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...

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...

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,...

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

Combining squares (answer)

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...

You invest $4000 in an account that grows up to $6,520 in 4 years. Find the annual interest rate (answer)

$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...

Find b if p = 32 and r = 66 2/3 (answer)

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)

marvel confusion (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...

Mathematical Induction. (answer)

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...

Multiply and simplify: (answer)

[(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,...

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

The volume of a particular rock is 30 cm cubed. If its mass is 120 grams, what is its density? (answer)

Density=mass/volume D=m/v D=120g/30cm3 D=4g/cm3 if you increase the mass, the density will increase if you increase the volume, the density will decrease

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