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# Recent problems solved by 'RAY100'

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 Inequalities/220760: 8x-y=20 -5x+y=-8 1 solutions Answer 165661 by RAY100(1637)   on 2009-10-02 15:34:45 (Show Source): You can put this solution on YOUR website!(1) 8x -y=20 (2) -5x +y =-8 . (1)+(2) 3x +12 . x=4,,,,,,,subst in (1) . 8(4) -y =20 . -y = 20-32= -12 . y =12 . . checking,,,(4, 12),,,,(1) 8(4) -(12) =20,,,,,,ok . (2) -5(4) +(12) =-8,,,,-20 +12 =-8,,,,ok .
 Linear-equations/220752: How do you solve this. How much whipping cream and 2%milk should be mixed to obtain 35gallons of milk with 4% butterfat? 2%milk has 2% butterfat Whipping cream has 9% butterfat 1 solutions Answer 165659 by RAY100(1637)   on 2009-10-02 15:26:50 (Show Source): You can put this solution on YOUR website!Let m = amt milk,,,,and c = amt of cream,,,,both in gallons . .02m +.09c = .04 (35) . but m+c =35,,,,,or m=35-c,,,,subst . .02(35-c) + .09 c = .04(35) . .7 -.02c + .09c = 1.4 . .07c = .7 . c= 10 gal,,,,,,,,,m=35-10=25 gal . . checking,,,,,.02(25) + .09(10) = .04(35) . .5 + .9 = 1.4,,,,,ok .
 Linear-equations/220750: what is the equation of the line of m=6/7 (8,-7)1 solutions Answer 165656 by RAY100(1637)   on 2009-10-02 15:17:59 (Show Source): You can put this solution on YOUR website!starting with the standard slope intercept form,,,y=mx+b . if m= (6/7) ,,,and (8, -7),,,,,,,,,substituting . (-7) = (6/7)(8) +b . -7 -48/7= b . -7 -6 6/7 =b . b= -13 6/7 . reviewing the std eqn,,,y = 6/7 *x - 13 6/7,,,answer in slope intercept form . multiplying by 7 . 7y =6x - 97 . or,,,,-6x +7y = -97,,,,mult by -1 . 6x -7y =97,,,,,answer in std form.. . . checking,,( 8,-7),,,,,6(8) -7(-7) = 97,,,,,ok .
 Graphs/219591: How to graph a fraction?1 solutions Answer 165111 by RAY100(1637)   on 2009-09-30 14:37:17 (Show Source): You can put this solution on YOUR website!If the axis of a graph can be set up (labeled) as fractions, just use axis,, , for example, if x axis is labeled every 1/16,,,and you want to locate x=1/2, just use 8/16 as location. . . If the graph is labeled as whole numbers, just convert fraction to decimal, by dividing numerator by denominator, and then estimate location between whole numbers. .
 Number-Line/219588: where is 5/3 on a number line?1 solutions Answer 165110 by RAY100(1637)   on 2009-09-30 14:32:20 (Show Source): You can put this solution on YOUR website!5/3 = 1.667,,,,,on number line it is between +1 and +2,,,,or more specifically,,it is 2/3 of way between +1 and +2 on number line .
 Linear-systems/219590: from this equation 5=7x+2 how do you determine if the answer will be odd or even without solving the problem? 1 solutions Answer 165109 by RAY100(1637)   on 2009-09-30 14:29:20 (Show Source): You can put this solution on YOUR website!odd(5)-even(2) yields odd(3) . odd(3) divided by odd (7) yields odd (3/7) .
 Reduction-of-unit-multipliers/219579: convert 70 meters to inches using two unit multipliers. work so far: 70m x 100cm/1m x 2.54cm/1 in = 70(100)(2.54)?1 solutions Answer 165108 by RAY100(1637)   on 2009-09-30 14:25:29 (Show Source): You can put this solution on YOUR website!70 m * (100cm)/(1m) * (1 in)/(2.54 cm) = 2755.9 in . Rough check, 1 m = 39.36 in approx , 70*39.36 = 2755.2 in ok . . Note: dimensions only,,,(m) * (cm)/(m) * (in)/ (cm) shows cancellation of dim's . hence,,,the name,,,,,,dimensionless analysis,,,, .
 Polynomials-and-rational-expressions/219584: X^2 - 3X i am suppose to determin the constant that should be added to the binomial so that it becomes a perfect square trinomial.1 solutions Answer 165106 by RAY100(1637)   on 2009-09-30 14:19:04 (Show Source): You can put this solution on YOUR website!if we review,,,(a+b)^2 = (a+b) * (a+b) = a^2 +2ab +b^2 . looking at coefficients, 2given / 2(half) =1,,,1^2 = 1(3rd coefficient) . therefore if we have 2nd coefficient, take half and square it to get 3rd coefficient. . . x^2 -3x + 2.25,,,,,,,-3/2=-1.5,,,,,-1.5^2 = 2.25 . . check,,,,(x-1.5)^2 = (x-1.5)(x-1.5) = x^2 -1.5x -1.5x +2.25 = x^2 -3x +2.25 . note,,,1.5 = 3/2 . .
 Reduction-of-unit-multipliers/219586: what is the answer 2qt= qt1 solutions Answer 165099 by RAY100(1637)   on 2009-09-30 14:10:37 (Show Source): You can put this solution on YOUR website!as 2qt = 1 qt is UNTRUE,,,there is NO SOLUTION to this problem .
 Reduction-of-unit-multipliers/219582: convert 50 square cm to square meters using two unit multipliers. work so far: 50sqcm x 100cm/1m=? how do you get two unit mulitpliers with this conversion?1 solutions Answer 165098 by RAY100(1637)   on 2009-09-30 14:08:35 (Show Source): You can put this solution on YOUR website!50 cm^2 * (1 m/100cm)^2= 50/100^2 m^2 = .005 m^2 .
 Polynomials-and-rational-expressions/219580: 4i(3i-2) i am suppose to write the result in standard form.1 solutions Answer 165097 by RAY100(1637)   on 2009-09-30 14:05:20 (Show Source): You can put this solution on YOUR website!4i(3i-2),,,,distribute . 4*3*i*i - 4*i*2 . 12i^2 - 8i,,,,but i^2 =-1,,,,subst . -12 -8i,,,,answer in std form(a+bi) .
 Geometry_Word_Problems/219578: For a fixed area, the length of a rectangle is inversly proportional to its width. A rectangle has a width of 18 feet and a length of 12 feet. If the length is increased to 16 feet, find the width.1 solutions Answer 165095 by RAY100(1637)   on 2009-09-30 14:02:26 (Show Source): You can put this solution on YOUR website!Length = K / Width . example is ,,,12 = K/18,,,,,K=216,,, . problem,,,,16=216/w,,,,,,w=13.5 ft . check: K=16*13.5 = 216,,,,ok .
 Mixture_Word_Problems/219575: Hi, I have a solution/miture question. I can solve the problem just fine once I get it in the right order... but this one I'm having a hard time putting all the info where it belongs. Q) A pharmacist has 20L of a 10% drug solution. How many liters of 5% solution must be added to get a mixture that is 8%? If you could just help me get this in the right format I would would be so thankful!! Thanks!!! Casie R1 solutions Answer 165093 by RAY100(1637)   on 2009-09-30 13:57:28 (Show Source): You can put this solution on YOUR website!Let x= amt added in liters . .1(20) + .05x = .08(20+x),,,drug amt,,,,,note total volume is x+20 . .(2) +.05x = 1.6 + .08x . .(.4) = .03 x . 13.33333 = x in liters . . check,,,.1*20 +.05*13.33333= .08*33.33333 . 2+.667 = 2.6667,,,ok .
 Numbers_Word_Problems/219569: Ok, heres another one, same principle as last one i just cant get it :( The sum of two numbers is 55. The greater number is seventeen times the smaller number plus one. Find the numbers. It doesn't give a second number like the other one does.1 solutions Answer 165091 by RAY100(1637)   on 2009-09-30 13:50:07 (Show Source): You can put this solution on YOUR website!Let x = greater number,,,y= other number . x+y= 55,,,,,or y=55-x . x=(17*y) +1,,,,,subst . x=17*(55-x) +1 . x=935 -17x +1 . 18x = 936 . x=52,,,,,,,y=55-52 = 3 . . check,,,,52+3=55,,,,ok . 52 = 17*3 +1 = 51+1 =52,,,,ok ,
 Number-Line/219571: Two-thirds of a number is negative six. Find the number. 1 solutions Answer 165085 by RAY100(1637)   on 2009-09-30 13:37:59 (Show Source): You can put this solution on YOUR website!Let x = number . (2/3)*x = -6,,,,,,multiply by 3/2 . x=-6*3/2 =-9 . . check ,,,,(2/3) * -9 = -6,,,,,,ok .
 Equations/218933: How fast should you drive if you want to travel 400 miles in 6 hours? (The distance formula is D=rt? if possible could you explain this problem step by step how to do it so i will understand how to do it?1 solutions Answer 164758 by RAY100(1637)   on 2009-09-29 13:51:23 (Show Source): You can put this solution on YOUR website!Velocity = Distance / time = 400 miles / 6 hrs = 66.67 miles per hr .
 Trigonometry-basics/218927: use a calculator to find 1n36.9 to the nearest ten thousandth1 solutions Answer 164756 by RAY100(1637)   on 2009-09-29 13:29:56 (Show Source): You can put this solution on YOUR website!ln 36.9 = 3.608211 = 3.6082 . technique,, 36.9, enter, ln, enter. .
 Trigonometry-basics/218932: write the standard form of the equation of the circle that is tangent to x= -2 and has its center at (2, -4)1 solutions Answer 164755 by RAY100(1637)   on 2009-09-29 13:25:47 (Show Source): You can put this solution on YOUR website!the standard form for a circle is,,,(x-h)^2 +(y-k)^2 = r^2 . with (h,k) as center of circle,,and r as radius . with center at (2, -4),,,,,h= 2,,,k= -4,,,and radius is the x distance from center to x=-2,,,|(-2-2)| = |(-4)| = 4 . substituting, (x-2)^2 + (y-(-4) )^2 =4^2 =16 . (x-2)^2 +(y+4)^2 = 16,,,,answer . . a rough sketch shows how this is possible on the x-y coordinate system. . .
 Equations/218928: The cost of 4 pillows, plus 5% sales tax, was 46.20. How much did each pillow cost? if possible i need it to be step by step on how to do this problem so i will understand how to do it??1 solutions Answer 164754 by RAY100(1637)   on 2009-09-29 13:15:18 (Show Source): You can put this solution on YOUR website!Let p = cost of one pillow . Total cost = 4*p + (4p*.05) = \$ 46.20 . 4p + .2p = 46.20 . 4.2 p =46.20 . p= \$11,,,,,answer . alternate solution,,,1.05 *4p = 46.20 . p= \$ 11 . . note increases in cost, like tip or taxes, use 1+ increase . for decreases in cost, like discounts, use 1- decrease . . check...46.20/44 = 1.05,,,or 5% increase,,,ok .
 Trigonometry-basics/218922: find the distance between points at (6, -3) and (-1, 4)1 solutions Answer 164752 by RAY100(1637)   on 2009-09-29 13:07:13 (Show Source): You can put this solution on YOUR website!the distance formula is ,,,,d= sqrt{y2-y1)^2 + (x2-x1)^2 } . for (6,-30,,,,(-1,4) . d= sqrt( -30 -4)^2 + (6-(-1) )^2 } . d= sqrt { (-34)^2 + (7)^2 } . d=sqrt { 1156 +49 } . d=sqrt { 1205) . d=34.713 . . a rough sketch always helps clarify. . the change in y = 34,,,and the change in x= 7,,,c^2 = a^2+b^2,, d^2=34^2+7^2,,,d=34.713,,,ok .
 Trigonometry-basics/218909: find the area of a sector if the central angle measures 5pi/6 radians and the radius of the circle is 8 centimeters. round to the nearest tenth.1 solutions Answer 164751 by RAY100(1637)   on 2009-09-29 12:54:38 (Show Source): You can put this solution on YOUR website!Area = pi*r^2 =pi*8^2 =64*pi . Area of Sector = Area * radians of sector/ 2*pi radians . a= ( 64 * pi) * (5/6 pi) / 2 (pi) = 26.67*pi = 83.7758= 83.8 cm ^2 . . check ,,,5/6 pi * 180/pi = 150 degrees, a= 64 pi * 150/360 = 83.7758 ,,,,ok .
 Numeric_Fractions/218907: If you want to find the % increase from 281 students in 2008 to 1425 in 2009 how do you set this up to solve? 1 solutions Answer 164749 by RAY100(1637)   on 2009-09-29 12:41:54 (Show Source): You can put this solution on YOUR website!% increase is the amt of increase divided by original number . (1425 - 281)/281 = 1144/281 =4.071 = 407.1 % .
 Length-and-distance/218888: the distance between santa fe and roswell is 185 miles. If the two cities are 4 5/8 inches apart on a mpa how many inches woud represent 30 miles on the same map1 solutions Answer 164747 by RAY100(1637)   on 2009-09-29 11:38:55 (Show Source): You can put this solution on YOUR website!185/30=4.625/x,,,,,,where x = # inches for 30 miles . cross multiply,,,,185 x = 30*4.625 . x=30*4.625/185 = .75 = 3/4 inch . . check,,,,,185/4.625 =30/.75 = 40,,,,,ok .
 Age_Word_Problems/218883: Nick walked a total of 30 blocks in 5 days. Each day he walked 3 blocks more than the previous day. How many blocks did he walk on Day 1. I think the answer is he did not walk any distance on day 1. Please explain the solution.1 solutions Answer 164746 by RAY100(1637)   on 2009-09-29 11:33:44 (Show Source): You can put this solution on YOUR website!Let x= distance for day 1,,,subsequent days are,,x+3,,x+6,,x+9,,,x+12 . as total for 5 days is 30,, . x +x+3 +x+6 +x+9 =x+12 =30 . 5x +30 =30 . 5x =0 . x= 0,,,,,,,or he doesn't have to walk at all 1st day,, . . check,,0+3+6+9+12 = 30,,,,ok .
 Trigonometry-basics/218882: Find an equation of variation for the given situation. problem: y varies jointly as x and z and inversely as w, and y=3/2 when x=2, z=3, and w=41 solutions Answer 164743 by RAY100(1637)   on 2009-09-29 11:12:31 (Show Source): You can put this solution on YOUR website!y=K*(x*z)/w,,,,,,,subst in values known . 3/2 = K*{ 2*3/4} = K* 6/4 =K*3/2 . K=1 . expression,,,y= x*z/w .
 Equations/218876: Solve for x: (the fractions are giving me problems) 75(x/60)=60((x+10)/60)1 solutions Answer 164742 by RAY100(1637)   on 2009-09-29 11:06:36 (Show Source): You can put this solution on YOUR website!75(x/60) =60( (x+10)/60 ) = x+10 . mult thru by 60 to clear fractions . 75x = 60x +600 . 15x = 600 . x=40 . . check,,,75{ (40)/60} = 60{ [(40)+10]/60 } . 50 = 60 {50/60} = 50,,,,,ok .
 Mixture_Word_Problems/218869: A bakery wants to make a dessert out of chocolate and almonds. If the cost of chocolate is \$.75 a pound, and almonds is \$.50 a pound, then how many pounds of chocolate should be used to make 30 pounds of the dessert that costs the bakery \$.65 a pound?1 solutions Answer 164741 by RAY100(1637)   on 2009-09-29 11:00:14 (Show Source): You can put this solution on YOUR website!Let a = amt of almonds,,,,,and c= amt of chocolate,,,,,in #'s . a+c=30,,,a=30-c . . .75*c + .50*a =.65 * 30,,,,,subst . .75c +.5(30-c) = .65*30 . .75c +15 -.5c = 19.5 . .25c =4.5 . c=18 #,,,,,a=30-18=12 # . . check,,,,.75(18) +.5(12) =.65*30 . 13.5 + 6 = 19.5,,,,ok
 Geometry_Word_Problems/218862: A 4 ft piece of PVC pipe is cut in three pieces. The longest piece is 12 in. longer than twice the smallest piece. The middle piece is 6 in. less than the longest piece. How long is each piece?1 solutions Answer 164737 by RAY100(1637)   on 2009-09-29 10:35:24 (Show Source): You can put this solution on YOUR website!Let a,,b,,c,,,be the pieces,,,a,, largest,,,c,,,smallest,,,,in inches . a+b+c=4ft = 48 inches . a=2c+12,,,,,b= a-6,,,,,,,substituting . (2c+12) +(a-6) +c =48,,,,,,but a=(2c+12) . (2c+12+ +{(2c+12)-6} +c = 48 . 2c+12 +2c+12 -6 +c = 48 . 5c = 30 . c=6,,,,a=2(6)+12= 24,,,,b=(26-6)= 18 . . check,,,,,a+b+c=48,,,,,24+18+6=48,,,,ok .
 Numeric_Fractions/218865: Use fractions to determine which wrench is larger. 3/8 0r 7/16?1 solutions Answer 164735 by RAY100(1637)   on 2009-09-29 10:20:29 (Show Source): You can put this solution on YOUR website!In fractions the numerator is the number of pieces,,,the denominator is the size of the pieces. . To compare, usually the denominator is the same . 3/8 vs 7/16,,,,,lets use LCD = 16 . 3/8 = 6/16....16/8=2,,,2*3=6 . now problem is 3/8 =6/16 vs 7/16,,,,,with 7/16 Larger than 6/16 or 3/8 . 7/16 > 3/8
 Proportions/218863: This is a real question I need answered. I have 1 gallon of grape juice with 20% sugar content. I have another gallon of grape juice that has 68% sugar content. How much of the 68% sugar juice do I add to the 20% sugar juice to get a Juice that has 24% sugar content. Please help if you can. Thanks, Jim1 solutions Answer 164733 by RAY100(1637)   on 2009-09-29 10:13:02 (Show Source): You can put this solution on YOUR website!Let x = amount added in gallons . .2*1 + .68*x = .24(1+x) . .2 +.68x =.24 +.24x . .44x = .04 . x=.091 gallons . . check,,,.2 +.68*.091 =1.091*.24 . .2618 = .2618,,,,ok .
 Angles/218352: A third of an angle is 4 more than its supplement. Find both angles.1 solutions Answer 164462 by RAY100(1637)   on 2009-09-28 14:49:36 (Show Source): You can put this solution on YOUR website!Let x = angle,,,,,Let y = supplement = 180-x . x/3 = 4+y = 4+(180-x) = 184 -x . 1.33333x=184 . x=138,,,,,,,y=42 . . check,,,138/3 = 46=4+42=46,,,,,ok .