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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...

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,...

x=rcosθ y=rsinθ 2x+3y=6 2(rcosθ)+3(rsinθ)=6 r(2cosθ)+r(3sinθ)=6 r(2cosθ+3sinθ)=6 which is B)

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)

the area of a rhombus is 1/2 times the product of the two diagonals A=(1/2)(d1)(d2) 72=(1/2)(n)(4n) 72=(1/2)(4n^2) 72=2n^2 36=n^2 n=6 meters 4n=24 meters

there is a special triangle called a 3-4-5 right triangle where 3 and 4 are the legs and 5 is the hypotenuse so this is the answer because 4 is 1 more than 3 however, you need to have the work, so... n and n+1 are the legs 5^2=n^2+(n+1)^2 25=n^2+n^2+2n+1 2n^2+2n+1-25=0 2n^2+2n-24=0 divide...

the tower, the cable, and the distance from the base of the tower to where the cable is secured in the ground form a right triangle the tower is 50 m and the distance from the base to where the cable is secured is 30 m use the tangent function tanθ=opposite/adjacent tanθ=30/50=3/5=0...

\$6520-\$4000=\$2520 in interest interest=principal*rate*time 2520=4000*r*4 divide both sides by 4 630=4000*r divide both sides by 10 63=400*r divide both sides by 400 r=63/400 divide both terms by 4 r=(63/4)/(400/4) r=15.75/100 r=15.75% also you...

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)

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...

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...

[(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)  (...

A=l*w w=width 9w-14=length 6183=(9w-14)(w) 6183=9w^2-14w 9w^2-14w-6183=0 9*6183==9*3*3*3*229=(9*3*3*3)*(229)=243*229 and 243-229=14 factor (9w+229)(w-27)=0 w-27=0 w=27 yards l=9*27-14=229 yards (answer)

the simplest thing to do is divide 63 by 3 (this gives the mean which will be the middle number of 3 consecutive integers) 63/3=21 is the age of the middle brother the other brothers are 20 and 22 if you need algebraic work... x+(x+1)+(x+2)=63 3x+3=6...

you could pick all of the 7 red balls first and then pick 2 blue balls you would have to pick 9 balls to be 100 % sure of getting 2 blue balls

x and x+7 are the numbers (x+7)^2-x^2=175 x^2+14x+49-x^2=175 14x+49=175 14x=175-49 14x=126 x=126/14 x=9 x+7=16 16 and 9 are the numbers 16^2-9^2=175 256-81=175 175=175

to be divisible by 12, the number must be divisible by both 3 and 4 how many 5 digit numbers are there ? 5*4*3*2*1=120 5 digit numbers any 5 digit number formed using 1, 2, 3, 4, and 5 is divisible by 3 because 5+4+3+2+1=15 and 15 is divisible by 3 to be divisible...

A=a^2+2a√[(a^2/4)+h^2] is the formula that you use h=vertical altitude and a=side length of the base 85=5^2+(2*5)√[25/4+h^2] 85-25=10√[25/4+h^2] 60/10=√[25/4+h^2] 6=√[25/4+h^2] 36=(25/4)+h^2 36-25/4=h^2 36-6.25=h^2 29.75=h^2 h,...