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 Proportions/205725: Clearing fractions; 1/2 * 4m - 3m - 5/2 The result I get is m - 2?1 solutions Answer 155349 by RAY100(1637)   on 2009-08-06 22:53:00 (Show Source): You can put this solution on YOUR website!1/2*4m -3m -5/2,,,,,,,check problem to assure we copied correctly . (1/2 * 4m) -3m -5/2 . 2m -3m -5/2 . -1m -5/2 . -m-2.5 .
 Miscellaneous_Word_Problems/205702: The sum of two numbers is 11. If the greater number is divided by the smaller number, the potential quotient is 2 and the remainder is 2. Find the numbers, using algebra. I cant figure out how to set this up. PLEASE HELP!!!1 solutions Answer 155339 by RAY100(1637)   on 2009-08-06 20:22:10 (Show Source): You can put this solution on YOUR website!Let x be larger of two variables, y the other . (1) x+y=11,,,,,or x=11-y . (2) x/y = 2 +Rem 2 = 2 + 2/y . subst (1) into (2) . (11-y) /y = 2 + 2/y . multiply thru by y . 11-y = 2y +2 . 11-2=2y+y . 9=3y . 3=y,,,,,,,,,x=11-y=11-3=8 . . CHECK,,,(1) 8+3=11,,,,ok . (2) 8/3=2 +2/3,,,,,ok
 Functions/205718: What is the difference between domain and range? Describe a real life situation that could be modeled by a function. 1 solutions Answer 155337 by RAY100(1637)   on 2009-08-06 20:13:59 (Show Source): You can put this solution on YOUR website!Domain is the set of the independent variable, usually x,, . while Range is the set of the dependent variable, usually y . Physically Domain might be time while Range is Weight, for a diet log . or Domain might be elapsed time vs Range , distance, for a travel log, . Usually Domain and Range are expressed as, "all Real Numbers" . or " all positive Real Numbers" . Exceptions occur when the value of the function, dependent variable, is . UNDEFINED,(denominator is zero),or COMPLEX (square root of a negative number) .
 Number-Line/205717: I need examples of when the sum of a positive number and several negative numbers will be positive. 1 solutions Answer 155334 by RAY100(1637)   on 2009-08-06 20:06:02 (Show Source): You can put this solution on YOUR website!Let P = positive number,,,and, N= sum of negative numbers . Given,,P+N>0 . P>-N, that is,,Positive Number greater than sum of negative numbers . Examples, P=5,,N=4=1+1+1+1, or 5-1-1-1-1>0 . or,,,,,P=5, N=3=1+1+1,,,,or 5-1-1-1>0 . or,,,,,,P=5, N=2=1+1,,,,,or 5-1-1 >0
 Quadratic_Equations/205712: I always have problems with word problems, Can you pleae help with this one A rectangular painting with a width of x centimeters has an area of x2+50x square centimeters. Find a binomial that represents the length1 solutions Answer 155332 by RAY100(1637)   on 2009-08-06 19:59:06 (Show Source): You can put this solution on YOUR website!Area = Length * Width . (x^2 +50x) = L*x . x(x+50) = L*x . (x+50) = L . check...A=LW,,,A=(x+50)(x) = x^2 +50x,,,,ok
 Percentage-and-ratio-word-problems/205709: Hi, I need help on my summer assignment, i did all of them except two...which i don't know how to do. I'm so sorry, they have parts to them. The first one is : "A Glass mirror is selling mirrors with frames. The store charges 10 cents for each square inch of mirror and 25 cents for each linear inch of frame. A. Show that a 20 inch by 30 inch mirror should cost 85 dollars (I tried solving this by multiplying the money by the inches, and by finding the area and stuff but either it equals more or less.) B. If there was a mirror that measures 40 inches on one side, what would the other measurement be if the price were still 85 dollars C. Write an equation that determines the price (p) given length (l) and width (W) D. Solve this equation for L" If you could just do A and B that would be great because then i could figure out c and D since u will show me the work and how u did it so I know....Thank You soooo much~! 1 solutions Answer 155331 by RAY100(1637)   on 2009-08-06 19:54:44 (Show Source): You can put this solution on YOUR website!(A) Cost = .10*Area + .25* Perimeter . If l=30,,& w=20,,,,Area = L*W,,,,Per = 2L + 2W . cost = .10(30*20) +.25( 2*30+2*20) . Cost = .10(600) + .25(100) . Cost = 60 + 25 = \$ 85 . (B) Let L=40,,,,find W . Cost = .1A + .25P = .1(40*W) + .25( 2*40+2*W)= 4W + 20 + .5W = 4.5 W +20 . If Cost is \$ 85,,85=4.5W +20,,,,65 = 4.5 W,,,,W= 14.444 in. . (C),,,, Cost = .1Area + .25Per . C= .1(L*W) + .25(2L+2W) . C= .1LW + .5L +.5W . (D) C-.5W = L (.1W +.5) . (C-.5W) / (.1W +.5) = L,,,,,,checking with original(20*30=\$85),,,ok
 Radicals/205705: I am having a problem solving this rational equation problem. Please help. Thank you. 3/x+1/4=5/81 solutions Answer 155327 by RAY100(1637)   on 2009-08-06 19:30:00 (Show Source): You can put this solution on YOUR website!3/x +1/4 = 5/8 . 3/x = 5/8 - 1/4 . 3/x = 5/8 -2/8 . 3/x = 3/8 . x=8 . check,,,3/8 +1/4 =3/8 +2/8 =5/8,,,,,ok
 Square-cubic-other-roots/205706: x to the 3/2th power = 271 solutions Answer 155326 by RAY100(1637)   on 2009-08-06 19:25:45 (Show Source): You can put this solution on YOUR website!x^(3/2) = 27 . raising both sides of eqn to (2/3) . x^1 = 27^(2/3) = {27^(1/3)}^2 = 3^2 = 9 . or x=9 . check,,,9^(3/2) = 27,,,,ok
 Rectangles/205703: This question is from textbook the length of a rectangle is 3 inches more than its width. Write an equation for the area of the rectangle in terms of width, w. 1 solutions Answer 155325 by RAY100(1637)   on 2009-08-06 19:12:53 (Show Source): You can put this solution on YOUR website!Area of Rectangle = Length * Width . but L = W +3 . A = L*W = (W+3)* W= W^2 + 3W .
 Miscellaneous_Word_Problems/205701: A dog owner has 250 feet of fencing to enclose a rectangular run for his dogs. If he wants the maximum possible area, what should the length and width of the rectangle be? 1 solutions Answer 155324 by RAY100(1637)   on 2009-08-06 19:09:46 (Show Source): You can put this solution on YOUR website!Perimeter of rectangle = 2* Length + 2* Width . P =250 = 2L +2W,,,,,dividing by 2 . 125 = L+W,,,,,W=125-L . Area = L*W = L*(125-L) = 125L -L^2 . making a table . L,,,,,,,Area . 1,,,,,,,124 . 60,,,,,,3900 . 62,,,,,,3906 . 62.5,,,,3906.25,,,,,max,,,,L=W=62.5 . 63,,,,,,3906 . The max area of the rectangle occurs when L=W=62.5 ft,,,, . This makes rectangle into a square .
 testmodule/205690: Do you know how to factor out (s + q)*2 - 64 = 1 solutions Answer 155323 by RAY100(1637)   on 2009-08-06 18:58:08 (Show Source): You can put this solution on YOUR website!Please see problem # 205691
 test/205691: Do you know how to factor out this equation (s + q)^2 - 64 =? 1 solutions Answer 155322 by RAY100(1637)   on 2009-08-06 18:56:43 (Show Source): You can put this solution on YOUR website!Let (s+q) =a . or substituting,,,a^2 -64 . factoring as difference of squares . (a+8)(a-8) . substituting back original variables . { (s+q) +8}{(s+q)-8} . {s+q+8}{s+q-8} .
 test/205696: There is a cross section of a clear spherical container with some fruit juice in it. The radius of the sphere is 18cm and the perpendicular distance from the centre of the sphere to the surface of the fruit juice is 9cm, calculate the diameter of the surface of the fruit juice in the sphere.1 solutions Answer 155321 by RAY100(1637)   on 2009-08-06 18:49:52 (Show Source): You can put this solution on YOUR website!The sphere, liquid, and radius, makes a right triangle, with a hypotenuse equal to the spherical radius of 18 cm, and one leg of length 9 cm. . Using the pythagorean theorem, the radius of the liquid can be found. . c^2 = a^2 +b^2,,,,or 18^2 = 9^2 + r^2,,,,r^2 = 18^2 -9^2 = 243,,,,r=15.588 cm . or the diameter = 2*15.588 = 31.177 cm .
 Numbers_Word_Problems/205667: If the average of ten consecutive odd integers is 20, what is the average of the last five of those integers? Please show me how to do it.1 solutions Answer 155290 by RAY100(1637)   on 2009-08-06 14:05:19 (Show Source): You can put this solution on YOUR website!1st integer,,,n,,,,,,,,,11 2nd integer,,,n+2,,,,,,,13 3rd integer,,,n+4,,,,,,,15,,,,,sum to 75,,,,,avg is 75/5 = 15 4th integer,,,n+6,,,,,,,17 5th integer,,,n+8,,,,,,,19 . 6th integer,,,n+10,,,,,,21 7th integer,,,n+12,,,,,,23 8th integer,,,n+14,,,,,,25,,,,,,sum to 125,,,,,avg is 125/5=25 9th integer,,,n+16,,,,,,27 10th integer,,,n+18,,,,,,29 . TOTAL,,,,,,,,,10n +90,,,,,,,,,,,,,,,,,,,,,,,,,,,,,sum to 200 . If (10n +90)/10 =20,,,,,n+9 =20,,,,n=11 . substitute back in above
 Equations/205662: This question is from textbook Algebra I:An Incremental Development PLEASE help me with this subscripter variable: 3N^N+3N^Q=9 2N^N=10-6N^Q1 solutions Answer 155287 by RAY100(1637)   on 2009-08-06 13:48:29 (Show Source): You can put this solution on YOUR website!(1) 3n^n +3n^q =9,,,,n^n = (9-3n^q)/3 = 3-n^q . (2) 2n^n +6n^q =10 . subst (1) into (2) . 2(3-n^q) +6n^q =10 . 6-2n^q +6n^q =10 . 4n^q=4 . n^q=1,,,,,,therefore q=0,,,,anything raised to 0 =1,,, . subst into (1),,,,3n^n +3n^0 =9 . n^n +n^0 =3 . n^n +1 =3 , n^n =2 . n= 1.56 . check(1) 3*1.56^1.56 +3*1.56^0 =9 . 6 +3=9,,,,,ok . (2) 2*1.56^1.56 = 10 - 6*1.56^0 . 4= 10 -6 =4,,,,ok .
 Percentage-and-ratio-word-problems/205664: This question is from textbook Algebra I : An Incremental Development Pleaase Help! Junior ate 5% of the sandwicher at the picnic. If he ate 2 1/2 sandwiches, how many sandwiches were there originally? Thank You : )1 solutions Answer 155285 by RAY100(1637)   on 2009-08-06 13:25:09 (Show Source): You can put this solution on YOUR website!5 % of X = 2.5,,,,, "%" means per centum (or per hundred),,"of" means multiply . 5/100 * X=2.5 . X= 2.5 / (5/100) = 2.5 / .05 = 50 . check,,,,2.5 / 50 = .05 = 5 %,,,,ok .
 Proportions/205658: please help.. they are indirect and direct variations, please show work.. asap 3.If y varies directly with x, and y = 8 when x = 16, find y when x = 46. 5. If y varies directly with x, and y = 2 when x = 4, find y when x = 45. i got this k=2/4=1/2(45)y=90 7.If y varies indirectly with x, and y = 10 when x = 25, find y when x = 35. i got k=10/25=2/5(35)y=14 some one please help me i really need to understand these problems they are due tonight. thanks a bunch if some one will help me//1 solutions Answer 155282 by RAY100(1637)   on 2009-08-06 13:19:48 (Show Source): You can put this solution on YOUR website!(3)y= kx,,,,,,,that is y varies directly with x . 8 = k * (16),,,,,,,when y=8, x=16,,,,,,find k . k=8/16 =1/2 . Variation is,,,,y = 1/2 * x . when x= 46,,,,,,,,y = (1/2) * 46 = 23 . check,,,8/16 = 23/46,,,,,ok . (5) y=kx,,y varies directly with x . 2=k*4,,,,when y=2,,,x=4,,,,find k . k=1/2 . Variation is ,,,,y= 1/2 *x . y= (1/2)*45 =22.5 . check 22.5 /45 = 2/4,,,,ok . (7) y= k/x,,,,,,,y varies in directly with x . 10=k/25, y=10 when x=25,,,find k . 250 = k . Variation is,,,,y = 250/x . y= 250/35 = 7.14,,,,,find y if x=35 . check,,,y=k/x,,,xy =k = 10 * 25 = 7.14 * 35 = 250,,,ok .
 Polynomials-and-rational-expressions/205601: This question is from textbook Please show me the steps on how to solve this problem. x+9/x-3 * x^3-27/x^2+3x+91 solutions Answer 155228 by RAY100(1637)   on 2009-08-05 22:00:09 (Show Source): You can put this solution on YOUR website!{ ( x+9) / (x-3) } * {(x^3 -27) / (x^2 +3x+9)} . factor cubic,,,x^3 -27 = x^3 -3^3 = (x-3)(x^2 +3x +9) . {(x+9)/(x-3)} * { (x-3)(x^2 +3x +9)/ (x^2 +3x+9)} . simplify by canceling like terms . (x+9) . check,,,let x=2,,, original and answer = 11,,,ok
 Graphs/205600: Starting with the graph of f(x) = 2^x, write the equation of the graph that results from reflecting f(x) about the y-axis. y = ? 1 solutions Answer 155225 by RAY100(1637)   on 2009-08-05 21:48:03 (Show Source): You can put this solution on YOUR website!f(x) =2^x,,,,,on reflection about y axis,,f(x) =2^(-x) . { logic,,,f(x) =y,,,, reflection about y axis,,,has same y value ,,but . negative x value . plot graph to check .
 Square-cubic-other-roots/205597: This is a 3 part question but i already answered the first part on my own. The other two parts are to Simplify: the square root of 44 and the square root of 11 over 161 solutions Answer 155223 by RAY100(1637)   on 2009-08-05 21:36:59 (Show Source): You can put this solution on YOUR website!sqrt44 = sqrt(4 *11) = sqrt4 * sqrt(11) = 2sqrt(11) . sqrt(11/16) = sqrt(11) / sqrt(16) = sqrt(11) / 4 = (1/4) sqrt(11) . check,,,sqrt(44) = 6.63 = 2 sqrt(11),,,,ok . sqrt(11/16) = .829 = (1/4)sqrt(11),,,ok .
 Graphs/205596: The question is: Find an equation of a line parrallel to -3x-3y=5. I have no idea what to do. I thought I might need a graph but it doesn't say to use one. I don't know if i should add anything or subtract. HELP ME PLEASE!1 solutions Answer 155221 by RAY100(1637)   on 2009-08-05 21:29:57 (Show Source): You can put this solution on YOUR website!-3x-3y=5,,,,,remember slope intercept form ,,,y=mx+b . -3y=3x+5,,,,,divide thru by (-3) . y= (-1)x +(-5/3),,,,,,,,,line of slope(-1),,y intercept of -(5/3) . a parallel line has same slope, different y intercept, . such as,,,,y= (-1)x +(+5/3) . but this in standard form is,,,3y = -3x + 5,,,or,,,-3x -3y = -5 . to generalize, a set of parallel lines ,,,has same form as original . except change constant. .
 Exponential-and-logarithmic-functions/205572: log(subscript 4)(2x+1)=log(subscript 4)(x-3)+log(subscript 4)(x+5) (so subscript is like pushing the downward arrow.) 1 solutions Answer 155216 by RAY100(1637)   on 2009-08-05 21:20:22 (Show Source): You can put this solution on YOUR website!log(4) {2x+1} = log(4){x-3} + log(4){x+5} . log (2x+1) / log(4) = log(x-3)/log(4) + log(x+5) / log(4) . multiply thru by log(4) . log (2x+1) = log(x-3) + log (x+5) . log(2x+1) = log(x-3)(x+5),,,,,,loga +logb = log ab . 2x+1 = (x-3)(x+5) = x^2 +2x -15 . 0 = x^2 -16,,,,factor . 0 = (x+4)(x-4),,,,set equal to zero . x= 4, -4 . check,,,(+4),,, log(4){9) = log(4){1)+log(4){9),,,but ,,,log(1)=0,,,,ok . (-4),,,log(4){-7} = log(4){-7}+log(4){1},,,but,,log(4){1}=0,,,,ok .
 Numbers_Word_Problems/205581: How many integers between 1 and 1000 (inclusive) do not contain the digits 8 or 9? (A) 200 (B)488 (C)512 (D)521 (E)8001 solutions Answer 155205 by RAY100(1637)   on 2009-08-05 20:15:38 (Show Source): You can put this solution on YOUR website!looking at a typical hundreds chart, . in each set of 0 to 10,,(1-10,,11-20,,21-30,,etc) we have one 8, and one nine, for a total of two. . this is times 8, for sets of 10 up to 80. . then the 80's and 90's, give 10 each. . for typical 100 set, 8*2 +10 +10 = 36, 8"s or 9"s . this happens for 8,,,,100 sets,,(0-100,100-200, ....700-800),,,or 8*36 = 288 . all,,800's,,have an 8,,,or +100 . and all 900's have a 9,,,or +100 . This brings total to 288 +100+100=488,,,8"s or 9"s,,,up to 1000 . total without is 1000 - 488 = 512,,,or answer (c)
 Linear_Equations_And_Systems_Word_Problems/205558: the average of nine numbers is 40. if 1 is added to the first number, 2 is added to the second number, 3 is added to the third number and so on up to the ninth number, what is the new average?1 solutions Answer 155180 by RAY100(1637)   on 2009-08-05 17:19:33 (Show Source): You can put this solution on YOUR website!(E n )/9 =40 . {E (n(1) +1) + n(2) +2 +......... } / 9 = ? . (E n)/9 + { 1+2+3+4+5+6+7+8+9 } /9 = ? . (En)/9 + { 45/9} = ? . 40 +5 = ? . 45 = ?
 Polynomials-and-rational-expressions/205557: Hi, Im trying to work this one out in steps to show all work.. Factor: 64y3 – 125z3 A) (4y – 5z)(16y2 – 20yz + 25z2) B) (4y + 5z)(16y2 – 20yz + 25z2) C) (4y – 5z)(16y2 + 20yz + 25z2) D) (4y – 5z)(4y2 + 20yz + 5z2) Thank you1 solutions Answer 155179 by RAY100(1637)   on 2009-08-05 17:11:26 (Show Source): You can put this solution on YOUR website!Remember that,,,a^3 -b^3 = (a-b)(a^2 +ab+b^2) . 64y^3 -125z^3 . 4^3y^3 -5^3z^3 . (4y)^3 -(5Z)^3,,,,,or a=(4y),,,b= (5z) . (4y-5z){ (4y)^2 + (4y)(5z) +(5z)^2 } . (4y -5z)(16y^2 +20yz + 25 z^2) . or answer (c)
 Polynomials-and-rational-expressions/205555: Factor completely 3x^5+3x^31 solutions Answer 155178 by RAY100(1637)   on 2009-08-05 17:00:59 (Show Source): You can put this solution on YOUR website!3x^5 +3x^3 = 3x^3 ( x^2 +1) = 3x^3 ( x+i)(x-i) . Remember that, i^2 = -1 .
 Divisibility_and_Prime_Numbers/204975: Find the prime factorization and match your result to the correct answer below. 180 a. 22•32•5 b...2•3•5 c...22•32•75 d....4•5•91 solutions Answer 154718 by RAY100(1637)   on 2009-07-31 18:01:42 (Show Source): You can put this solution on YOUR website!180 . 2----90 . ,,,,,2---45 . ,,,,,,,,,5----9 . ,,,,,,,,,,,,,,3-3 . summary, 2*2*3*3*5 = 180,,,,ok . or 2^2, 3^2, 5,,,,,,which is answer (a)
 Coordinate-system/204974: Find the slope of the line that contains the points (–4, –2) and (1,1).1 solutions Answer 154716 by RAY100(1637)   on 2009-07-31 17:56:43 (Show Source): You can put this solution on YOUR website!(-4,-2),,,(1,1) . m= (y2-y1)/(x2-x1) = (1-(-2))/(1-(-4)) = 3/5 ,,,,slope is positive 3/5 . a rough graph, showing the points, connecting line, and rise / run confirms the calculation.
 Functions/204971: Complete the ordered pair so that it satisfies the given equation. Match your result to the correct answer below. 2x – 5y = –12: (–1, ___)1 solutions Answer 154715 by RAY100(1637)   on 2009-07-31 17:51:56 (Show Source): You can put this solution on YOUR website!2x -5y = -12 . if x= -1,,,,,y= ? . 2(-1) -5y = -12 . -2 -5y = -12 . -5y = -10 . y=2,,,,,,,,(-1,2) satisfies eqn . check,,2(-1) -5(2) = -2 -10 =-12 ,,,,,,ok .
 Miscellaneous_Word_Problems/204957: a snail climbs all the way up a pole 12m high. it climbs 3m each day but slides down 2m each night. How long will it take the snail to reach the top of the pole?1 solutions Answer 154714 by RAY100(1637)   on 2009-07-31 17:47:36 (Show Source): You can put this solution on YOUR website!net gain per day is (3-2) =1 m / day . to gain 12 m,, would take 12 days,,,(12 m/1 m/day = 12 days) . . Recognize that on the 10th day, the snail will start at the 9 m level,,and . gain 3 m during the day to just reach 12 m. . If some sort of platform exists to prevent his sliding back, . he could achieve his journey at the end of 10 days . .
 Radicals/204969: Hi! I am having trouble with the problem: Expressed in a + bi form, 5/3 + i is equivalent to... Thanks in advance. 1 solutions Answer 154710 by RAY100(1637)   on 2009-07-31 17:33:03 (Show Source): You can put this solution on YOUR website!a+bi,,,,,,is an expression of a complex number . Real part (a) ,,,,complex part (b) . (5/3) + (1) i,,,,,,,shows (a) = (5/3) ,,,,,(b) =(1) . . it is really a +/- bi,,,,,so just recognize real and complex in the . same way for a-bi as we did above for a+bi . . Usually this is plotted on an x - y axis graph, . with x as the real part(a) and y as the imaginary part (b)