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 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
 Trigonometry-basics/151161: tan ((5pi/3)-pi/4))1 solutions Answer 111129 by checkley77(12569)   on 2008-08-07 19:03:47 (Show Source): You can put this solution on YOUR website!tan ((5pi/3)-pi/4)) TAN((5PI/3)-PI/4)=.0778 ACCORDING TO MY TI30X CALCULATOR.
 Numbers_Word_Problems/151172: The sum of the reciprocals of two consecutive even integers is 7/24. Find these integers.1 solutions Answer 111128 by checkley77(12569)   on 2008-08-07 18:55:52 (Show Source): You can put this solution on YOUR website!1/X+1/(X+2)=7/24 (X+2+X)/X(X+2)=7/24 (2X+2)/X^2+2X=7/24 7(X^2+2X)=24(2X+2) 7X^2+14X=48X+48 7X^2+14X-48X-48=0 7X^2-34X-48=0 (7X+8)(X-6)=0 X-6=0 X=6 ANSWER FOR THE SMALLER INTEGER. 6+2=8 FOR THE LARGER INTEGER. PROOF: 1/6+1/8=7/24 (8+6)/48=7/24 14/48=7/24 7/24=7/24
 Travel_Word_Problems/151180: Richard's average driving speed is 23 km per hour faster than Kirk's. In the same length of time it takes Richard to drive 651 km, Kirk drives on 490 km. What is Richard's average speed?1 solutions Answer 111126 by checkley77(12569)   on 2008-08-07 18:31:03 (Show Source): You can put this solution on YOUR website!651/(X+23)=490/X 651X=490(X+23) 651X=490X+11,270 651X-490X=11,270 161X=11,270 X=11,270/161 X=70 KMH FOR kIRK'S SPEED 70+23=93 KMH FOR rICHARDS SPEED. PROOF: 651/93=490/70 7=7
 Travel_Word_Problems/151181: a motorboat can go 8 miles downstream in 20 minutes. It takes the same motorboat 30 minutes to go back upstream the same 8 miles. find the speed of the current.1 solutions Answer 111125 by checkley77(12569)   on 2008-08-07 18:21:55 (Show Source): You can put this solution on YOUR website!8/.333= 24.024 MPH GOING DOWNSTREAM WITH THE CURRENT. 8/.5=16 MPH GOING UPSTREAM WITH THE CURRENT. (24.024-16)/2=8.024/2=4.012 MPH IS THE SPEED OF THE CURRENT.
 Travel_Word_Problems/151182: Les and Gil drove a total of 733 miles in 11.6 hours. Les drove the first part of the trip and averaged 55 mph. Gilbert drove the remainder of the trip and averagerd 65 mph. How long did Les drive?1 solutions Answer 111123 by checkley77(12569)   on 2008-08-07 18:09:44 (Show Source): You can put this solution on YOUR website!55X+65(11.6-X)=733 55X+754-65X=733 -10X=733-754 -10X=-21 X=-21/-10 X=2.1 HOURS FOR LES' DRIVING TIME. 11.6-2.1=9.5 HOURS FOR gILS' DRIVING TIME. PROOF: .55*2.1+65*9.5=733 115.5+617.5=733 733=733
 Money_Word_Problems/151211: This question is from textbook 102. Diversification. Helen has 1/5 of her portfolio in U.S. stocks, 1/8 of her portfolio in European stocks, and 1/10 of her portfolio in Japanese stocks. The remainder is invested in municipal bonds. What fraction of her portfolio is invested in municipal bonds? What percent is invested in municipal bonds? (Be sure to write the fraction in correct form.) M = municipal bond fraction m = % municipal bonds 1 solutions Answer 111122 by checkley77(12569)   on 2008-08-07 18:02:49 (Show Source): You can put this solution on YOUR website!1/5+1/8+1/10 (8+5+4)/40 17/40=.425=42.5% OF THE MONEY IS INVESTED IN MUNICIPAL BONDS.
 Radicals/151092: This question is from textbook Please help, how do you find the length of a side of a cube if the volume is 700^3 and round it up to three decimal places? Thank you in advance.1 solutions Answer 111023 by checkley77(12569)   on 2008-08-06 17:09:12 (Show Source): You can put this solution on YOUR website!V=1/6S(S^2+S^2+4S^2) 700=1/6S(6S^2 700=S^S^2 700=S^3 S=8.879 IS THE LENGTH OF THE SIDES OF THE CUBE.
 Human-and-algebraic-language/151094: a motorist travels 632 miles. assuming the car averages 29.3 miles per gallon, how many gallons of gasoline (to the nearest tenth of a gallon) were used?1 solutions Answer 111022 by checkley77(12569)   on 2008-08-06 17:02:35 (Show Source): You can put this solution on YOUR website!632/29.3=21.6 gal.
 Quadratic_Equations/151087: 1. Rewrite with a rational exponent... √(7&23) 2. Factor out the greatest common factor... 2x^6-10x^5+14x^4 3. Factor Completely... 24-11r+r^2 4. Find the x-intercepts... 24-11r+r^2 1 solutions Answer 111021 by checkley77(12569)   on 2008-08-06 17:01:01 (Show Source): You can put this solution on YOUR website!sqrt7 & sqrt23=7^(1/2), 23^(1/2) 2x^6-10x^5+14x^4 ---------------------- 2x^4(x^2-5x+7) --------------------- 24-11r+r^2 (8-r)(3-r) --------------------- y=x^2+2x-3 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, x^2 +2x -3 ). x intercepts=(1,0) & (-3,0)
 Equations/151088: a boxing club charges nonmembers \$4 per day to workout and \$10 per day for equipment rental. Members pay a yearly fee of \$400 and a daily fee of \$5 for equipment rental. write and solve an equation to find out how many times you should use the gym to jusify membership.1 solutions Answer 111019 by checkley77(12569)   on 2008-08-06 16:52:10 (Show Source): You can put this solution on YOUR website!(4+10)x=400+5x 14x=400+5x 14x-5x=400 9x=400 x=400/9 x=44.44 visits would make the membership equal to the non membership fees. proof: 14*44.44=400+5*44.44 622.2=400+222.2 622.2=622.2
 Equations/151091: a motorist travels 337 miles while using 13.7 gallons of gasoline. find the gasoline consumption in miles per gallon to one decimal place.1 solutions Answer 111018 by checkley77(12569)   on 2008-08-06 16:46:16 (Show Source): You can put this solution on YOUR website!337/13.7=24.6 mpg. answer.
 Mixture_Word_Problems/151089: This question is from textbook a survey of mathematics with applications I really need help figuring this problem out can anyone please help? Find the mean, median, and mode for the following set of data which shows the number of pages per article in a random sample of magazine articles. 4 6 4 6 5 4 4 5 7 4 3 6 5 8 4 1 solutions Answer 111017 by checkley77(12569)   on 2008-08-06 16:44:37 (Show Source): You can put this solution on YOUR website!first you need to arrange these integers in assending values: 3 4 4 4 4 4 4 5 5 5 6 6 6 7 8 the mean (average )=sum/number of integers: mean=75/15=5 answer. medium=the middle integer: medium=5 answer. mode=the most frequent integer. mode=4 (freqency=6) answer.
 Equations/150777: 3x + 6x-9 -6 = 0 for x over x-1 over x-1 3x over x-1 plus 6x-9 over x-1 minus 6 equals 0 solve for x?1 solutions Answer 111014 by checkley77(12569)   on 2008-08-06 16:25:36 (Show Source): You can put this solution on YOUR website!3x/(x-1)+(6x-9)/(x-1)-6=0 (3x+6x-9)/(x-1)=6 3x+6x-9=6(x-1) 9x-9=6x-6 9x-6x=-6+9 3x=3 x=3/3 x=1 answer. proof: 3*1/(1-1)+(6*1-9)/(1-1)-6=0 3/0+3/0-6=0 this is an invalid process by dividing by 0 thus there is no valid solution.
 test/151079: [88-(4 to the second power divided by 2)]-3] 1/2x28-4 to the second power 1 solutions Answer 111011 by checkley77(12569)   on 2008-08-06 16:12:26 (Show Source): You can put this solution on YOUR website![88-(4^2/2)](-3) [88-(16/2)](-3) [88-8]-3 80*-3=-240 answer. 1/2*28-4^2 14-16=-2 answer.
 Expressions-with-variables/151085: -6= t+5s : solve for s1 solutions Answer 111010 by checkley77(12569)   on 2008-08-06 16:05:48 (Show Source): You can put this solution on YOUR website!-6=t+5s 5s=-6-t s=(-6-t)/5=-(6+t)/5
 Quadratic-relations-and-conic-sections/151065: Please find all appropriate critical points and graph (conic) f(x)= x^2+x-2 Please show work Thank You 1 solutions Answer 111009 by checkley77(12569)   on 2008-08-06 16:04:10 (Show Source): You can put this solution on YOUR website!f(x)= x^2+x-2 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, x^2 +x -2). (-2,0),(1,0),(-.5,-2.25),(0,-2) are some of the critical points.
 test/151084: Write the verbal phrase as an equation or an inequality. Difference of x and thrity is equal to fifty Sum of x and eleven is greater than or equal to forty Product of three and x is less then fourteen Quotient of x and 3.5 is equal to nine1 solutions Answer 111008 by checkley77(12569)   on 2008-08-06 15:53:29 (Show Source): You can put this solution on YOUR website!x-30=50 x+11>=40 3x<14 x/3.5=9
 Geometry_Word_Problems/151033: This question is from textbook The perimeter of a rectangle is 40m. The base is four less than five times the height. what is the height?1 solutions Answer 110972 by checkley77(12569)   on 2008-08-06 11:23:17 (Show Source): You can put this solution on YOUR website!P=2B+2S 40=2*(5S-4)+2S 40=10S-8+2S 40=12S-8 12S=40+8 12S=48 S=48/12 S=4 LENGTH OF THE SIDES. B=5*4-4 B=20-4 B=16 ANSWER FOR THE LENGTH OF THE BASE. PROOF: 40=2*4+2*16 40=8+32 40=40
 Geometry_Word_Problems/151034: This question is from textbook What is the perimeter of a parallelogram with base 9cm, side length 27cm, and height 20cm?1 solutions Answer 110969 by checkley77(12569)   on 2008-08-06 11:19:17 (Show Source): You can put this solution on YOUR website!perimeter=2b+2s perimeter=2*9+2*27 perimeter=18+54 perimeter=72cm.
 Geometry_Word_Problems/151035: This question is from textbook If the height of a rectangle is 1&1/4m and the base is 6 1/2m, what is the area of the rectangle?1 solutions Answer 110967 by checkley77(12569)   on 2008-08-06 11:14:09 (Show Source): You can put this solution on YOUR website!1.25*6.5=8.125m is the area of the rectangle.
 Rational-functions/151055: 2xsquared - 4x = 3 how do i start to solve this? i tried it and got something with sqrt of 10...???1 solutions Answer 110966 by checkley77(12569)   on 2008-08-06 11:11:26 (Show Source): You can put this solution on YOUR website!2x^2 - 4x = 3 2x^2-4x-3=0 using the quadratic equation:we get: x=(4+-sqrt[-462-4*2*-3])/2*2 x=(4+-sqrt[16+24])/4 x=(4+-sqrt40)/4 x=(4+-6.325)/4 x=(4+6.325)/4 x=10.325/4 x=2.58 answer. x=(4-6.325)/4 x=-2.325/4 x=-.58 answer.
 Rational-functions/151049: Find an equation of a line through (1,-3) that is perpendicular to 5x+2y=141 solutions Answer 110963 by checkley77(12569)   on 2008-08-06 11:04:22 (Show Source): You can put this solution on YOUR website!5x+2y=14 2y=-5x+14 y=-5x/2+14/2 y=-5x/2+7 (red line) with a slope=-5/2 the perpendicular line has a slope of 2/5 through (1,-3) Y=mX+b -3=2/5*1+b -3=2/5+b b=-3-2/5 b=(-13-2)/5 b=-15/5 b=-3 for the y intercept for this line with a slope=2/5 y=2x/5-3 (green line) (graph 300x300 pixels, x from -6 to 8, y from -6 to 8, of TWO functions -5x/2 +7 and 2x/5 -3).
 Geometry_Word_Problems/151038: This question is from textbook If AD=(x+6)cm, AB=5cm and the perimeter of ABCD is 26cm, find the area of rectangle ABCD.1 solutions Answer 110957 by checkley77(12569)   on 2008-08-06 10:42:41 (Show Source): You can put this solution on YOUR website!2(x+6)+2*5=26 2x+12+10=26 2x=26-12-10 2x=4 x=4/2 x=2 6+2=8 is the ad measurement. 8*5=40 answer for the area of the rectangle. proof: 2*8+2*5=26 16+10=26 26=26
 Geometry_Word_Problems/151036: This question is from textbook The area of a rectangle is 243m squared. The height is nine less than four times the base. What is the perimeter?1 solutions Answer 110955 by checkley77(12569)   on 2008-08-06 10:37:11 (Show Source): You can put this solution on YOUR website!xy=243 x=243/y x=4y-9 (4y-9)y=243 4y^2-9y=243 4y^2-9y-243=0 (4y+27)(y-9)=0 y-9=0 y=9 answer for the height. x=4*9-9 x=36-9 x=27 answer for the base. proof: 9*27=243 243=243
 Polynomials-and-rational-expressions/151041: The formula b(t) = 1.353(1.9025)^t represents the number of broadband internet users (in millions) where t is the time in years measured from 1998. How many broadband users (to the nearest million) does this formula predict for 2004?1 solutions Answer 110954 by checkley77(12569)   on 2008-08-06 10:23:58 (Show Source): You can put this solution on YOUR website!b(t) = 1.353(1.9025)^t t=2004-1998=6 b(t)=1.353(1.9025)^6 b(t)=1.353*47.4185 b(t)=64 million broadband users in 2004 is the projection.
 Linear-equations/151044: Use the Substitution method to solve the system of equations. x + y = -4 x - y = 2 1 solutions Answer 110952 by checkley77(12569)   on 2008-08-06 10:19:01 (Show Source): You can put this solution on YOUR website!x + y = -4 x=-4-y x - y = 2 (-4-y)-y=2 -4-y-y=2 -2y=2+4 -2y=6 y=6/-2 y=-3 answer. x+(-3)=-4 x-3=-4 x=-4+3 x=-1 answer. proof: -1-(-3)=2 -1+3=2 2=2
 Linear-equations/151045: Use the Substitution method to solve the system of equations. x + y = 10 y = x + 8 1 solutions Answer 110951 by checkley77(12569)   on 2008-08-06 10:15:18 (Show Source): You can put this solution on YOUR website!x + y = 10 x=10-y y = x + 8 y=(10-y)+8 y=10-y+8 2y=18 y=18/2 y=9 answer. x+9=10 x=10-9 x=1 answer. proof: 9=1+8 9=9
 Linear-equations/151047: Use the Substitution method to solve the system of equations. y - 2x = -5 3y - x = 5 1 solutions Answer 110950 by checkley77(12569)   on 2008-08-06 10:12:47 (Show Source): You can put this solution on YOUR website!3x + y = 5 y=-3x+5 now replace y with(-3x+5) for x in the other equation & solve for x. 4x - 7y = -10 4x-7(-3x+5)=-10 4x+21x-35=-10 25x=-10+35 25x=25 x=25/25 x=1 answer. y=-3*1+5 y=-3+5 y=2 answer. proof 4*1-7*2=-10 4-14=-10 -10=-10
 Linear-equations/151046: Use the Substitution method to solve the system of equations. 1 solutions Answer 110949 by checkley77(12569)   on 2008-08-06 10:10:31 (Show Source): You can put this solution on YOUR website!3x + y = 5 y=-3x+5 now replace y with(-3x+5) for x in the other equation & solve for x. 4x - 7y = -10 4x-7(-3x+5)=-10 4x+21x-35=-10 25x=-10+35 25x=25 x=25/25 x=1 answer. y=-3*1+5 y=-3+5 y=2 answer. proof 4*1-7*2=-10 4-14=-10 -10=-10
 Polynomials-and-rational-expressions/151043: The time t required to empty a tank varies inversely as the rate r of the pumping. If a pump can empty a tank in 45 mintutes at a rate of 600kl/min, how long will it take a pump to empty the same tank if its rate is 1000 kl/min?1 solutions Answer 110948 by checkley77(12569)   on 2008-08-06 10:02:32 (Show Source): You can put this solution on YOUR website!600/1,000=x/45 1,000x=27,000 x=27,000/1,000 x=27 min. to empty the tank @ 1000 kl. per min.