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edjones answered: 7568 problems
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Rational-functions/131835: How do you solve this so I can understand f(x)=-2x^2+2x+6 1 solutions Answer 96256 by edjones(7569)   on 2008-03-12 22:54:45 (Show Source): You can put this solution on YOUR website! f(x)=-2x^2+2x+6 -2(x^2-x-3) To find the zeroes: x^2-x-3=0 x^2-x =3 x^2-x+ 1/4=3+ 1/4 complete the square by taking 1/2 the middle term and squaring it. (x- 1/2)^2=13/4 x- 1/2=+-sqrt(13)/2 sqrt of each side. x=1/2+-sqrt(13)/2 x=(1+sqrt(13))/2, (1-sqrt(13))/2 . The 2 places the graph crosses the x axis (the x intercepts[where y=0]) also give the answer. You could also use the quadratic equation. Ed

Quadratic_Equations/131836: This question is from textbook Introductory Algebra The length of a rectangle is approximately 1.6 times the width. Find the dimensions of a rectangle if its area is 9000m^2. I think I understand this problem, but could use some help. Thanks! 1 solutions Answer 96251 by edjones(7569)   on 2008-03-12 22:28:48 (Show Source): You can put this solution on YOUR website! Let w=width; L=1.6w L*w=A 1.6w*w=9000 1.6w^2=9000 w^2=9000/1.6 w^2=5625 w=75 m Take sqrt of each side. L=75*1.6=120 m . Ed

Linear-systems/131837: Factor completely: x^3 – 2x^2 + 6x – 12 . Factor completely: x^2 + 17x + 16 Factor completely: 8x^2 + 6x – 5 1 solutions Answer 96250 by edjones(7569)   on 2008-03-12 22:27:08 (Show Source): You can put this solution on YOUR website! x^3 – 2x^2 + 6x – 12 x^2(x-2)+6(x-2) Factoring by grouping. (x^2+6)(x-2) . x^2 + 17x + 16 (x+16)(x+1) . 8x^2 + 6x – 5 8*-5=-40 What 2 factors -40 when added equal +6? Ans: 10, -4 8x^2+10x-4x-5 Put -4x and 10xin the middle in either order. 2x(4x+5)-(4x-5) Factoring by grouping again. (2x-1)(4x+5) . Ed

Geometry_Word_Problems/131834: This question is from textbook I need help solving this word problem. Thanks a ton! The so-called golden rectangle is said to be extremely pleasing visually and was used often by ancient Greek and Roman architects. The length of a golden rectangle is approximately 1.6 times the width. Find the dimensions of a golden rectangle if its area is 9000 m^2. 1 solutions Answer 96247 by edjones(7569)   on 2008-03-12 22:12:06 (Show Source): You can put this solution on YOUR website! Let w=width; L=1.6w L*w=A 1.6w*w=9000 1.6w^2=9000 w^2=9000/1.6 w^2=5625 w=75 m Take sqrt of each side. L=75*1.6=120 m . Ed

Inequalities/131797: (x/-5) > -4 1 solutions Answer 96246 by edjones(7569)   on 2008-03-12 22:03:20 (Show Source): You can put this solution on YOUR website! x/-5 > -4 x<20 multiply each side by -5 to eliminate the fraction. Reverse the sign when multiplying by a negative number. . Ed

Inverses/131543: Find a number such that 1 less than the number divided by the reciprocal of the number is equal to 1. (Leave the answeres in exact form, that is with the square root.) 1 solutions Answer 96120 by edjones(7569)   on 2008-03-12 01:33:22 (Show Source): You can put this solution on YOUR website! let x be the number. (x-1) / 1/x =1 (x-1) *x=1 x^2-x=1 x^2-x-1=0 x^2-x =1 x^2-x+ 1/4=1+ 1/4 (x- 1/2)^2=5/4 x- 1/2=+-sqrt(5/4) x=1/2+-sqrt(5)/2 x=(1+sqrt(5))/2, x=(1-sqrt(5))/2 . Ed

Average/131588: Please help me solve this Open-ended problem: At one point early this season, Clipper was batting .500. After getting 3 hits in 10 at-bats in his next games, his average dropped to .333. B. How many hits and at-bats must he have altogether. 1 solutions Answer 96119 by edjones(7569)   on 2008-03-12 00:59:42 (Show Source): You can put this solution on YOUR website! This is tough especially if you don't follow baseball. Let x be the number of hits when he batted .500, 2x are the number of at bats. x/2x=1/2=.500 3/10=.300 . (x+3)/(2x+10)=1/3 3(x+3)=2x+10 Multiply each side by 3(2x+10) to eliminate fractions. 3x+9=2x+10 x=1 So, he had 1 hit in 2 at bats. . Check: (1+3)/(2+10)=1/3=.333 So he had 4 hits in 12 at bats altogether. Answer. . Ed

Quadratic_Equations/131591: Any help is appreciated. Thank You Rational Exponents to simplify 3 sqrt x^12 1 solutions Answer 96118 by edjones(7569)   on 2008-03-12 00:22:45 (Show Source): You can put this solution on YOUR website! 3x^6

Quadratic_Equations/131604: How do I solve? Thanks for your help. sqrt 12a^2b= 1 solutions Answer 96117 by edjones(7569)   on 2008-03-12 00:18:55 (Show Source): You can put this solution on YOUR website! sqrt(12a^(2b)) =sqrt(4*3a^(2b)) =2sqrt(3a^(2b)) . Ed

Quadratic_Equations/131595: Any help is appreciated. Thank You 8sqrt32-7sqrt2= 1 solutions Answer 96115 by edjones(7569)   on 2008-03-12 00:10:27 (Show Source): You can put this solution on YOUR website! 8sqrt32-7sqrt2 =8sqrt(2*16)-7sqrt(2) =32sqrt(2)-7sqrt(2) =25sqrt(2) . Ed

Quadratic_Equations/131656: Please help me solve for x. I keep getting stuck. f(x)= x^4+x^2-12. 1 solutions Answer 96114 by edjones(7569)   on 2008-03-12 00:04:52 (Show Source): You can put this solution on YOUR website! f(x)= x^4+x^2-12 =(x^2+4)(x^2-3) Zeroes for x: x^2=3 x=+-sqrt(3) . x^2=-4 x=+-sqrt(-4) x=+-2i imaginary numbers. . Ed

Functions/131659: ok, what is the domain of the function 5x - 4 1 solutions Answer 96113 by edjones(7569)   on 2008-03-11 23:57:50 (Show Source): You can put this solution on YOUR website! all real numbers

Finance/131379: The question is: How much must you invest each quarter in a bond fund yielding 9.7% compounded quarterly to become a millionaire in 20 years? For some reason I'm completely stuck. 1 solutions Answer 95954 by edjones(7569)   on 2008-03-11 02:49:34 (Show Source): You can put this solution on YOUR website! Let A=1,000,000, r=.097, n=4, t=20 P=principal . A=P(1+ r/n)^nt 1000000=P(1+ .097/4)^(4*20) P=10^6/(1.02425)^100 =10^6/10.9799... =$91,075.75 Final answer . Ed

Probability-and-statistics/131446: plzzzzzzzzzz help me In the cafeteria of Karachi University 40% drink Coca-cola,50% drink pepsi-cola and 25% drink both. If a person is selected ,find the probability he/she drinks either coca-cola or pepsi-cola. 1 solutions Answer 95953 by edjones(7569)   on 2008-03-11 02:18:00 (Show Source): You can put this solution on YOUR website! The 25% who drink both are included in the 40% and 50%. Since this is an either-or question we must eliminate th 25% from the statistics before adding. 40-25=15% 50-25=25% 15+25=40% drink either coke or pepsi (but not both). . Ed

Miscellaneous_Word_Problems/131398: I have been unable to come up with an equation to solve this problem. Could I get some help with figuring it out. I appreciate it. A father and son are digging a garden that is 7 feet long and 5 feet wide. The father, working alone takes 3 hrs. The son working alone takes 4 hrs. If they work together how long would it take? 1 solutions Answer 95952 by edjones(7569)   on 2008-03-11 02:04:31 (Show Source): You can put this solution on YOUR website! Let t be the time it takes them working together Father does 1/3 of the job in 1 hr. Son does 1/4 of the job in 1 hr. Together they do 1/t of the job in 1 hr. 1/3 + 1/4 = 1/t 4t+3t=12 multiply each side by 12t to eliminate fractions. 7t=12 t=12/7 hrs or 1 hr 43 min (approx.) . Ed

Polynomials-and-rational-expressions/131439: This question is from textbook intermediate algebra 3. Factor completely: x^2 + 17x + 16 1 solutions Answer 95951 by edjones(7569)   on 2008-03-11 01:48:41 (Show Source): You can put this solution on YOUR website! x^2 + 17x + 16 (x+16)(x+1) . Ed

Radicals/131441: the square root of x-4 - the square root of x+8 =2 1 solutions Answer 95950 by edjones(7569)   on 2008-03-11 01:45:51 (Show Source): You can put this solution on YOUR website! sqrt(x-4)-sqrt(x+8)=2 sqrt(x-4)-2=sqrt(x+8) x-4-4sqrt(x-4)+4=x+8 square both sides. -4sqrt(x-4)=8 (-4sqrt(x-4))^2=8^2 16(x-4)=64 16x-64=64 16x=128 x=8 . Check: sqrt(8-4)-sqrt(8+8)=2 2-4=2 False There is no answer to this equation. . Ed

Polynomials-and-rational-expressions/131442: This question is from textbook intermediate algebra 5. Factor completely: 8x^2 + 6x – 5 1 solutions Answer 95949 by edjones(7569)   on 2008-03-11 01:17:01 (Show Source): You can put this solution on YOUR website! 8x^2 + 6x – 5 8*-5=-40 What 2 factors of -40 when added equal 6? Ans: 10, -4 8x^2-4x+10x-5 Multiply those 2 numbers by x and replace +6x in the original equation with them (in either order!). =4x(2x-1)+5(2x-1) Factoring by grouping =(4x+5)(2x-1) . Ed

Quadratic_Equations/131434: i have a problem about my math homework. my problem says: THE SUM OF THE LENGTHS OF THE TWO LEGS OF A RIGHT ANGLE TRIANGLE IS 14. FIND THE LENGTH OF THE SHORTEST HYPOTENUSE. please solve my problem but using quadratic equations, i just cant figure out how to set up the whole thing. thank you very much! 1 solutions Answer 95948 by edjones(7569)   on 2008-03-11 00:33:41 (Show Source): You can put this solution on YOUR website! a^2+b^2=c^2 The hypotenuse will be the shortest when the legs are equal. 2*7^2 =2*49 =98 c=sqrt(98) =sqrt(2*49) =7sqrt(2) . Ed

Quadratic_Equations/131261: This question is from textbook Introductory Algebra The problem states to solve. 4/(m^2-7) = 1 I came up with m = + or - sqrt of 11. Not sure if I'm on the right track or not. Any help would be greatly appreciated. Thanks! 1 solutions Answer 95819 by edjones(7569)   on 2008-03-10 01:15:56 (Show Source): You can put this solution on YOUR website! ur correct.

Equations/131201: Can you pls solve for a and b. I've tried and got a= -3, and b= 10, but the answer is a=10, b=3. I do not understand how they arrived at that answer. The equations are: a - b = 7, and a - 4b = -7. Please solve for a and b and explain how you arrived at the answer. Thanks. 1 solutions Answer 95787 by edjones(7569)   on 2008-03-09 19:40:22 (Show Source): You can put this solution on YOUR website! X) a-b=7 Y) a-4b=-7 . X) a=b+7 Y) (b+7)-4b=-7 b+7-4b=-7 -3b=-14 b=14/3 . X) a- 14/3=-7 3a-14=21 3a=35 a=35/3 . Did you copy the question incorrectly? . Ed

Age_Word_Problems/131173: The square of Sam's age increased by twice his age is 48. What is Sam's age? I chose 2(a)2=48 and got a=4.9 years old. Am I right? 1 solutions Answer 95785 by edjones(7569)   on 2008-03-09 19:24:54 (Show Source): You can put this solution on YOUR website! Let x be Sam's age. x^2+2x=48 x^2+2x-48=0 (x+8)(x-6)=0 x=6 y.o. . Always check: 6^2+2*6=48 36+12=48 true . Ed

Quadratic_Equations/131171: This question is from textbook Introductory Algebra Please help me solve this equation: (x^2)+(sqrt22)(x)=0 Thank you! 1 solutions Answer 95783 by edjones(7569)   on 2008-03-09 19:19:22 (Show Source): You can put this solution on YOUR website! x^2 + sqrt(22)x=0 x(x+sqrt(22))=0 Factor. x=0 Ans. . x+sqrt(22)=0 x= -sqrt(22) Ans. . Ed

Probability-and-statistics/131195: Hi tutors at algebra.com, I have this question and its difficult. It has some connection with probability and thats what I know, and with a bit of chance and finding out various probabilities, etc..but I'm not sure how you can work it. I've tried thinking of it the number of ways, but its different from the correct answer that I was given, which was 20. If you could explain to me how you got the answer I would really appreciate it. Here's the question: "In the school band 5 children each own their own trumpet. In how many different ways can exactly three of the five children take home the wrong trumpet, while the other two take home the right trumpet." Any help and an explanation would be appreicated. Thankyou so much, Jasmine (13 years old) 1 solutions Answer 95782 by edjones(7569)   on 2008-03-09 19:09:52 (Show Source): You can put this solution on YOUR website! We want to know the different Combinations of 3 of the 5 kids there can be. n=5, r=3, nCr= 5C3= = = =10 different ways . Ed

Miscellaneous_Word_Problems/131174: Thanks for any help you can give me. The digits 1, 2, and 5 can be scrambled to form three digit numbers. How many of these are prime numbers? 1 solutions Answer 95781 by edjones(7569)   on 2008-03-09 18:54:56 (Show Source): You can put this solution on YOUR website! When 2 or 5 is at the end there are none. 251 and 521 are both prime. . Ed

Miscellaneous_Word_Problems/131177: Thanks in advance for your help. In how many different ways can three students be seated in a row of 5 desks? 1 solutions Answer 95779 by edjones(7569)   on 2008-03-09 18:50:02 (Show Source): You can put this solution on YOUR website! This is a permutation question because we care about which way they are arranged. nPr= n!/(n-r)! 5P3=5!/(5-3)! =5*4*3*2/2 =5*4*3 =60 . Ed

Miscellaneous_Word_Problems/131176: Could someone please help me with this problem thanks. A set of weights for a balance scale us made of a one pond weight, a two pound weight, a four pound weight and a five pound weight. Using any combination of these weights, how many different quantities can be measured? 1 solutions Answer 95778 by edjones(7569)   on 2008-03-09 18:37:05 (Show Source): You can put this solution on YOUR website! 1, 2, 4, 5 The lowest wt is 1 and the highest is 12 and all the wts. in between. 12 in all. . Ed

Linear-equations/131183: Plot the graph of the equations 2x - 3y = 6 and 2x + y = -10 and interpret the result 1 solutions Answer 95777 by edjones(7569)   on 2008-03-09 18:25:04 (Show Source): You can put this solution on YOUR website! 2x - 3y = 6 2x + y = -10 . Interpretation: x=-3 y=-4 . Ed

Polynomials-and-rational-expressions/131192: This question is from textbook INTERMEDIATE ALGEBRA factor, if possible: 5x2(x+y+1)-15x3(x+y+1) 1 solutions Answer 95776 by edjones(7569)   on 2008-03-09 18:14:41 (Show Source): You can put this solution on YOUR website! 5x^2(x+y+1)-15x^3(x+y+1) -5x^2(3x-1)(x+y+1) . Ed

Quadratic_Equations/131125: What is the range of the function y=2(7)^(2x)-4??? I think it is y is less than -4????????????? 1 solutions Answer 95767 by edjones(7569)   on 2008-03-09 14:42:10 (Show Source): You can put this solution on YOUR website! y>=-4 . Ed

Exponents/131150: Can you please tell me if this is figured right? Simplify: ( x/x^2 – 9 ) – ( x/x^2 + 2x – 15 ) (1 - 9) - (3x - 15) -8 - - 12 -8 + 12 = 4 1 solutions Answer 95765 by edjones(7569)   on 2008-03-09 14:33:23 (Show Source): You can put this solution on YOUR website! ( x/(x^2 – 9) ) – ( x/(x^2 + 2x – 15) ) =(x/((x+3)(x-3)))-(x/((x+5)(x-3))) =(x(x+5))-(x(x+3))/((x+3)(x-3)(x+5)) =(x^2+5x)-(x^2+3x)/((x+3)(x-3)(x+5)) =2x/((x+3)(x-3)(x+5)) . Ed