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# Recent problems solved by 'funmath'

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 Polynomials-and-rational-expressions/59060: This question is from textbook elementary and intermediate algebra [(3x^2)^3]x^2 -------------. 9x^3 STATES TO SIMPLIFY?????1 solutions Answer 40514 by funmath(2925)   on 2006-10-31 10:19:02 (Show Source): You can put this solution on YOUR website!Rules we'll use: : Happy Calculating!!!
 Distributive-associative-commutative-properties/59061: This question is from textbook elementary and intermediate algebra Expand (4x - 2)^21 solutions Answer 40513 by funmath(2925)   on 2006-10-31 10:09:28 (Show Source): You can put this solution on YOUR website!Expand (4x - 2)^2 Remember this is the same thing as: (4x-2)(4x-2) 4x(4x-2)-2(4x-2) First distribute 4x times the second parenthesese, then distribute the -2 4x(4x)+4x(-2)-2(4x)-2(-2) 16x^2-8x-8x+4 Finally Combine your like terms. Happy Calculating!!!
 Linear-systems/59063: Find values for m and b in the following system so that the solution to the system is (-3, 4). 5x + 7y = b mx + y = 22 Thank you 1 solutions Answer 40512 by funmath(2925)   on 2006-10-31 10:04:36 (Show Source): You can put this solution on YOUR website!Find values for m and b in the following system so that the solution to the system is (-3, 4). L1) 5x + 7y = b L2) mx + y = 22 Let x=-3 and y=4 in L1 and solve for b: 5(-3)+7(4)=b -15+28=b 13=b : Now let x=-3 and y=4 in L2 and solve for m: m(-3)+4=22 -3m+4=22 -3m+4-4=22-4 -3m=18 -3m/-3=18/-3 : Check it out. Your system for which (-3,4) is a solution is: 5x+7y=13--->>5(-3)+7(4)=13---->>-15+28=13--->>13=13 -6x+y=22---->>>-6(-3)+(4)=22--->>18+4=22---->>22=22 We're Right!!! Happy Calculating!!!
 Linear-systems/59064: Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. 2x+3y=1 5x+3y=16 and x+5y=10 -2x-10y= -20 thank you1 solutions Answer 40511 by funmath(2925)   on 2006-10-31 09:52:51 (Show Source): You can put this solution on YOUR website!Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. L1) 2x+3y=1 L2) 5x+3y=16 Multiply either L1 or L2 by -1 and add it to L1 and the y's will be eliminated and you can solve for x. I'm going with L2: L2) -1(5x+3y)=-1(16) ---->> -5x-3y=-16 : 2x+3y=1 -5x-3y=-16 __________ -3x=-15 -3x/-3=-15/-3 x=5 Substitute that into either L1 or L2 and solve for y. I'm going with L1: 2(5)+3y=1 10+3y=1 -10+10+3y=-10+1 3y=-9 3y/3=-9/3 y=-3 The unique solution is: (5,-3) ::::::::::::::::::::::::::::::::: and L1)x+5y=10 L2)-2x-10y= -20 Multiply L1 by 2 and add to L2 in an attempt to eliminate the x's. L1) 2(x+5y)=2(10)---->> 2x+10y=20 2x+10y=20 -2x-10y=-20 ___________ 0+0=0 0=0 There is no unique solution for this one. because 0 does = 0 this one is dependent. It has an infinite number of solutions because graphically they are the same line and have all points in common. Happy Calculating!!!
 Linear-systems/59066: Solve each of the following systems by substitution. 5x - 2y=-5 y - 5x = 31 solutions Answer 40510 by funmath(2925)   on 2006-10-31 09:38:39 (Show Source): You can put this solution on YOUR website!Solve each of the following systems by substitution. L1) 5x - 2y=-5 L2) y - 5x = 3 Solve L2 for y (because y doesn't have a coefficient to worry about dividing) and substitute that in for y in L1 and solve L1 for x: L2) y-5x+5x=5x+3 ----->>> y=5x+3 L1) 5x-2(5x+3)=-5 5x-10x-6=-5 -5x-6=-5 -5x-6+6=-5+6 -5x=1 -5x/-5=1/-5 x=-1/5 Plug this value into L2 and solve for y: L2) y-5(-1/5)=3 y+1=3 y+1-1=3-1 y=2 The solution is (x,y)=(-1/5,2) Happy Calculating!!!
 Geometry_Word_Problems/59070: the distance between (2,3) and (6,0) is?1 solutions Answer 40509 by funmath(2925)   on 2006-10-31 09:19:39 (Show Source): You can put this solution on YOUR website!the distance between (2,3) and (6,0) is? The distance formula is: (x1,y1)=(2,3) and (x2,y2)=(6,0) Happy Calculating!!!
 Equations/59010: -4y - (5y +6) = -7y + 31 solutions Answer 40496 by funmath(2925)   on 2006-10-31 06:57:28 (Show Source): You can put this solution on YOUR website!-4y - (5y +6) = -7y + 3 -4y-5y-6=-7y+3 -9y-6=-7y+3 7y-9y-6=7y-7y+3 -2y-6=3 -2y-6+6=3+6 -2y=9 -2y/-2=9/-2 y=-9/2 : Happy Calculating!!!
 Divisibility_and_Prime_Numbers/59052: This question is from textbook What is a five-digit number divisible by both 2 and 5? What is a three digit number divisible by 2 and not 4? What is a three-digit number not divisible by 2, 3, or 5?1 solutions Answer 40495 by funmath(2925)   on 2006-10-31 06:51:21 (Show Source): You can put this solution on YOUR website!What is a five-digit number divisible by both 2 and 5? Any five digit number that ends in a 0 would be divisible by 10 and thus divisible by both 2 and 5. I'm going with 9,2340. You pick another. : What is a three digit number divisible by 2 and not 4? If the number ends in an even number, but the last two numbers aren't 0 or divisible by 4, then the number will be divisible by 2 and not 4. I'm going with 902. You find another. : What is a three-digit number not divisible by 2, 3, or 5? The number can't end in an even number, or it's divisible by 2, the sum of the digits can't be divisible by 3 or the number will be divisible by 3, the number can't end in 0 or 5 or it's divisible by 5. I'm going with 931. What number can you think of? : Happy Calculating!!!
 Linear-equations/59053: Please show me the graph and the answer to this equation I get confuse with the setting up here is my situation 10y+15x=20 my answer was 4 please show me thank you1 solutions Answer 40494 by funmath(2925)   on 2006-10-31 06:41:12 (Show Source): You can put this solution on YOUR website! 10y+15x=20 Let x=0 and solve for y 10y+15(0)=20 10y+0=20 10y=20 10y/10=20/10 y=2 Plot (0,2) : Let x=2 and solve for y 10y+15(2)=20 10y+30=20 10y+30-30=20-30 10y=-10 10y/10=-10/10 y=-1 Plot (2,-1) For lines you only need to plot two points unless otherwise specified. If you need to plot more, let x be even numbers to avoid fractions. Connect the two points and you have a line that looks like: Happy Calculating!!!
 Polynomials-and-rational-expressions/59030: x^4-8x^2+7=0 1 solutions Answer 40479 by funmath(2925)   on 2006-10-30 21:20:44 (Show Source): You can put this solution on YOUR website! Factor, (there are other methods.) Set each parenthesese equal to 0 and solve for x. and and and and and and Happy Calculating!!!
 Polynomials-and-rational-expressions/59015: can some one please help, i do not knwo how to figure this out. thanks 76. x^3-1/x^2+1 divided by 9x^2+9x+9/x^2-x1 solutions Answer 40476 by funmath(2925)   on 2006-10-30 21:11:29 (Show Source): You can put this solution on YOUR website!Formula used: divided by Flip and multiply the second fraction. Happy Calculating!!!
 Polynomials-and-rational-expressions/59011: factor completely with respect to the intergers x^4-13x^2+361 solutions Answer 40473 by funmath(2925)   on 2006-10-30 20:51:36 (Show Source): You can put this solution on YOUR website!factor completely with respect to the intergers Replace middle term with two terms that multiply to give you the product of the outer terms: x^4*36=36x^4, but add to give you the middle term:-13x^2. Then factor by grouping. Both parenthesese are the differences of perfect squares. Happy Calculating!!!
 Exponents/58989: (10x^2)^-3 OVER (5xy^-3)3 TIMES (y^8 x^2)^4 OVER (xy^2)^4 if you can help me with this that would be fantastic!!1 solutions Answer 40471 by funmath(2925)   on 2006-10-30 20:42:11 (Show Source): You can put this solution on YOUR website! Happy Calculating!!!
 Polynomials-and-rational-expressions/59005: factor comletely with respect to the intergers 4x^3-8x^2+3x-61 solutions Answer 40470 by funmath(2925)   on 2006-10-30 20:20:44 (Show Source): You can put this solution on YOUR website!HINT: When there are four terms, they usually want you to factor by grouping. factor comletely with respect to the intergers Group the first 2 terms and the last four terms Factor the GCF out of each group Factor the group out Happy Calculating!!!
 Polynomials-and-rational-expressions/58996: This question is from textbook Elementary and Intermediate Algebra Sum the polynomials 2x^2 - 3x - 4, 2x - 5 and 3x^3 + 2x^2 - 61 solutions Answer 40467 by funmath(2925)   on 2006-10-30 20:15:33 (Show Source): You can put this solution on YOUR website!Sum the polynomials 2x^2 - 3x - 4, 2x - 5 and 3x^3 + 2x^2 - 6 Combine like terms. Happy Calculating!!!
 Polynomials-and-rational-expressions/59003: factor completely with respect to the intergers 10x^4- 1601 solutions Answer 40465 by funmath(2925)   on 2006-10-30 20:10:15 (Show Source): You can put this solution on YOUR website!Two rules to remember on this one: Factorization of difference of perfect squares Sums of perfect squares are prime. : factor completely with respect to the intergers Factor out GCF of 10 Factor the difference of perfect squares a=x^2 and b=4. Factor the difference of perfect squares a=x and b=2. Happy Calculating!!!
 Distributive-associative-commutative-properties/58998: what is distributive properties and how do you do it? and also how do you factor expression?1 solutions Answer 40462 by funmath(2925)   on 2006-10-30 20:02:15 (Show Source): You can put this solution on YOUR website!The distributive property says: a(b+c)=ab+bc the a gets multiplied by everything in the parenthesese For instance: 2(4+3)=2(4)+2(3)=8+6=14 : Proof that it's true: 2(4+3)=2(7)=14 : Ex: 3(x+4)=3x+3(4)=3x+12 : There are too many ways to factor. You'll have to give me an example of what you're working on. I don't want to discourage you with something you're not up to yet. : Since you asked about the distributive property, I will tell you that factoring out the GCF (greatest common factor) is the opposite of factoring: 3x+12=3(x)+3(4)=3(x+4) : Happy Calculating!!!
 Expressions-with-variables/58999: 4n-6n=2n1 solutions Answer 40461 by funmath(2925)   on 2006-10-30 19:52:41 (Show Source): You can put this solution on YOUR website!I'm guessing this is probably mis-typed, but if not: 4n-6n=2n -2n=2n -2n+2n=2n+2n 0=4n 0/4=4n/4 Check: 4(0)-6(0)=2(0) 0-0=0 0=0 We're right!!! Happy Calculating!!!
 Polynomials-and-rational-expressions/58916: Am i correct in that y=x^2-2x+4 has no x-intercept.1 solutions Answer 40408 by funmath(2925)   on 2006-10-30 13:30:53 (Show Source): You can put this solution on YOUR website!Am i correct in that y=x^2-2x+4 has no x-intercept? Yes. An easy way to check that is to take the inside part of the square root in the quadratic equation b^2-4ac, and if it's negative, there is no x intercept. a=1, b=-2, and c=4 (-2)^2-4(1)(4) 4-16 -12 <---no x-intercept. Happy Calculating!!!
 Polynomials-and-rational-expressions/58897: simplify =? thank you very much.1 solutions Answer 40394 by funmath(2925)   on 2006-10-30 11:12:12 (Show Source): You can put this solution on YOUR website!simplify =? A lot of people use the acronym FOIL to remember to distribute everything (First, Outer, Inner, Last). I like to just distribute the first term then distribute the second term in the first parenthesis throught the second parenthesis. Combine your like terms: Happy Calculating!!!
 Percentage-and-ratio-word-problems/58894: joe purchased a jacket at a 10% discount sale for 121.50 what was the original price of the jacket1 solutions Answer 40391 by funmath(2925)   on 2006-10-30 11:05:42 (Show Source): You can put this solution on YOUR website!joe purchased a jacket at a 10% discount sale for 121.50 what was the original price of the jacket Let the original price of the jacket be:x The discount then is: (10/100)x=.10x The amount he paid: 121.50 : Equation to solve: x-.10x=121.50 .90x=121.5 .90x/.90=121.50/.90 x=1215/9 x=\$135 : Happy Calculating!!!
 Linear-equations/58896: Hi! What's the formula for finding a slope1 solutions Answer 40388 by funmath(2925)   on 2006-10-30 11:00:37 (Show Source): You can put this solution on YOUR website!The formula for finding a slope (m) is: Slope formula: when given two points: (x1,y1) and (x2,y2) : If you're ginven an equation and asked for a slope, or given an angle of elevation and asked for a slope we get it differently. Happy Calculating!!!
 Linear-systems/58854: This question is from textbook Beginning Algebra Could someone be so kind in helping me with this problem? I need to solve the following systems by substitution: 4x - 12y = 5 -x + 3y = -1 Thanks so much, Ashley1 solutions Answer 40362 by funmath(2925)   on 2006-10-29 21:23:13 (Show Source): You can put this solution on YOUR website!Solve the following systems by substitution: L1) 4x - 12y = 5 L2) -x + 3y = -1 Solve L2) for x and substitute that in for x in L1): -x+3y-3y=-1-3y -x=-1-3y -(-x)=-(-1-3y) x=1+3y : 4(1+3y)-12y=5 4+12y-12y=5 4+0=5 4=5 Your variables were eliminated and 4 does not = 5, there is no solution. These are parallel lines that will never intersect. Happy Calculating, Ashley!!!
 Quadratic-relations-and-conic-sections/58855: This question is from textbook I need a hand on this one please Given f(x)=-2(x+4)^2+5, find the vertex, domain,range and axis of symmetry. Thank you for your time1 solutions Answer 40361 by funmath(2925)   on 2006-10-29 21:16:51 (Show Source): You can put this solution on YOUR website!Given f(x)=-2(x+4)^2+5, find the vertex, domain,range and axis of symmetry. : This is in vertex form:, vertex=(h,k), domain is all real numbers, axis of symmetry is x=h, if a is positive, the range is (h,infinity) because it opens upward, if a is negative, the range is (-infinity,h). : a=-2, h=-4, k=5 The vertex is: (h,k)=(-4,5) Domain: all real numbers, (-infinity,infinity) Range, because a=-2 is: (-infinity,5) Axis of symmetry is: x=-4 Happy Calculating!!!
 Linear-systems/58851: This question is from textbook Beginning Algebra Could someone be so kind in helping me with this problem? I need to solve the following systems by substitution: 8x - 4y = 16 y = 2x - 4 Thank you so much, Ashley1 solutions Answer 40359 by funmath(2925)   on 2006-10-29 21:06:32 (Show Source): You can put this solution on YOUR website!Hi Ashley, Solve the following systems by substitution: L1) 8x - 4y = 16 L2) y = 2x - 4 Substitute 2x-4 for y in L2) and solve for x: 8x-4(2x-4)=16 8x-8x-16=16 0+16=16 16=16 Your variable was eliminated and 16 = 16, therefore there is an infinite number of solutions. The lines are lying on top of each other, they are graphically the same line and have all points in common. Some books list the solution to something with an infinite number of solutions as (x,2x-4). Most are happy with "all real numbers" or "infinite solutions." : Just to prove a point, watch what happens when you try to solve L1 for y: 8x-4y=16 -8x+8x-4y=-8x+16 -4y=-8x+16 -4y/-4=-8x/-4+16/-4 y=2x-4 It turns right into L2! Happy Calculating!!!
 Linear-equations/58844: This question is from textbook algerba 2 I struggle with inequalities and some equations, here is one that i have to graph: y=3/5x-41 solutions Answer 40355 by funmath(2925)   on 2006-10-29 20:54:25 (Show Source): You can put this solution on YOUR website!graph: y=(3/5)x-4 Let x=0 and solve for y. y=(3/5)(0)-4 y=0-4 y=-4 Plot (0,-4) : Let x=5 and solve for y y=(3/5)(5)-4 y=3-4 y=-1 Plot (5,-1) Connect the two points and you have a line that looks like: You can plot more points if your teacher requires it, but you only need two points when graphing a line. If you pick more points, make x numbers that are divisible by 5 and you'll avoid plotting fractions. Happy Calculating!!!
 Exponential-and-logarithmic-functions/58817: I need help on logarithms. This is a precalculus homework question. "Write the expression as one logarithm. 2ln x - 4ln (1/y) - 3ln(xy)" Thanks1 solutions Answer 40352 by funmath(2925)   on 2006-10-29 20:45:17 (Show Source): You can put this solution on YOUR website!Rules I will use: : Write the expression as one logarithm. 2ln(x)-4ln(1/y)-3ln(xy) Happy Calculating!!!
 Coordinate-system/58838: W hen giving a coordinates of a point graph, does y comes first or x1 solutions Answer 40350 by funmath(2925)   on 2006-10-29 20:32:51 (Show Source): You can put this solution on YOUR website!The x comes first. They're in alphabetical order: (x,y). Later on you will have a z and they will still be in alphabetical order: (x,y,z) That observation has helped me with a few formulas too. Happy Calculating!!!
 Polynomials-and-rational-expressions/58830: Find the value of x x-3 over 2 = x over 51 solutions Answer 40345 by funmath(2925)   on 2006-10-29 20:26:40 (Show Source): You can put this solution on YOUR website!Find the value of x The LCD is 2*5 so multiply both sides by 10 : check by letting x=5 and seeing if both sides equal. We're right!!! Happy Calculating!!!
 Expressions-with-variables/58831: 3(w+2)-(12-w)1 solutions Answer 40344 by funmath(2925)   on 2006-10-29 20:19:24 (Show Source): You can put this solution on YOUR website!3(w+2)-(12-w) distribute the - through 12-w 3w+6-12+w 3w+w+6-12 combine like terms 4w-6 Happy Calculating!!!