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# Recent problems solved by 'funmath'

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 Complex_Numbers/59332: determine whether the following pairs of lines are perpendicular or not perpendicular y=-x+4 y=x-31 solutions Answer 40667 by funmath(2925)   on 2006-11-01 18:57:00 (Show Source): You can put this solution on YOUR website!determine whether the following pairs of lines are perpendicular or not perpendicular y=-x+4 y=x-3 : These lines are in slope intercept form , where m=slope and (0,b)=y-intercept. Perpendicular lines have slopes that are negative reciprocals of each other, that means they are opposite signs and upside down, because of this quality, if we multiply their slopes we get -1 . y=-x+4 -->> m=-1 y=x-3 -->> m=1 : If you multiply their slopes -1*1=-1, therefore the lines are perpendicular. Happy Calculating!!!
 Exponents/59320: This question is from textbook Algebra 1 5 cubed (5a to the fourth)cubed1 solutions Answer 40665 by funmath(2925)   on 2006-11-01 18:49:43 (Show Source): You can put this solution on YOUR website!5^3(5a^4)^3 Is this what you meant? Happy Calculating!!!
 Linear-systems/59323: what is 2x-3y=12 x=4y+1 substituion form1 solutions Answer 40664 by funmath(2925)   on 2006-11-01 18:45:58 (Show Source): You can put this solution on YOUR website!what is L1) 2x-3y=12 L2) x=4y+1 substituion form : Substitute the right side of L2 into L1 for x and solve for y 2(4y+1)-3y=12 8y+2-3y=12 5y+2=12 5y+2-2=12-2 5y=10 5y/5=10/5 y=2 : Substitute 2 in for y in L2 and solve for x x=4(2)+1 x=8+1 x=9 The solution (x,y)=(9,2) This is the point that both equations share. Garphically, its' the point of intersection of the two lines. Happy Calculating!!!
 Polynomials-and-rational-expressions/59327: This question is from textbook Alegbra concepts and applications I need help solving the following problem please : Find the excluded values for : 6 (over or divided by) m(m+1) thank u1 solutions Answer 40662 by funmath(2925)   on 2006-11-01 18:39:01 (Show Source): You can put this solution on YOUR website!Find the excluded values for : Excluded values for m would be anything that causes the denominator to = 0 because that causes the fraction to be undefined. m(m+1)=0 m=0 and m+1=0 m=0 and m+1-1=0-1 m= 0 and m=-1 The excluded values for m are 0 and -1. That means that m cannot equal 0 or -1. Happy Calculating!!!
 Linear-equations/59322: This question is from textbook here's a table. x y 4 14 8 15.5 12 17 16 18.5 i know the rate of change is 1.5, but how would i find the value of y when x=120?? how about finding the value of x when y=50?? 1 solutions Answer 40661 by funmath(2925)   on 2006-11-01 18:33:25 (Show Source): You can put this solution on YOUR website!here's a table. x y 4 14 8 15.5 12 17 16 18.5 How would i find the value of y when x=120?? how about finding the value of x when y=50?? Your rate of change is the slope between various points. I checked this out and this is indeed a linear relation. The formula to find the slope between two points is: You can choose any two points to find the slope, so let's choose the ones without decimals to make it a little easier. (x1,y1)=(4,14) and (x2,y2)=(12,17) We can now find the equation of the line using the point-slope formula:, m=slope,(x1,y1)=any point on the line. (x1,y1)=(4,14) and m=3/8 : When x=120 3(120)-8y=-100 360-8y=-100 -360+360-8y=-360-100 -8y=-460 -8y/-8=-460/-8 y=115/2 : When y=50 3x-8(50)=-100 3x-400=-100 3x-400+400=400-100 3x=300 3x/3=300/3 : If I just blew your mind and you've never seen any of this before, another way you can do this is to plot the points on a graph and using graph paper and a ruler you can approximate the same thing. : Happy Calculating!!!
 Linear-equations/59321: This question is from textbook how would i write an equation in point slope form, when it only gives me the coordinates: (-4,-6)??1 solutions Answer 40659 by funmath(2925)   on 2006-11-01 18:13:18 (Show Source): You can put this solution on YOUR website!how would i write an equation in point slope form, when it only gives me the coordinates: (-4,-6)?? In order to make an equation of a line you're supposed to have a point AND a slope. The point slope form is , where m=slope and (x1,y1) is the given point. Since you were only given: (x1,y1)=(-4,-6) all you can do is: y-(-6)=m(x-(-4)) y+6=m(x+4) Happy Calculating!!!
 Functions/59299: if f(x) =2x+5 find the following. f(-4) f(3)-51 solutions Answer 40654 by funmath(2925)   on 2006-11-01 17:53:48 (Show Source): You can put this solution on YOUR website!if f(x) =2x+5 find the following. : f(-4) Substitute -4 in for x and simplify. f(-4)=2(-4)+5 f(-4)=-8+5 f(-4)=-3 : f(3)-5 Substitute 3 in for x subtract 5 and simplify. f(3)-5=(2(3)+5)-5 f(3)-5=6+5-5 f(3)-5=6 : Happy Calculating!!!
 Equations/59306: -8-t=-25 8=b-3+19 16=8+s ---- -7 (8+s over -7) It would be very helpful if you could help me solve these problems. Thank you. 1 solutions Answer 40650 by funmath(2925)   on 2006-11-01 17:33:56 (Show Source): You can put this solution on YOUR website!-8-t=-25 8-8-t=8-25 -t=-17 -(-t)=-(-17) check by substituting 17 in for t and see if the sides are =. -8-17=-25 -25=-25 We're right!!! : 8=b-3+19 8=b+16 8-16=b+16-16 -8=b Check: 8=(-8)-3+19 8=-11+19 8=8 We're right again!!! : Check: Three for three!!! Happy Calculating!!!
 Mixture_Word_Problems/59288: You have 20 stampes that have a total value of \$6.62. Some of the stamps are worth \$0.24 each and others are worth \$0.37 each. How many stamps of each type do you have? Please show how to solve this question.1 solutions Answer 40646 by funmath(2925)   on 2006-11-01 17:08:36 (Show Source): You can put this solution on YOUR website!You have 20 stampes that have a total value of \$6.62. Some of the stamps are worth \$0.24 each and others are worth \$0.37 each. How many stamps of each type do you have? It's easier to deal with money in terms of cents to avoid decimals. Let the number of 24 cent stamps be:x then because there is 20 stamps all together the number of 37 cent stamps is:20-x The total value is: 662 cents : 24x+37(20-x)=662 24x+740-37x=662 -13x+740=662 -13x+740-740=662-740 -13x=-78 -13x/-13=-78/-13 x=6 The number of 24cent stamps: x=6 The number of 37 cent stamps:20-x=20-6=14 : Check, if you had 6 \$.24 stamps and 14 \$.37 stamps would the value be \$6.62? 6(.24)+14(.37)=6.62 ? 1.44+5.18=6.62 ? 6.62=6.62 !!! We're right!!! Happy Calculating!!!
 Number-Line/59287: This question is from textbook Holt Middle School Math 3t<=27 1 solutions Answer 40637 by funmath(2925)   on 2006-11-01 14:38:33 (Show Source): You can put this solution on YOUR website! Because t is less than or equal to 9, put either a closed circle or a ] over 9 and shade to the left over the numbers less than 9. <<=================]----> -1,0,1,2,3,4,5,6,7,8,9,10 Happy Calculating!!!
 logarithm/59281: Given log10 11=wand log10 5=x, find log10 551 solutions Answer 40635 by funmath(2925)   on 2006-11-01 14:34:22 (Show Source): You can put this solution on YOUR website!Rule: loga (b*c)=(loga b)+(loga c) Given log10 11=wand log10 5=x, find log10 55 log10 (11*5) (log10 11)+(log10 5) Happy Calculating!!!
 logarithm/59282: log3 x=21 solutions Answer 40632 by funmath(2925)   on 2006-11-01 14:29:39 (Show Source): You can put this solution on YOUR website!Rule loga b=c ---> b=a^c log3 x=2 I think you mean log base 3 of x =2. If so rewrite it as an exponential equation: Happy Calculating!!!
 Quadratic_Equations/59260: Would someone be able to help me through a couple of these so I can get a better grip on how to do them? Determine the number of solutions to the quadratic equation using the discriminant to determine if the answers are real or complex. (no need to find the roots, just the numer & solution type) i. 2x^2+5x+5=0 ii. 3z^2+z-1=0 Many thanks!1 solutions Answer 40631 by funmath(2925)   on 2006-11-01 14:24:27 (Show Source): You can put this solution on YOUR website! Determine the number of solutions to the quadratic equation using the discriminant to determine if the answers are real or complex. (no need to find the roots, just the numer & solution type) : The discriminant of a quadratic equation written in standard form is Notice that this is just the inside of the square root in the quadratic equation. If the discriminant is positive there are 2 real solutions. If the discriminant is 0 there is one real solution. If the discriminant is negative there are 2 complex solutions. : i. 2x^2+5x+5=0 a=2, b=5,c=5 The discriminant is negative. There are 2 complex solutions. : ii. 3z^2+z-1=0 a=3, b=1,c=-1 The discriminant is positive. There are two real solutions. Happy Calculating!!!
 Proportions/59278: namethree fraction whose decimal equivalent is 0.40. 1 solutions Answer 40627 by funmath(2925)   on 2006-11-01 14:13:07 (Show Source): You can put this solution on YOUR website!namethree fraction whose decimal equivalent is 0.40. This is read 40 one-hundredths, so start there. 40/100 4/10 reduce the top and bottom by 10 2/5 reduce the top and bottom by 2 There's an infinite number of possibilities!!! 400/1000 6/15 12/30 What can you come up with? Happy Calculating!!!
 Linear-systems/59266: This question is from textbook algebra 1 i dont understand how to do this problem: y=3x-7 y=-x+11 solutions Answer 40624 by funmath(2925)   on 2006-11-01 14:07:33 (Show Source): You can put this solution on YOUR website!y=3x-7 y=-x+1 We're looking for when their x=x and y=y, so set the problems equal to each other. 3x-7=-x+1 3x+x-7=x-x+1 4x-7=1 4x-7+7=1+7 4x=8 4x/4=8/4 x=2 Let x=2 and solve for y in one of the equations. y=-(2)+1 y=-1 The solution is:(2,-1) Graphically, it's their point of intersection: Happy Calculating!!!
 absolute-value/59277: 2x^2 + 3xy-4y^2 when x=2 and y= -41 solutions Answer 40622 by funmath(2925)   on 2006-11-01 13:59:59 (Show Source): You can put this solution on YOUR website! when x=2 and y= -4 Happy Calculating!!!
 Equations/59262: x/5=x-2/71 solutions Answer 40621 by funmath(2925)   on 2006-11-01 13:55:34 (Show Source): You can put this solution on YOUR website!It helps to put parenthesese around the fractions so that we know where they begin and end. If this isn't what you meant, let me know and I'll redo it. The LCD is 7*5=35, multiply both sides by 35 and clear your fractions. : Check by letting x=-5 and see if the sides actually equal. we're right if I interpretted your problem correctly. Happy Calculating!!!
 Radicals/59274: I don't know if I am inputting this correctly, but I will try.... Use only radicals in answer: ^3(radical sign)-54x^15y^6 (all are under radical except ^3)1 solutions Answer 40620 by funmath(2925)   on 2006-11-01 13:40:54 (Show Source): You can put this solution on YOUR website!I haven't found an easy way of indicating cubed roots either. I've used: \3/ Find the perfect cubes within the radical sign. \3/ \3/ Take the perfect cubes out and leave the rest inside the radical sign. -3x^5*y^2\3/ -3x^5y^2 the cubed root of 2. Happy Calculating!!!
 Numeric_Fractions/59272: One-third X plus two-fifths X equals one-fifteenth What is X?1 solutions Answer 40617 by funmath(2925)   on 2006-11-01 13:30:15 (Show Source): You can put this solution on YOUR website!One-third X plus two-fifths X equals one-fifteenth What is X? This can be easier if we clear the fractions by multiplying everything by the LCD, 15: Happy Calculating!!!
 Functions/59178: Find the domain of the rational function: f(x) = (2x^2 - 4) / (3x^2 + 6x - 45)1 solutions Answer 40611 by funmath(2925)   on 2006-11-01 11:39:05 (Show Source): You can put this solution on YOUR website!Find the domain of the rational function: The domain of a simple rational function is all real numbers EXCEPT the numbers that make the denominator equal 0. (x+5)(x-3)=0 x+5=0 and x-3=0 x=-5 and x=3 will make the denominator 0 and the fraction undefined. Therefore the domain includes all real numbers except:-5, and 3. set builder notation:{x|x not= -5,3} interval notation:(-infinity,-5)U(-5,3)U(3,infinity) Happy Calcualting!!!
 Exponential-and-logarithmic-functions/59245: Please find derivative and simplify: y=ln(3x-5)^3/(5x+4)^41 solutions Answer 40610 by funmath(2925)   on 2006-11-01 11:11:17 (Show Source): You can put this solution on YOUR website!Please find derivative and simplify: d/dx[ln(x)]=1/x d/dx[cf(x)]=cf'(x) d/dx[c]=0 Chain Rule: d/dx[f(g(x))]=f'(g(x))*g'(x) : y=ln((3x-5)^3/(5x+4)^4) Use properties of logs to simplify first. y=ln((3x-5)^3)-ln((5x+4)^4) y=3ln(3x-5)-4ln(5x+4) Now take the derivative using the chain rule: Happy Calculating!!!
 Quadratic_Equations/59229: Given the following quadratic function: f(x) = x squared - 2x - 8, (1) Rewrite the function in vertex form. Identify the vertex.1 solutions Answer 40608 by funmath(2925)   on 2006-11-01 11:01:24 (Show Source): You can put this solution on YOUR website!Given the following quadratic function: f(x) = x ^2 - 2x - 8, (1) Rewrite the function in vertex form. Identify the vertex. Vertex form is: , where (h,k)=vertex. We need to create a perfect square trinomial by adding and subtracting the same number, so you are really only adding 0. : f(x)=x^2-2x-8 f(x)=(x^2-2x+__)-___-8 Fill the blanks with (1/2(-2))^2=(-1)^2=1 The vertex (h,k)=(1,-9) Happy Calculating!!!
 Quadratic_Equations/59230: This question is from textbook elementary and intermediate algebra Use the discriminant to determine whether or not the quadratic 2x^2 + 3x + 2 is prime. If it is not prime, factor it.1 solutions Answer 40607 by funmath(2925)   on 2006-11-01 10:42:43 (Show Source): You can put this solution on YOUR website!Use the discriminant to determine whether or not the quadratic 2x^2 + 3x + 2 is prime. If it is not prime, factor it. The discriminant of a quadratic equation written in standard form: is , if this is negative there is no real number solution, if it's not a perfect square, it's not factorable. : a=2, b=3, and c=2 : It's not factorable and has no real solution. Happy Calculating!!!
 Quadratic_Equations/59242: X 2/3 - X 1/3-6=01 solutions Answer 40604 by funmath(2925)   on 2006-11-01 10:14:35 (Show Source): You can put this solution on YOUR website! Let Factor as usual. p-3=0 and p+2=0 p=3 and p=-2 But we want to know what X is, so let again. and and and Check by substitution: 27 checks out -8 checks too Happy Calculating!!!
 Functions/59236: Please Find the Derivatives of the following and simplify: y=5e^3x y=1/e^x y=e^3 y=e^x2e^2x Thanks! 1 solutions Answer 40602 by funmath(2925)   on 2006-11-01 10:00:54 (Show Source): You can put this solution on YOUR website!Find the Derivatives of the following and simplify: d/dx[cf(x)]=cf'(x) d/dx[e^x]=e^x d/dx[c]=0 The chain rule: d/dx[f(g(x)]=f'(g(x))g'(x) : Use the chain rule: : ---->> Use the chain rule again: : There is no x, this is a constant even though it doesn't look like one. . The derivative of a constant is 0. : I'm not sure if I'm interpretting you right on this one, let me know if there's a misunderstanding!!! -------->> --->> Use chain rule: : Happy Calculating!!!