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Arthur D.'s Resources

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Hi Rachel Corvette-My favorite car !!   distance-rate*time 400=r*t 400=(r+20)*(t-2) 400=rt --------> 400/t=r substitute 400=([400/t]+20)(t-2) 400=([400+20t]/t)(t-2) multiply both sides by t 400t=(400+20t)(t-2) 400t=400t+20t^2-800-40t cancel...

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functions f(5) (answer)

f(1)=3 f(n)=-2f(n-1)+1 f(1)=-2f(1-1)+1 f(1)=-2f(0)+1, 3=-2f(0)+1, 3-1=-2f(0), 2=-2f(0), -1=f(0) f(0)=-1 f(1)=3 f(2)=-2f(2-1)+1, f(2)=-2f(1)+1, f(2)=-2(3)+1, f(2)=-6+1, f(2)=-5 f(3)=-2f(3-1)+1, f(3)=-2f(2)+1, f(3)=-2(-5)+1, f(3)=10+1,...

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n and 2n are the sides n^2+(2n)^2=45 n^2+4n^2=45 5n^2=45 n^2=9 n=3 cm 2n=6 cm (answer)

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assuming b=base, p=percentage, and r=rate... percentage=rate*base 32=(66 2/3%)*b 66 2/3%=(66 2/3)/100=(200/3/100=200/300=2/3 32=(2/3)*b multiply both sides by 3/2 (3/2)(32)=(3/2)(2/3)*b 48=b  (answer)

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c) it doesn't matter how many times you repeat this procedure, c) is the answer look at the blue barrel; if there are 50 red marbles in the blue barrel, then where are the 50 blue marbles the red marbles displaced ? they are in the red barrel each barrel will contain the same number of the...

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show P(1) is true (replace all k's with the number 1) assume P(k) is true: 3+7+11+...+(4k-1)=(k)(2k+1) is assumed to be true show P(k+1) is true in other words show that the left side equals (k+1)(2[k+1]+1) 3+7+11+...+(4k-1)+(4[k+1]-1)=(k)(2k+1)+(4[k+1]-1) working...

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[(x^2-4x)/(4x)]*(1/(16-x^2) [x(x-4)/(4x)]*(1/[4-x][4+x]) [(x-4)/4]*(-1/[x-4][x+4]) (x was eliminated from the first fraction) now eliminate x-4 from the numerator of the first fraction and the denominator of the second fraction (1/4)(-1/x+4) -1/4(x+4)  (...

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problem solving (answer)

distance=rate*time d=r*t d=44*t  (to the park) d=77*(11-t) 44t=77(11-t) divide both sides by 11 4t=7(11-t) 4t=77-7t 4t+7t=77 11t=77 t=77/11 t=7 hours d=44*7 d=308 miles, or... d=77*4=308 miles again

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