Jane takes x minutes Joan takes 5x minutes Jane does 1/x of the job in 1 minute Joan does 1/5x of the job in 1 minute together they take 30 minutes (1/x)(30)+(1/5x)(30)=1 (job finished) (30/x)+(30/5x)=1 (30/x)+(6/x)=1 multiply both sides by...
Jane takes x minutes Joan takes 5x minutes Jane does 1/x of the job in 1 minute Joan does 1/5x of the job in 1 minute together they take 30 minutes (1/x)(30)+(1/5x)(30)=1 (job finished) (30/x)+(30/5x)=1 (30/x)+(6/x)=1 multiply both sides by...
a=longest side b=middle side c=shortest side a=b+c-1 which implies b=a-c+1 2c=a-9 which implies c=(a-9)/2 P=a+b+c 51=a+(a-c+1)+c 51=a+a-c+1+c 51=2a+1 50=2a a=25 c=(25-9)/2 c=16/2 c=8 b=a-c+1 b=25-8+1 b=18 a=25...
V=(pi)(r^2)(h) V=(3.14)(11^2)(20) V=(3.14)(121)(20) V=(3.14)(2420) V=7598.8 cubic feet
the frog is in the well 78 m deep every day he gains 4 m and loses 2 m for a net gain of 2 m each day 78/2=39 days to get to the top
draw the diagram draw triangle ABC draw line segment AM perpendicular to line segment BC draw line segment AD to the left, parallel to line segment MC and equal in length to MC draw line segment DC to form rectangle ADCM you now also have quadrilateral ABCD now find the area...
x+y=34 xy=max x=34-y y(34-y)=0 34y-y^2=0 use -b/2a -34/-2=17 17*17=289 16*18=288 15*19=285 14*20=280
find a common denominator the LCD is 3*4=12 write them as equal fractions with a common denominator of 12 (-1/3)=(-4/12) (7/4)=(21/12) (21/12)+(-4/12)=[21+(-4)]/12=[21-4]/12=17/12=1 5/12
putting the salaries in or from least to greatest 8, 9.2, 9.6, 12.3, 13.8, 14.1, 26.7, 35.8, 36.2, 37.3 mean: 203/10=20.3 median: the median is the middle number when there is an odd number of numbers and the numbers have been arranged according to size; however there...
distance=rate*time d=rt the wasp flies until it is squashed by the trains how long does the wasp fly for ? the wasp flies until the trains collide when do the trains collide ? 200=50t+50t 200=100t t=200/100 t=2 hours in 2 hours each train travels 100 kilometers...
first person takes 1/2 of 1 which is 1/2 second person takes 1/2 of 1/2 which is 1/4 third person takes 1/2 of 1/4 which is 1/8 fourth person takes 1/2 of 1/8 which is 1/16 fifth person takes 1/2 of 1/16 which is 1/32 sixth person takes 1/2 of 1/32 which is 1/64 seventh...
distance=rate*time d=50*t d=55*(32-t) 50t=55(32-t) 50t=1760-55t 50t+55t=1760 105t=1760 t=1760/105 t=16.7619 hours d=50*16.7619 d=838.09 miles
E' is the complement of set E the complement of E consists of all the elements in the Universal Set that are not in E U={a,b,c,d,e,f,1,2,3} E={a,b,2,3} E'={c,d,e,f,1}
2(x+2y)=12 -6x=5y-8 using the first equation... 2(x+2y)=12 (x+2y)=6 x=6-2y substitute -6(6-2y)=5y-8 -36+12y=5y-8 12y-5y=36-8 7y=28 y=4 using the second equation... -6x=5(4)-8 -6x=20-8 -6x=12 x=-2 (-2,4) is...
the number of subsets is 2^n where n=# of elements of the set set D has 7 elements there are 2^7=128 subsets therefore there are 128-1 proper subsets, or 127 proper subsets because we leave out the set D itself that contains all of the elements
log(3)(27)=2^x 3^(2^x)=27 3^(2^x)=3^3 if the bases are equal the exponents are equal (or log(3)27=log(3)(3^3)=3log(3)3=3*1=3) 2^x=3 log(2^x)=log(3) xlog2=log3 x=log3/log2 x=0.47712125472/0.30162999566 x=1.581809707
perimeter=210 feet area can't exceed 1350 square feet possible lengths are: (using whole numbers) 1x104 2x103 3x102 4x101 5x100 6x99 7x98 8x97 9x96 10x95 11x94 12x93 13x92 14x91 15x90 16x89=1424 which exceeds 1350...
2*2*11=44 2*2*13=52 3*3*5=45 5*5*2=50 there are 4 funny numbers or... 31 32=2*2*2*2*2 33=3*11 34=2*17 35=5*7 36=2*2*3*3 37 38=2*19 39=3*13 40=2*2*2*5 41 42=2*3*7 43 44=2*2*11 45=3*3*5 46=2*23 47...
the hare runs 20 m in 5 seconds so it takes the hare 100/20=5, 5*5=25 seconds to run 100 m the tortoise runs 2 m in 5 seconds so it takes the tortoise 100/2=50, 50*5=250 seconds to run 100 m if the race was a tie, the hare had to stop for 250-25=225 seconds
2/(x-3)-4/(x+3)=8/(x^2-9) x^2-9=(x+3)(x-3) multiply both sides by (x-3)(x+3) 2(x+3)-4(x-3)=8 2x+6-4x+12=8 -2x+18=8 -2x=8-18 -2x=-10 x=-10/-2 x=5 Check your work by replacing x by 5 in the original equation, which I did.
x=# of pennies (1/10)x+240=(2/5)x 240=(2/5)x-(1/10)x 240=(4/10)x-(1/10)x 240=(3/10)x (10/3)(240)=(10/3)(3/10)x 800=x x=800 pennies