anonymous
  • anonymous
please help...... ((2z-8)/(z^2-4))/((z^2+6z+8)/(z-4)) simplify completly..... show work
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
do you know how to do this?
dumbcow
  • dumbcow
First Flip bottom fraction and Multiply Then factor and things will cancel \[2z-8 = 2(z-4)\] \[z^{2}-4 = (z+2)(z-2)\] \[z^{2}+6z+8=(z+4)(z+2)\]
anonymous
  • anonymous
wow i forgot that the things cancelled.... okay what did you get for your answer?

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anonymous
  • anonymous
im not sure how you did that can you show me?
dumbcow
  • dumbcow
\[=\frac{2(z-4)(z-4)}{(z+2)(z+2)(z-2)(z+4)}\] hmm maybe they dont cancel in this case..haha
anonymous
  • anonymous
yea and i think you factored wrong.....
anonymous
  • anonymous
wait how did you factor that?
dumbcow
  • dumbcow
no everything is factored correctly
dumbcow
  • dumbcow
which one
anonymous
  • anonymous
how did you do it then? i got something completly different but i thrust what you got....
dumbcow
  • dumbcow
are you sure its division and not multiplying the 2 fractions ??
anonymous
  • anonymous
you flip the second one and change to multi.
dumbcow
  • dumbcow
correct
anonymous
  • anonymous
and then can you show me what you did im completly lost
dumbcow
  • dumbcow
oh for the factoring part. well for 2z -8 i just pulled out a 2 from each term 2(z-4) = 2z - 8
anonymous
  • anonymous
ok
dumbcow
  • dumbcow
For z^2 - 4, find factors of -4 that add up to 0 since there is no "z" term -2*2 = -4 and -2+2=0 (z-2)(z+2)
anonymous
  • anonymous
wow thats sooo much easier now thanks :) can you help me with a couple more?
dumbcow
  • dumbcow
z^2 +6z +8 same thing, look for factors of 8 that add up to 6 4*2 =8 and 4+2 =6 (z+4)(z+2)
dumbcow
  • dumbcow
ok
anonymous
  • anonymous
okay....... ((4)/(2x+1))-((3)/(2x))=
anonymous
  • anonymous
can you show me step by step please?
dumbcow
  • dumbcow
adding/subtracting fractions you need to get common denominator 2x+1 cannot be factored 2x cannot be factored common denominator is 2x(2x+1) just like adding 1/2 + 1/3, common denominator is 2*3=6
dumbcow
  • dumbcow
now change numerators \[\frac{4}{2x+1} = \frac{(2x)(4)}{2x(2x+1)}\] \[\frac{3}{2x} = \frac{3(2x+1)}{2x(2x+1)}\] combine into 1 fraction \[\frac{(2x)(4) - 3(2x+1)}{2x(2x+1)}\]
anonymous
  • anonymous
ok
dumbcow
  • dumbcow
multiply and add like terms on top \[\frac{8x -6x -3}{2x(2x+1)} = \frac{2x-3}{2x(2x+1)}\]
anonymous
  • anonymous
can you help me with this one? ((m+5)/(2m^2-2))+((3)/(1-m))+((5)/(2m+2))
dumbcow
  • dumbcow
factor all the denominators 2m^2 -2 = 2(m-1)(m+1) 1-m = -(m-1) 2m+2 = 2(m+1) common denominator will include everything w/out repeats -2(m-1)(m+1)
anonymous
  • anonymous
okay i can do it from there can you help me with this one? ((n+1)-(2/n))/((n+4)+(4/n))
dumbcow
  • dumbcow
\[=\frac{-(m+5)+(2(m+1))(3) + (-(m-1))(5)}{-2(m+1)(m-1)}\]
anonymous
  • anonymous
can you help me with this one? please???? ((n+1)-(2/n))/((n+4)+(4/n))
dumbcow
  • dumbcow
ok combine fractions on top and bottom, then flip and multiply
dumbcow
  • dumbcow
common denominator will just be n
anonymous
  • anonymous
ok
dumbcow
  • dumbcow
answer should be (n-1)/(n+2)
anonymous
  • anonymous
yup that what i got are you good with summation notation and geometric means/sequences?
dumbcow
  • dumbcow
sure
anonymous
  • anonymous
okay.... wellthe question is... insert four geometirc means between -7 and -224
dumbcow
  • dumbcow
hmm dont understand?
anonymous
  • anonymous
nevermind i figured that one out......
anonymous
  • anonymous
what about....
anonymous
  • anonymous
\[\sum_{n=1}^{50}(1/4)(n+2)\]
dumbcow
  • dumbcow
\[=\frac{1}{4}\sum_{n=1}^{50}n+2 = \frac{1}{4}(\sum_{n=1}^{50}n +\sum_{n=1}^{50}2)\]
anonymous
  • anonymous
im stuck on this one.. which term of the geometric sequence 243, -81, 27, . . . is (-1/9)?
dumbcow
  • dumbcow
8 th term
anonymous
  • anonymous
how did you figure that out?
dumbcow
  • dumbcow
haha tried proving it using geometric sequence formula but got stuck when taking log anyway just continue the sequence of dividing by 3 and flipping the sign
anonymous
  • anonymous
o so you flip the sign every other time? could you help me with this one? there are seven houses; in each are seven cats. each cat kills seven mice. each mouse would hvae eaten seven ears of wheat. each ear of wheat prodece seven measures of grain. how much grain is saved? i got 16807 grains saved
dumbcow
  • dumbcow
correct 7^3 mice 7^4 ears 7^5 grain
anonymous
  • anonymous
ok that equals 16807 which is what i got:)
anonymous
  • anonymous
okay change the repeating decimal .25 (sopposto have the bar above the 25) to an equivlant common fraction
dumbcow
  • dumbcow
?? why do you need to know that some fraction close to proportional of 1/4
anonymous
  • anonymous
i dontk know its on my homework though ydo you know what it'd be?
dumbcow
  • dumbcow
haha i just guessed and put it in my calculator 25/99
anonymous
  • anonymous
wow your good.... do you know how i would show that? just say guess and check? we turn this in for a grade thats why im asking
dumbcow
  • dumbcow
actually any n/99 = .nnnnnn
anonymous
  • anonymous
in a certain credit union, money left on deposit for one year earns 4% intrest at the end ot the year. if you invested $100 at the beginning of each year in this credit union and did NOT withdraw the intrest due at the end of the year, how much would you hvae on deposit at the end of the tenth year?
dumbcow
  • dumbcow
=100(1.04 + 1.04^2+... +1.04^10) need sum of geometric sequence sum = a(1-r^n)/(1-r) sum = 1.04(1-1.04^10)/(1-1.04)
dumbcow
  • dumbcow
i get 1248.64
anonymous
  • anonymous
so when you get your answer are you sopposto multiply it by 100?
dumbcow
  • dumbcow
yes
anonymous
  • anonymous
okay just stay right there i have a couple more i just have to go and get another pencil mine just broke
anonymous
  • anonymous
ok im back i dont know what formula you used
dumbcow
  • dumbcow
for finding sum of geometric sequence
anonymous
  • anonymous
yea but can you tell me it with all of the variable in it please? i need to look and see if i have that one
dumbcow
  • dumbcow
\[s _{n} = \frac{a _{1}(1-r ^{n})}{1-r}\]
anonymous
  • anonymous
i only have SofN=(Asub1-Asub1R^n)/(1-R) and... SofN=(Asub1-AsubnR)/(1-R) sooo.. which one should i use, and what numbers?
dumbcow
  • dumbcow
ues the first one, only difference is mine has factored out the a1 on top
dumbcow
  • dumbcow
a1 = first term r = common ratio
anonymous
  • anonymous
ummmm... i should get the same answer right? i think im doing someting wrong im getting 1200.610712
dumbcow
  • dumbcow
1-(1.04)^10 = -.4802 1.04(-.4802) = -.49945 -.49945/(1-1.04) = 12.48635
anonymous
  • anonymous
wait shouldnt it be..... (100-100(1.04)^10)/(1-1.04)
dumbcow
  • dumbcow
no im leaving the 100 on outside of sequence then we multiply the sum by 100
anonymous
  • anonymous
but when i do it shouldnt i be getting the same thing? and i dont understand how your doing it
dumbcow
  • dumbcow
ok if you include the 100 then sequence will look like this =100(1.04) + 100(1.04^2) +...+100(1.04^10) a1 = 100(1.04) r = 1.04 sn = 100(1.04)(1-1.04^10)/(1-1.04)
anonymous
  • anonymous
but my equation is Sn=(A1-A1R^n)/(1-R)
dumbcow
  • dumbcow
same thing factor out the A1
anonymous
  • anonymous
can you do it my way when you factor out the A1 it confuses me
anonymous
  • anonymous
....^because when you factor....
dumbcow
  • dumbcow
ok Sn = 100(1.04) -100(1.04)(1.04^10) / (1-1.04)
anonymous
  • anonymous
ok ... a ball which rolls off a penthouse terrace falls 16 feet the first second, 48 feet the next second, and 80 feet the third second. if it continues to fall in this mannor, how far does it fall in the seventh second?
dumbcow
  • dumbcow
i believe this models a parabola of y=-16x^2 the change in y from 6 to 7 is how far it falls in 7th second 16(7^2) - 16(6^2) = 16(49-36) = 16(13) = 208
anonymous
  • anonymous
a rubber ball dropped 40 feet rebounds on each bounce 2/5 of the distance from which it fell. how far will it travel before comming to a rest?
dumbcow
  • dumbcow
geometric sequence 40+40(2/5)+ 40(2/5)^2 +... looks like an infinite sequence before you get 0 lim n->inf (2/5)^n = 0 so in formula r^n = 0 a1=40 r=2/5 sum = 40 - 40(0) / 1-(2/5) sum = 40 /3/5 = 200/3 = 66.666
anonymous
  • anonymous
what formula is that?
dumbcow
  • dumbcow
same as before sum of geometric sequence
anonymous
  • anonymous
no but which one of mine because yours confuse me
dumbcow
  • dumbcow
\[s _{n}=\frac{a _{1}-a _{1}r^{n}}{1-r}\]
anonymous
  • anonymous
what would i put for n?
dumbcow
  • dumbcow
infinity
anonymous
  • anonymous
hu?
dumbcow
  • dumbcow
just substitute r^n=0
anonymous
  • anonymous
would my answer be iin feet?
dumbcow
  • dumbcow
yes
anonymous
  • anonymous
what does the graph for ..... look like? -cubic with one real solution and two complex solutions look like? -cubic with no real solutions? -quartic with no real solutions? -a quadratic with one real solution and one complex solution? -a quartic with two real solutions and two complex solutions? -a quadratic with no real solutions? -a quartic with no real solutions? -a cubic with 3 real solutions, but one is a double root? -a quartic with for real roots, but both are double roots?
dumbcow
  • dumbcow
umm number of real solutions represents number of x_intercepts cubic with no real solutions does not exist i believe

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