 58 mph then 5.75 - 3 = 2.75 hrs at 52 mph ; : Check solution by finding the total dist 58(3) + 52(2.75) = 174 + 143 = 317 mi; confirms our solutions
 Angles/217874: Two angles are complementary. The sum of the measure of one angle and half the second angle equal 70 degrees. What are the measures of the angles?1 solutions Answer 164222 by ankor@dixie-net.com(15649)   on 2009-09-27 18:33:53 (Show Source): You can put this solution on YOUR website!Two angles are complementary. x And (90-x) : The sum of the measure of one angle and half the second angle equal 70 degrees. x + .5(90-x) = 70 x + 45 - .5x = 70 x -.5x = 70 - 45 .5x - 25 x = 50 : What are the measures of the angles? The angles would be 50 and 40 degrees ; 50 + .5(40) = 70
 Numbers_Word_Problems/217850: Two numbers such that one is 30% more than the other. Answer is x & 1/3x, But HOW do you get the 1/3?1 solutions Answer 164185 by ankor@dixie-net.com(15649)   on 2009-09-27 16:55:12 (Show Source): You can put this solution on YOUR website!Two numbers such that one is 30% more than the other. Answer is x & 1/3x, But HOW do you get the 1/3? : I think they meant: x and 1.3x : When you write x, you actually mean 1x : the decimal equiv or 30% is .30 or just .3 30% more can be written: 1x + .3x = 1.3x
 test/188078: Five equal squares are joined together to form a rectangle whose perimeter is 372cm. What is the area of one square? Thanks.. 1 solutions Answer 164183 by ankor@dixie-net.com(15649)   on 2009-09-27 16:43:44 (Show Source): You can put this solution on YOUR website!Five equal squares are joined together to form a rectangle whose perimeter is 372cm. : What is the area of one square? : Would look like this __________ |_|_|_|_|_|x : P = 372 Divide by the number of sides : 12x = 372 x = 31 : 31^2 = 261 sq cm each square
 Numbers_Word_Problems/217724: A palindrome is a number that reads the same forwards and backwards. The sum of a particular set of three consecutive positive integers is a three-digit palindrome. If the sum is less than 220, what is the greatest possible value for the largest of the three integers in the set?1 solutions Answer 164100 by ankor@dixie-net.com(15649)   on 2009-09-27 10:06:46 (Show Source): You can put this solution on YOUR website! palindrome is a number that reads the same forwards and backwards. The sum of a particular set of three consecutive positive integers is a three-digit palindrome. If the sum is less than 220, what is the greatest possible value for the largest of the three integers in the set? : Less than 220 therefore the number is 212 or the 1st and 3rd digit = 1 I tried 212, does not have an integer solution. Let the 1st and 3rd digit = 1 Let the middle digit = x Let consecutive integers = y, y+1, y+2 : y + (y+1) + (y+2) = 100 + 10x + 1 ; combine like terms 3y + 3 = 10x + 101 ; 3y = 10x + 101 - 3 ; 3y = 10x + 98 y = : Find a value for x that will give an integer value for y The sum of the numerator has to be a multiply of 3 x = 7 y = y = y = 56 : Try this 56 + 57 + 58 = 171, satisfies the problem
 Numbers_Word_Problems/217489: A palindrome is a number that reads the same forwards and backwards. The sum of a particular set of three consecutive positive integers is a three-digit palindrome. If the sum is less than 220, what is the greatest possible value for the largest of the three integers in the set?1 solutions Answer 164098 by ankor@dixie-net.com(15649)   on 2009-09-27 10:00:36 (Show Source): You can put this solution on YOUR website! palindrome is a number that reads the same forwards and backwards. The sum of a particular set of three consecutive positive integers is a three-digit palindrome. If the sum is less than 220, what is the greatest possible value for the largest of the three integers in the set? : Less than 220 therefore the number is 212 or the 1st and 3rd digit = 1 I tried 212, does not have an integer solution. Let the 1st and 3rd digit = 1 Let the middle digit = x Let consecutive integers = y, y+1, y+2 : y + (y+1) + (y+2) = 100 + 10x + 1 ; combine like terms 3y + 3 = 10x + 101 ; 3y = 10x + 101 - 3 ; 3y = 10x + 98 y = : Find a value for x that will give an integer value for y The sum of the numerator has to be a multiply of 3 x = 7 y = y = y = 56 : Try this 56 + 57 + 58 = 171, satisfies the problem
 Percentage-and-ratio-word-problems/217626: If twice a number added to 3 is divided by the number plus 1, the result is three halves. Find the number.1 solutions Answer 164045 by ankor@dixie-net.com(15649)   on 2009-09-26 21:38:04 (Show Source): You can put this solution on YOUR website!If twice a number added to 3 is divided by the number plus 1, the result is three halves. Find the number. : Let x = " a number" : = Cross multiply 2(2x+3) = 3(x+1) : 4x + 6 = 3x + 3 : 4x - 3x = 3 - 6 : x = -3 ; ; Check in original equation = : = : =
 Miscellaneous_Word_Problems/217471: Can you show the work as well as the answer please. Problem: A 2 mile cab ride costs \$5.25. A 5 mile cab ride costs \$10.50. How much does a 3.8 mile cab ride cost?1 solutions Answer 164043 by ankor@dixie-net.com(15649)   on 2009-09-26 21:30:52 (Show Source): You can put this solution on YOUR website!A 2 mile cab ride costs \$5.25. A 5 mile cab ride costs \$10.50. How much does a 3.8 mile cab ride cost? : Write a linear equation using the given values as follows x1 = 2; y1 = 5.25 x2 = 5; y2 = 10.50 : Find slope (m) using the slope formula: m = m = = = 1.75 : Use the point/slope equation: y - y1 = m(x - x1) y - 5.25 = 1.75(x - 2) y - 5.25 = 1.75x - 3.5 y = 1.75x - 3.5 + 5.25 y = 1.75x + 1.75; the equation ; Find the cost of a 3.8 mi cab ride, substitute 3.8 for x and find y y = 1.75(3.8) + 1.75 y = 6.65 + 1.75 y = \$8.40 for 3.8 mi ride
 Miscellaneous_Word_Problems/217461: can you show the work as well as the answer please Problem: An empty 5 gallon water jug weighs 0.75 lbs. With 3 cups of water inside, the jug weighs 2.25 lbs. Predict the weight of the jug with 5 cups of water inside.1 solutions Answer 164039 by ankor@dixie-net.com(15649)   on 2009-09-26 21:01:28 (Show Source): You can put this solution on YOUR website!An empty 5 gallon water jug weighs 0.75 lbs. With 3 cups of water inside, the jug weighs 2.25 lbs. Predict the weight of the jug with 5 cups of water inside. : Find the weight of the 3 cups of water : Jug&water - emptyJug = 3 cups of water ; 2.25 - .75 = 1.5 lb is the weight of 3 cups ; Find the weight of 1 cup of water = .5 lb weight of 1 cup : "Predict the weight of the jug with 5 cups of water inside." : Jug + 5 cups = total weight .75 + 5(.5) = .75 + 2.5 = 3.25 lb
 Money_Word_Problems/217443: Write an algebraic equation: 1.The perimeter of a rectangle is x yards and t feet. What is the perimeter in inches? 2.The width of a rectangle is w feet, and its length is 7 feet more than five times its width. What is the perimeter of the rectangle in feet? Please help me i need to pass my classes. thanks.1 solutions Answer 164038 by ankor@dixie-net.com(15649)   on 2009-09-26 20:46:53 (Show Source): You can put this solution on YOUR website!Write an algebraic equation: : 1.The perimeter of a rectangle is x yards and t feet. What is the perimeter in inches? : We know there are 36" in a yard and 12" in a foot Therefore: P(inches) = 36x + 12t : : 2.The width of a rectangle is w feet, W = the width : its length is 7 feet more than five times its width. L = 5W + 7 ; What is the perimeter of the rectangle in feet? P = 2L + 2W Replace L with (5W+7) P = 2(5W+7) + 2W P = 10W + 14 + 2W P = 12W + 14
 Equations/217419: the diffrence between 72 and the product of a number and 4 equals five times the number.1 solutions Answer 164036 by ankor@dixie-net.com(15649)   on 2009-09-26 20:30:51 (Show Source): You can put this solution on YOUR website!the difference between 72 and the product of a number and 4 equals five times the number. : 72 - 4x = 5x 72 = 5x + 4x 72 = 9x x = x = 8 ; ; Check: 72 - 4(8) = 5(8)
 Money_Word_Problems/217380: Mary Auburn makes three investm,ents. The investment that pays 12% is twice the amount of the account that pays 9%. The amount inveted at 10% is \$500 more than the amount invested at 9%. If the annual interest income is \$1555, how much money is invested at each rate? Please help!! Thank you!!1 solutions Answer 164030 by ankor@dixie-net.com(15649)   on 2009-09-26 19:32:57 (Show Source): You can put this solution on YOUR website! three investments. The investment that pays 12% is twice the amount of the account that pays 9%. The amount inveted at 10% is \$500 more than the amount invested at 9%. If the annual interest income is \$1555, how much money is invested at each rate? : Let x = amt invested at 9% : "The investment that pays 12% is twice the amount of the account that pays 9%." therefore: 2x = amt invested at 12% : "The amount invested at 10% is \$500 more than the amount invested at 9%." therefore: (x+500) = amt invested at 10% : If the annual interest income is \$1555, how much money is invested at each rate? .09x + .12(2x) + .10(x+500) = 1555 .09x + .24x + .10x + 50 = 1555 .43x = 1555 - 50 .43x = 1505 x = x = \$3500 invested at 9% then 2(2500) = \$7000 invested at 12% and 3500 + 500 = \$4000 invested at 10% ; : Is that true? .09(3500) + .12(7000) + .10(4000) 315 + 840 + 400 = 1555
 Rectangles/217459: I'm trying to determine the height of a shed if the cubic feet = 230 and the length is 6' and width is 8'. I calculated 4'7 but the company stated it's 8' tall. From what I remember, Length x width x height gives you cubic feet.1 solutions Answer 164006 by ankor@dixie-net.com(15649)   on 2009-09-26 18:44:44 (Show Source): You can put this solution on YOUR website!you're almost right, 4.8 is the ht: 4.8 * 6 * 8 ~ 230 Certainly not 8'
 Equations/217521: I am having difficulty creating my own algebraic equation for class. I have to write an equation which models how old in years I will be when I am 3 times as old as my younger cousin. I am 33 she is 14. here is what I have tried: 33x=19(3) also I have tried 19x=33(3) I am so confused right now. I think I am going about this all wrong, can you just guide me in the right direction please. Thank you.1 solutions Answer 164002 by ankor@dixie-net.com(15649)   on 2009-09-26 18:34:54 (Show Source): You can put this solution on YOUR website!write an equation which models how old in years I will be when I am 3 times as old as my younger cousin. I am 33 she is 14. : Let y = no. of years for this to happen : 33 + y = 3(14 + y) 33 + y = 42 + 3y y - 3y = 42 - 33 -2y = 9 2y = -9 y = -4.5 yrs : this means you were 3 times as old as your cousin, 4.5 years ago Will not happen in the future. : To answer the question; your age 4.5 yrs ago = 28.5; cousin was 9.5 : Check: 33 - 4.5 = 3(14 - 4.5) 28.5 = 3(9.5)
 Miscellaneous_Word_Problems/217536: A room contains 96 chairs. The number of chairs per row is 4 more than the number of rows. Find the number of rows and the number of chairs per row. C+R = 96 Chairs 4c + R= 96 can you please help me with this problem..THanks1 solutions Answer 163995 by ankor@dixie-net.com(15649)   on 2009-09-26 18:13:30 (Show Source): You can put this solution on YOUR website!A room contains 96 chairs. The number of chairs per row is 4 more than the number of rows. Find the number of rows and the number of chairs per row : Let c = no. of chairs per row Let r = no. of rows : r * c = 96 : "The number of chairs per row is 4 more than the number of rows. c = r + 4 : Replace c with (r+4) in the 1st equation r(r+4) = 96 : r^2 + 4r - 96 = 0; a quadratic equation Factors to (r+12)(r-8) = 0 The positive solution r = 8 rows and obviously 12 chairs in each row
 Radicals/217462: Jens boat cruised 45 miles upstream and 45 miles back in a total of 8 hr. The speed of the river is 3 mph. Find the speed of the boat in still water. 1 solutions Answer 163970 by ankor@dixie-net.com(15649)   on 2009-09-26 15:59:21 (Show Source): You can put this solution on YOUR website!Jens boat cruised 45 miles upstream and 45 miles back in a total of 8 hr. The speed of the river is 3 mph. Find the speed of the boat in still water. : Let s = speed in still water then (s+3) = speed downstream and (s-3) = speed upstream : write a time equation: Time = : Time up + time down = 8 hrs + = 8 Multiply equation by (s-3)(s+3), results 45(s-3) + 45(s+3) = 8(s+3)(s-3) : 45s - 135 + 45s + 135 = 8(s^2 - 9) : 90s = 8s^2 - 72 : 8s^2 - 90s - 72 = 0; a quadratic equation : Simplify, divide by 2 4s^2 - 45s - 36 = 0 : Factor (4s + 3)(s - 12) = 0 : Positive solution: s = 12 mph boat speed in still water ; ; Check solution: + = 8 3 + 5 = 8 hrs
 Travel_Word_Problems/217360: Assume the distance b/w Washington DC and Philadelphia is 120 miles. Suppose on a recent trip, driving from DC to Philly, your average speed for the first half of the trip was 40 mph. If you wanted to average 50 mph for the entire trip, what must be the average speed for the second half of you trip?1 solutions Answer 163955 by ankor@dixie-net.com(15649)   on 2009-09-26 14:06:05 (Show Source): You can put this solution on YOUR website!Assume the distance b/w Washington DC and Philadelphia is 120 miles. Suppose on a recent trip, driving from DC to Philly, your average speed for the first half of the trip was 40 mph. If you wanted to average 50 mph for the entire trip, what must be the average speed for the second half of you trip? : let s = speed required to do this: ; Write a time equation: Time = + = : Multiply equation by 200s, results 5s(60) + 200(60) = 4s(120) : 300s + 12000 = 480s : 12000 = 480s - 300s : 12000 = 180s s = s = 66 mph to average 50 mph ; ; Check solution + = 1.5 + .9 = 2.4
 Polynomials-and-rational-expressions/217367: The circumference of the world is 25,000 miles and there is a band placed around it. To the band is added 10ft and moved off the earth at an equal distance of x. Which is the largest that can walk under the band. Using C=6.28R. Can a bee 1 inch tall, a snake 1 ft tall, a 3ft child or a 6ft adult walk under the band?1 solutions Answer 163947 by ankor@dixie-net.com(15649)   on 2009-09-26 13:15:53 (Show Source): You can put this solution on YOUR website!The circumference of the world is 25,000 miles and there is a band placed around it. To the band is added 10ft and moved off the earth at an equal distance of x. Which is the largest that can walk under the band. Using C=6.28R. Can a bee 1 inch tall, a snake 1 ft tall, a 3ft child or a 6ft adult walk under the band? : Actually you can do this easily = 1.59 ft; enough for the snake and the bee ; Prove this using the given values : Add 10' to the circumference 25000 + = 25000.0018939394 mi Find the difference the in radii with the circumferences - * 5280 = 1.59'
 Quadratic_Equations/217201: find the x and y intercepts of each line and write the equation in standard form y=2/7x-11 solutions Answer 163927 by ankor@dixie-net.com(15649)   on 2009-09-26 10:33:58 (Show Source): You can put this solution on YOUR website!find the x and y intercepts of each line and write the equation in standard form: y = x - 1 : Find the y intercept (occurs when x = 0) y = (0) - 1 y = -1 : Find the x intercept (occurs when y = 0) x - 1 = 0 x = + 1 multiply both sides by 7 2x = 7 Divide both sides by 2 x = x = 3.5 : Write in standard form y = x - 1 Subtract x from both sides y - x = - 1 Multiply by -7, (gets rid of the denominator and changes the signs) -7y + 2x = + 7 which is the standard form 2x - 7y = 7
 Quadratic_Equations/217305: Find the quadratic function satisfying the given conditions. The axis of symmetry is the line x = 5. The y-intercept is 25. There is only one x-intercept. 1 solutions Answer 163882 by ankor@dixie-net.com(15649)   on 2009-09-25 21:57:13 (Show Source): You can put this solution on YOUR website!Find the quadratic function satisfying the given conditions. The axis of symmetry is the line x = 5. The y-intercept is 25. There is only one x-intercept. : That would have to be: : (x-5)(x-5) = 0 FOIL y = x^2 - 10x + 25
 Miscellaneous_Word_Problems/217218: A projectile is fired directly upward with a muzzle velocity of 860 feet per second from a height of 7 feet above the ground. a. Determine a function for the height of the projectile t seconds after it's released. b. How long does it take the projectile to reach of height of 100 feet on its way up? c. How long is the projectile in the air?1 solutions Answer 163820 by ankor@dixie-net.com(15649)   on 2009-09-25 19:02:40 (Show Source): You can put this solution on YOUR website!A projectile is fired directly upward with a muzzle velocity of 860 feet per second from a height of 7 feet above the ground. : a. Determine a function for the height of the projectile t seconds after it's released. Assuming the equation: h = -16t^2 + vt + c h = -16t^2 + 860t + 7 ; b. How long does it take the projectile to reach of height of 100 feet on its way up? -16^2 + 860t + 7 = 100 -16t^2 + 860t + 7 - 100 = 0 -16t^2 + 860t - 93 = 0 Use the quadratic formulas to find t In this equation: x = t: a=-16; b=860; c=-93 Do the math here and you get: t =.108 seconds for 100' on the way up : c. How long is the projectile in the air? h = 0, the equation for this -16t^2 + 860t + 7 = 0 Use the quadratic formulas to find t In this equation: x = t: a=-16; b=860; c=7 Do the math here and you get: t = 53.758 seconds to return to earth
 Age_Word_Problems/217079: Two years ago a father was four times as old as his son. Three years from now the father will be only three times as old as the son. How old is each now? 1 solutions Answer 163812 by ankor@dixie-net.com(15649)   on 2009-09-25 17:08:09 (Show Source): You can put this solution on YOUR website!Let f = father's present age Let s = son's present age : Just write an equation for what it says; : "Two years ago a father was four times as old as his son." f - 2 = 4(s - 2) f - 2 = 4s - 8 f = 4s - 8 + 2 f = 4s - 6 : " Three years from now the father will be only three times as old as the son." f + 3 = 3(s + 3) f + 3 = 3s + 9 f = 3s + 9 - 3 f = 3s + 6 : Replace f with (4s-6) from the 1st statement 4s - 6 = 3s + 6 4s - 3s = 6 + 6 s = 12 yrs is the son's age : I'll let you find the father's age, using one of the equations, then check your solutions in the other equation
 Polynomials-and-rational-expressions/217072: Baseballs are packed one dozen per box. There are 208 baseballs to be packed. How many more baseballs will be needed to fill the last partially filled box. Please show me how to express in an equation. Thank you.1 solutions Answer 163800 by ankor@dixie-net.com(15649)   on 2009-09-25 16:44:13 (Show Source): You can put this solution on YOUR website!Baseballs are packed one dozen per box. There are 208 baseballs to be packed. How many more baseballs will be needed to fill the last partially filled box. Please show me how to express in an equation. Thank you. : Let r = no. of balls required to fill the last box : r = 12 balls - (208 - (integer value of (208/12) * 12) : r = 12 - (208 - (int(208/12) * 12)) : r = 12 - (208 - (17 * 12)) : r = 12 - (208 - 204) : r = 12 - 4 : r = 8 balls to fill the last box
 Quadratic_Equations/216956: I am having difficulty with a question. The question is as follows: A parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the equation of the parabola. I am setting up my problem as y = ax^2 + bx + c and I since x = 4, y must be 0 o = 16 + 4 + c. I'm confused and I don't think I am setting up the equation correctly. Thanks - Lori1 solutions Answer 163789 by ankor@dixie-net.com(15649)   on 2009-09-25 15:58:43 (Show Source): You can put this solution on YOUR website!I am having difficulty with a question. ; The question is as follows: A parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the equation of the parabola. : I am setting up my problem as y = ax^2 + bx + c and I since x = 4, y must be 0 Not right: the axis of symmetry is given as 4 and y coordinate as 6 so you have: : x = 4; y = 6 (vertex) (4^2)a + 4b + c = 6 16a + 4b + c = 6 : and the intercept x = 2; y = 0 (2^2)a + 2b + c = 0 4a + 2b + c = 0 : Here we can reason: the two intercepts are equidistant from the axis of symmetry One intercept is +2, the axis symmetry is +4 then the other intercept is +6 : x = 6; y = 0 (6^2)a + 6b + c = 0 36a + 6b + c = 0 : Three equations to find three unknowns, a, b, c : use the 1st two equations to eliminate c 16a + 4b + c = 6 4a + 2b + c = 0 -------------------Subtraction eliminates c 12a + 2b = 6 : do the same with the 1st and 3rd equation 36a + 6b + c = 0 16a + 4b + c = 6 ------------------Subtraction eliminates c 20a + 2b = -6 ; Use these two equations, and eliminate b and find a 20a + 2b = -6 12a + 2b = 6 --------------Subtraction eliminates b 8a = -12 a = a = -1.5 : Find b using eq: 12a + 2b = 6 12(-1.5) + 2b = 6 -18 + 2b = 6 2b = 6 + 18 2b = 24 b = 12 : Find c using eq: 4a + 2b + c = 0 4(-1.5) + 2(12) + c = 0 -6 + 24 + c = 0 18 + c = 0 c = -18 : The equation: y = -1.5x^2 + 12x -18 : Check this by graphing it Two x intercepts at +2 and +6; vertex: 4,6.
 Quadratic_Equations/217164: How do I solve this quadratic equation? 2x^2+12x+19 I need to find the leftmost x-int and the right most x-int for the graph of this equation1 solutions Answer 163782 by ankor@dixie-net.com(15649)   on 2009-09-25 14:23:32 (Show Source): You can put this solution on YOUR website!2x^2 + 12x + 19 : There are no real roots to this equation, (no x intercepts) This can be shown by the discriminant: D = a^2 - 4*a*c In this equation: a = 2; b = 12; c = 19 ; D = 12^2 - 4*2*19 D = 144 - 152 D = -8; a neg quantity means no real roots ; The graph:
 Geometry_Word_Problems/216994: The perimeter of a rectangle is 76 m. If the width were doubled and the length were increased by 5m, the perimeter would be 120 m. What are the length and width of the rectangle?1 solutions Answer 163761 by ankor@dixie-net.com(15649)   on 2009-09-25 12:29:40 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 76 m. If the width were doubled and the length were increased by 5m, the perimeter would be 120 m. What are the length and width of the rectangle? : 2L + 2W = 76 Simplify divide by 2 L + W = 38 or L = 38 - W : "If the width were doubled and the length were increased by 5m, the perimeter would be 120 m." 2(L+5) + 2(2W) = 120 2L + 10 + 4W = 120 2L + 4W = 120 - 10 2L + 4W = 110 Simplify divide by 2, subtract the 1st equation L + 2W = 55 L + W = 38 -------------Subtraction eliminates L, find W W = 17 is the width then L = 38 - 17 L = 21 is the length ; : Check solution in original perimeter equation 2(21) + 2(17) = 76