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 Numbers_Word_Problems/151566: A vending machine will accept nickels and dimes only. The attendant checks the machine and finds a total of 42 coins whose value is \$3.40. How many coins of each type were there?1 solutions Answer 111421 by checkley77(12569)   on 2008-08-11 10:39:13 (Show Source): You can put this solution on YOUR website!D+N=42 OR D=42-N .10D+.05N=3.40 .10(42-N)+.05N=3.40 4.20-.10N+.05N=3.40 -.05N=3.40-4.20 -.05N=-.80 N=-.80/-.05 N=16 NUMBER OF NICKELS. 42-16=26 NUMBER OF DIMES. PROOF: .10*26+.05*16=3.40 2.6+.80=3.40 3.40=3.40
 Percentage-and-ratio-word-problems/151571: How many ounces of a 10% baking soda solution must be added to 40 ounces of a 2% baking soda solution to make a 5% baking soda solution?1 solutions Answer 111420 by checkley77(12569)   on 2008-08-11 10:32:59 (Show Source): You can put this solution on YOUR website!.10X+.02*40=.05(40+X) .10X+.08=2+.05X .10X-.05X=2-.8 .05X=1.2 X=1.2/.05 X=24 OZ. OF 10% IS NEEDED. .10*24+.02*40=.05(40+24) 2.4+.8=.05*64 3.2=3.2
 Linear_Equations_And_Systems_Word_Problems/151574: The length of the longest side of a triangle is twice the length of the shortest side. The length of the middle-sized side is five more than the length of the shortest side. Find the lengths of the sides of the triangle if the perimeter is 33 feet. Draw and label a picture representing this solution.1 solutions Answer 111419 by checkley77(12569)   on 2008-08-11 10:28:54 (Show Source): You can put this solution on YOUR website!.10X+.02*40=.05(40+X) .10X+.8=2+.05X .10X-.05X=2-.08 .05X=1.2 X=1.2/.05 X=24 OZ. OF 10% BAKING SODA MUST BE ADDED. PROOF: .10*24+.02*40=.05(40+24) 2.4+.8=.05*64 3.2=3.2
 Percentage-and-ratio-word-problems/151588: How many ounces of a 10% baking soda solution must be added to 40 ounces of 2% baking soda solution to make a 5% baking soda solution?1 solutions Answer 111418 by checkley77(12569)   on 2008-08-11 10:26:55 (Show Source): You can put this solution on YOUR website!.10X+.02*40=.05(40+X) .10X+.8=2+.05X .10X-.05X=2-.08 .05X=1.2 X=1.2/.05 X=24 OZ. OF 10% BAKING SODA MUST BE ADDED. PROOF: .10*24+.02*40=.05(40+24) 2.4+.8=.05*64 3.2=3.2
 Geometry_Word_Problems/151589: The length of the longest side of a triangle is twice the length of the shortest side. The length of the middle-sized side is five more than the length of the shortest side. Find the lengths of the sides of the triangle if the perimeter is 33 feet.1 solutions Answer 111417 by checkley77(12569)   on 2008-08-11 10:22:38 (Show Source): You can put this solution on YOUR website!LONGEST SIDE=2X SHORTEST SIDE=X MIDDLE SIDE=X+5 2X+X+X+5=33 4X=33-5 4X=28 X=28/4 X=7 FOR THE SHORTEST SIDE. 7+5=12 FOR THE MIDDLE SIDE 2*7=14 FOR THE LONGEST SIDE. PROOF: 7+12=14=33 33=33
 logarithm/151505: This question is from textbook precalculus Example 4 on page 352 shows how to do this problem, but I am having problems factoring once I get to the point of setting the 2-x-x^2>0 and then solving for x (factoring is one of my major weaknesses). I seem to have trouble with factoring whenever I am faced with needing to combine the same variable in two different forms (e.g. the -x-x^2). Thanks. 1 solutions Answer 111374 by checkley77(12569)   on 2008-08-10 16:08:58 (Show Source): You can put this solution on YOUR website!2-x-x^2>0 -X^2-X+2>0 (-X+1)(X+2)=0 -X+1=0 -X=-1 X=1 ANSWER. X+2=0 X=-2 ANSWER.
 Money_Word_Problems/151434: Find the interest earned at the end of the first year on 6,800. invested at 4% I started with I=0.4x1/12=6800 then is it0.4 /12=6800/12 I am stuck1 solutions Answer 111373 by checkley77(12569)   on 2008-08-10 16:01:54 (Show Source): You can put this solution on YOUR website!YOU HAVE THE WRONG FORMULA. I=PR^T WHERE I=INTEREST, P=PRINCIPLE, R=ANNUAL % RATE, T=NUMBER OF YEARS. I=6,800*.04^1 I=\$272 IS THE INTEREST AT THE END OF 1 YEAR.
 Polynomials-and-rational-expressions/151463: simplify: (5Lm)^3 / (-2L)^4 thank you1 solutions Answer 111370 by checkley77(12569)   on 2008-08-10 15:33:34 (Show Source): You can put this solution on YOUR website!(5LM)^3 / (-2L)^4 125L^3M^3/16L^4 125M^3/16L^(4-3) 125M^3/16L ANSWER.
 test/151471: if you osve this,can you please break down the steps and explain what to do because i dont know what to do when you 3 equations like these: A=11B A+x=5(B+x) A+x+5=3(B+x+5)1 solutions Answer 111369 by checkley77(12569)   on 2008-08-10 15:30:17 (Show Source): You can put this solution on YOUR website!First you replace A by 11B in the remaing 2 equations. A+x=5(B+x) 11B+x=5(B+x) 11B+x=5B+5x x-5x=5B-11B -4x=-6B (EQUATION #1) A+x+5=3(B+x+5) 11B+x+5=3(B+x+5) 11B+x+5=3B+3x+15 x-3x=-11B+3B+15 -2x=-8B+15 (EQUATION #2) MULTIPLY THIS EQUATION BY -2 & ADD IT TO EQUATION #1. 4X=16B-30 -4x=-6B ------------------ 0=10B-30 10B=30 B=30/10 B=3 ANSWER. A=11*3 A=33 ANSWER. -4x=-6*3 -4x=-18 x=-18/-4 X=4.5 ANSWER. PROOF 33+4.5=5(3+4.5) 37.5=5*7.5 37.5=37.5
 Distributive-associative-commutative-properties/151504: please help me to solve this equation (x-3)(8x+12)1 solutions Answer 111366 by checkley77(12569)   on 2008-08-10 15:15:54 (Show Source): You can put this solution on YOUR website!(x-3)(8x+12) 8x^2+12x-24x-36 8x^2-12x-36 4(2x^2-3x-9)
 Mixture_Word_Problems/151483: Please help me my friends all have the same answer but I don't. 7.)How many quarts of a 60% alcohol solution must be added to 40 quarts of a 20% alcohol solution to obtain a mixture whic is 30% alcohol? All percentages are by volume. 6.) What weight of water must be evaporated from 40lb of a 20% salt solution to produce a 50% solution? All percentages are by weight. thank you1 solutions Answer 111365 by checkley77(12569)   on 2008-08-10 15:13:09 (Show Source): You can put this solution on YOUR website!7) .6x+40*.2=.3(40+x) .6x+8=12+.3x .6x-.3x=12-8 .3x=4 x=4/.3 x=13.33 quarts of 60% alcohol is needed. proof: .6*13.33+8=.3(40+13.33) 8+8=.3*53.33 16=16 --------------------------------------------------- 6) 40*.2=8 pounds of salt. For a 50% solution you need 2*8=16 pounds of water. 40-16=24 pounds of water must be evaporated.
 Equations/151485: please solve and show your work for me 3/x < 2/x+1 Thanks1 solutions Answer 111364 by checkley77(12569)   on 2008-08-10 14:58:38 (Show Source): You can put this solution on YOUR website!3/x < 2/x+1 2x<3(x+1) 2x<3x+3 2x-3x<3 -x<3 x>-3 (the sign changes from < to > when dividing by a negative number. proof: let x=-3.1 3/-3.1<2/(-3.1+1) -.96774<2/-2.1 -.96774<-.9524
 Geometry_Word_Problems/151445: a developer wants to enclose a rectangular lot that borders a city street. if the developer has 248ft of fence and DOES NOT fence the side bordering the street, what is the largest area that can be enclosed?1 solutions Answer 111327 by checkley77(12569)   on 2008-08-10 09:28:21 (Show Source): You can put this solution on YOUR website!TO SOLVE THESE PROBLEMS JUST DIVIDE THE TOTAL LENGTH BY 3. 248/3=62 THIS IS THE SHORT SIDES OF THE FENCE. THE REMAINING FENCE (248-2*62)=248-124=124 IS THE LONG SINGLE SIDE. PROOF; 62*124=7,688 SQUARE FT. IS THE LARGEST AREA. TRY A SQUARE BY DIVIDING THE FENCE LENGTH BY 3. 248/3=82.67 NOW SQUARE 62.67^2=6,834 SQUARE FT.
 Square-cubic-other-roots/151453: sqrt(t+12)-t=0 is the problem. solve algebraically and check potential solutions I'm not sure whether to add t+12 then square or distribute after t^2+12^2-t=01 solutions Answer 111325 by checkley77(12569)   on 2008-08-10 09:19:16 (Show Source): You can put this solution on YOUR website!sqrt(t+12)-t=0 SQRT(T+12)=T NOW SQUARE BOTH SIDES. (T+12)=T^2 T^2-T-12=0 (T-4)(T+3)=0 T-4=0 T=4 ANSWER. T=3=0 T=-3 ANSWER.
 Travel_Word_Problems/151407: A freight train takes 2 hours longer to travel 300 miles than an express train to travel 280 miles. The rate of the express train is 20mph greater than the rate of the freight train. Find the time for the express train. Please help!1 solutions Answer 111302 by checkley77(12569)   on 2008-08-09 18:20:34 (Show Source): You can put this solution on YOUR website!300=r(t+2) r=300/(t+2) 280=(r+20)t 280=(300/(t+2)+20)t 280=300t/(t+2)+20t 280=(300t+20t(t+2))/(t+2) 280(t+2)=300t+20t^2+40t 280t+560=340t+20t^2 20t^2+340t-280t-560=0 20t^2+60t-560=0 20(t^2+3t-28)=0 20(t+7)(t-4)=0 t-4=0 t=4 hours for the express train 280=4(r+20) 280=4r+80 4r=280-80 4r=200 r=200/4 r=50 mph is the rate of the freight train. proofs: 300=50(4+2) 300=300 280=(50+20)*4 280=70*4 280=280
 Polynomials-and-rational-expressions/151355: simplify: L^9m^8 / n^3 L1 solutions Answer 111301 by checkley77(12569)   on 2008-08-09 17:45:00 (Show Source): You can put this solution on YOUR website!L^9m^8 / n^3 L=L^8m^8/n^3 (if L is in the denominator). L^10m^8/n^3 (if L is a multiplier)
 Travel_Word_Problems/151403: I am having difficulty setting up this word problem. If a taxi charges .50 for the first 1/5 of a mile, and .20 for every 1/10 of a mile after that, how much would it cost to go 2 miles?1 solutions Answer 111300 by checkley77(12569)   on 2008-08-09 17:39:40 (Show Source): You can put this solution on YOUR website!1/5 mile=.50 2-1/5=1 4/5 mile or 9/5 or 18/10 miles. 18*.20=3.60 for the rest of the 2 mile ride. Thus the total for the 2 mile ride=.50+3.60=\$4.10
 Graphs/151408: You are told that a line has a slope of -3 / 4 and that the line passes through the point given by ( -2, 3 ). Choose two other points from those given below which are on this same line. 1 solutions Answer 111299 by checkley77(12569)   on 2008-08-09 17:34:29 (Show Source): You can put this solution on YOUR website!SLOPE=-3/4 POINT=(-2,3) 4=-3/4*-3+b 4=9/4+b b=4-9/4 b=(16-9)/4 b=7/4 ANOTHER POINT IS (0,7/4) THUS THE EQUATION OF THIS LINE IS: Y=-3X/4+7/4 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, -3x/4 +7/4).
 Rectangles/151409: If the perimeter is 210 yards and the area is 2250 square yards, what are the dimensions?1 solutions Answer 111298 by checkley77(12569)   on 2008-08-09 17:28:46 (Show Source): You can put this solution on YOUR website!sORRY i DIDN'T NOTICE THE RECTANGLE IN THE 'Move to a better place box'. XY=2250 X=2250/Y 2(2250/Y)+2Y=210 4500/Y+2Y=210 (4500+2Y*Y)/Y=210 4500+2Y^2=210Y 2Y^2-210Y+4500=0 2(Y^2-105+2250)=0 2(Y-75)(Y-30)=0 Y-75=0 Y=75 Y-30=0 Y=30 Y=75 THEN X=30 Y=30 THEN X=75 PROOF: 2*75+2*30=210 150+60=210 75*30=2250 2250=2250
 Geometry_Word_Problems/151410: can someone help me with this word problem? i have tried everything, but i just cant seem to figure it out... three circles have to be cut into a piece of metal. the specifications state that each of the diameters must be within 0.001 centimeter of the given measurements. let D represent the given measurement and let x respresent the actual diameter of the circle. write an absolute value inequality that descrides the acceptible diameters of the circle. if the circles are to be 13 centimeters, 9 centimeters, nad 6 centimeters, describe the acceptable diameters of each circle. 1 solutions Answer 111296 by checkley77(12569)   on 2008-08-09 17:14:00 (Show Source): You can put this solution on YOUR website!D=13+/-.001=12.999 TO 13.001 cm. D=9+/-.001=8.999 TO 9.001 cm. D=6+/-.001=5.999 TO 6.001 cm.
 Exponential-and-logarithmic-functions/151073: using the formula w=0.00185h^2.67 where w is a boy's weight in pounds and h is his height in inches, find the height of a boy whose weight is 100 pounds.1 solutions Answer 111216 by checkley77(12569)   on 2008-08-08 16:51:02 (Show Source): You can put this solution on YOUR website!w=0.00185h^2.67 100=0.00185H^2.67 H^2.67=100/0.00185 H^2.67=54,054 H=2.67\/54,054 H=59.237 INCHES TALL.
 Polynomials-and-rational-expressions/151142: I= E/R+r for rfor r. 1 solutions Answer 111215 by checkley77(12569)   on 2008-08-08 16:45:17 (Show Source): You can put this solution on YOUR website!I= E/R+r SUBTRACT E/R FROM BOTH SIDES. r=I-E/R ANSWER.
 Trigonometry-basics/151160: tan ((4pi/3)-pi/4))1 solutions Answer 111214 by checkley77(12569)   on 2008-08-08 16:42:38 (Show Source): You can put this solution on YOUR website!tan ((4pi/3)-pi/4))=.05947
 logarithm/151170: using formula w=0.00185h^2.67 where w is a boy's weight in pounds and h is his height in inches, estimate the height of a boy whose weight is 100 pounds.1 solutions Answer 111213 by checkley77(12569)   on 2008-08-08 16:39:10 (Show Source): You can put this solution on YOUR website!w=0.00185h^2.67 100=0.00185H^2.67 H^2.67=100/0.00185 H^2.67=54,054 2.67\/54,054=59.24 INCHES TALL.
 Polynomials-and-rational-expressions/151303: find the area of a rectangle which shows the answer as a polynomial in descending powers of x. length: 4x+5, width: 4x-11 solutions Answer 111212 by checkley77(12569)   on 2008-08-08 16:26:30 (Show Source): You can put this solution on YOUR website!length: 4x+5, width: 4x-1 AREA=(4X+5)(4X-1) AREA=16X^2+20X-4X-5 AREA=16X^2+16X-5
 Angles/151232: Solve the formula for h: V=1/3 Bh Thanks, Pat1 solutions Answer 111144 by checkley77(12569)   on 2008-08-07 20:08:36 (Show Source): You can put this solution on YOUR website!V=1/3 Bh V=BH/3 MULTIPLY BOTH SIDES BY 3. BH=3V DIVIDE BOTH SIDES BY B. H=3V/B ANSWER.
 Linear-equations/151237: Find the x- and y-intercepts of x + 3y + 2 = 0 1 solutions Answer 111139 by checkley77(12569)   on 2008-08-07 19:59:39 (Show Source): You can put this solution on YOUR website!x + 3y + 2 = 0 3y=-x-2 y=-x/3-2/3 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, -x/3 -2/3). intercepts=(-2,-2/3)
 Linear-equations/151239: y = 1/7x -20 y = 7x + 151 solutions Answer 111137 by checkley77(12569)   on 2008-08-07 19:52:48 (Show Source): You can put this solution on YOUR website!y = 1/7x -20 (RED LINE) y = 7x + 15 (GREEN LINE) (graph 300x200 pixels, x from -6 to 5, y from -20 to 22, of TWO functions x/7 -20 and 7x +15). intersection=(-5.104,-20.728)
 Linear-equations/151240: x/4 - y/11 = -9/44 x/6 - y/13 = -1/261 solutions Answer 111133 by checkley77(12569)   on 2008-08-07 19:43:30 (Show Source): You can put this solution on YOUR website!x/4 - y/11 = -9/44 (11X+4Y)/44=-9/44 DIVIDE BOTH SIDES BY 1/44. 11X-4Y=-9 x/6 - y/13 = -1/26 (13X-6Y)/84=-1/26 DIVIDE BOTH SIDES BY 1/26. (13X-6Y)/3=-1 13X-6Y=-3 NOW MULTIPLY THIS EQUATION BY 2 & MULTIPLY THE OTHER EQUATION BY -3 & ADD THEM: 26X-12Y=-6 -33X+12Y=27 ------------------------ -7X=21 X=21/-7 X=-3 ANSWER. 11*-3-4Y=-9 -33-4Y=-9 -4Y=-9+33 -4Y=24 Y=24/-4 Y=-6 ANSWER. PROOF: -3/6-(-6/13)=-1/26 -1/2+6/13=-1/26 (-13+12)/26=-1/26 -1/26=-1/26
 Polynomials-and-rational-expressions/151143: 5 3 ____ + ______ =⅔ x – 1 7X – 7 1 solutions Answer 111131 by checkley77(12569)   on 2008-08-07 19:20:34 (Show Source): You can put this solution on YOUR website!5 3 ____ + ______ =2/3 x – 1 7X – 7 [5(7X-7)+3(X-1)]/(X-1)(7X-7)=2/3 [35X-35+3X-3]/(7X^2-14X+7)=2/3 2(7X^2-14X+7)=3(38X-38) 14X^2-28X+14=114X-114 14X^2-28X-114X+14+114=0 14X^2-142X+128=0 2(7X^2-71X+64)=0 2(7X-64)(X-1)=0 7X-64=0 7X=64 X=64/7 X=9.1428 ANSWER. X-1=0 X=1 NOT A VALID ANSWER BECAUSE THIS WOULD REQUIRE DIVIDING BY 0. PROOF 5/(9.1428-1)+3/(7*9.1428-7)=2/3 5/8.1428+3/(64-7)=2/3 .614+3/57=2/3 .614+.0526=2/3 .666=.666