anonymous
  • anonymous
What is the simplified form of x plus 1 over x squared plus x minus 6 ÷ x squared plus 5x plus 4 over x plus 4 ? 1 over the quantity x plus 3 times the quantity x plus 4 1 over the quantity x plus 3 times the quantity x minus 2 1 over the quantity x plus 4 times the quantity x minus 2 1 over the quantity x plus 3 times the quantity x plus 1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@satellite73
anonymous
  • anonymous
\[\frac{ x + 1 }{ x^2 + x -6 } \div \frac{ x^2 + 5x + 4 }{ x + 4 }\] @satellite73
anonymous
  • anonymous
@satellite73

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More answers

anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=%28x%2B1%29%2F%28x^2%2Bx-6%29*%28x%2B4%29%2F%28x^2%2B5x%2B4%29
anonymous
  • anonymous
you go that right?
anonymous
  • anonymous
nice use of the equation tool btw
anonymous
  • anonymous
i can show you another trick in using wolfram
anonymous
  • anonymous
okay and heres the question
anonymous
  • anonymous
simplify (12z^2 - 25z + 12)/ (3z^2 + 2z - 8)
anonymous
  • anonymous
using the link i got (4z - 3)/(x + 2)
anonymous
  • anonymous
ok i so take what you wrote, copy and paste it directly in to wolfram
anonymous
  • anonymous
yeah i did that and got (4z - 3)/(x + 2)
anonymous
  • anonymous
yeah i get that too, but of course with a z
anonymous
  • anonymous
i could also show you how to do it without wolfram, it is "factor and cancel"
anonymous
  • anonymous
oh yeah typo lol sorry okay i think it'll be better without wolframe alpha in case my teacher asks
anonymous
  • anonymous
ok then here is the deal do you know how to factor?
anonymous
  • anonymous
sometimes but not really it'll be helpful if you showed me though
anonymous
  • anonymous
i don't actually, believe it or not if i wanted to factor i would cheat
anonymous
  • anonymous
what i mean is that i have no good way to show you how
anonymous
  • anonymous
i usually use a site for factoring
anonymous
  • anonymous
that works, of course wolfram will do that too
anonymous
  • anonymous
so in case the teacher asks, you can say something like this ;
anonymous
  • anonymous
\[ (12z^2 - 25z + 12)=(4 z-3) (3 z-4)\] and \[(3z^2 + 2z - 8)= (3 z-4) (z+2)\]
anonymous
  • anonymous
so \[\frac{12z^2+25z+12}{3z^2+2z-8}=\frac{4z-3)(3z-4)}{(3z-4)(z+2)}\]
anonymous
  • anonymous
oh and then you cross out (3z - 4)?
anonymous
  • anonymous
there is a common factor top and bottom of \(3z-4\) which cancels, you get \[\frac{(4z-3)(3z-4)}{(3z-4)(z+2)}=\frac{4z-3}{z+2}\]
anonymous
  • anonymous
exactly what you said
anonymous
  • anonymous
that is the idea of all of these factor and cancel
anonymous
  • anonymous
okay cool i get it now
anonymous
  • anonymous
as to how to factor, you are pretty much on your own, but you can use wolfram to do it for sure
anonymous
  • anonymous
okay thnx
anonymous
  • anonymous
and you can use wolfram to give the final answer too, but once you have it factored it is easy to cancel
anonymous
  • anonymous
ill also ask someone else on os
anonymous
  • anonymous
want to try another one ?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
ok i get a cup of coffee, you post
anonymous
  • anonymous
ok What polynomial identity should be used to prove that 21 = 25 - 4?
anonymous
  • anonymous
wow do you have any choices? \(21=25-4\) is simple arithmetic
anonymous
  • anonymous
What polynomial identity should be used to prove that 21 = 25 - 4? Difference of Cubes Difference of Squares Square of Binomial Sum of Cubes
anonymous
  • anonymous
ooh ok
anonymous
  • anonymous
25 and 4 are two squares
anonymous
  • anonymous
then B?
anonymous
  • anonymous
\[25=5^2\] and \[2^2\] so yeah B
anonymous
  • anonymous
what a dumb retricequestion next?
anonymous
  • anonymous
thnx
anonymous
  • anonymous
given the parent function of f(x) = x3, what change will occur when the function is changed to f(x - 3)? Shift to the right 3 units Shift to the left 3 units Shift up 3 units Shift down 3 units
anonymous
  • anonymous
when you subtract inside the function it move is 3 units to the RIGHT
anonymous
  • anonymous
thnx
anonymous
  • anonymous
ased on the table of values below, find the slope between points where x = 1 and where x = 4. x y 1 8 3 6 4 −1
anonymous
  • anonymous
what is the corresponding y value when x = 1?
anonymous
  • anonymous
ok ok
anonymous
  • anonymous
8
anonymous
  • anonymous
\[\frac{-1-8}{4-1}\] is whatyou have to compuote
anonymous
  • anonymous
i get \[\frac{-9}{3}=-3\]
anonymous
  • anonymous
thnx
anonymous
  • anonymous
yw
anonymous
  • anonymous
how many more?
anonymous
  • anonymous
a couple Which of the following expressions is the conjugate of a complex number with 2 as the real part and 3i as the imaginary part? 2 + 3i 2 − 3i 3i + 2 3i − 2
anonymous
  • anonymous
the conjugate of \(a+bi\) is \(a-bi\)
anonymous
  • anonymous
so b?
anonymous
  • anonymous
the conjugate of \(2+3i\) is \(2-3i\) that was an easy one
anonymous
  • anonymous
yeah b
anonymous
  • anonymous
okay thnx
anonymous
  • anonymous
yw next?
anonymous
  • anonymous
Two car washers, Michelle and Nancy, are working on your car. Michelle can complete the work in 6 hours, while Nancy can complete the work in 3 hours. How many hours does the car washing take if they work together? 3 2 six eighths four thirds
anonymous
  • anonymous
we go right to the answer (otherwise it take like forever) but remember this simple trick \[\frac{6\times 3}{6+3}\]
anonymous
  • anonymous
got that ?
anonymous
  • anonymous
so 18/9 = 2
anonymous
  • anonymous
yes
anonymous
  • anonymous
Bob and Susie wash cars for extra money over the summer. Bob's income is determined by f(x) = 6x + 13, where x is the number of hours. Susie's income is g(x) = 4x + 18. If Bob and Susie were to combine their efforts, their income would be h(x) = f(x) + g(x). Assume Bob works 3 hours. Create the function h(x) and indicate if Bob will make more money working alone or by teaming with Susie. h(x) = 2x + 5, work alone h(x) = 2x + 5, team with Susie h(x) = 10x + 31, team with Susie h(x) = 10x + 31, work alone
anonymous
  • anonymous
see the trick? it is easy
anonymous
  • anonymous
yup
anonymous
  • anonymous
\[g(x) = 4x + 18\] \[h(x)=6x+13\] \[g(x)+h(x)=4x+18+6x+13\]
anonymous
  • anonymous
combine like terms,what do you get?
anonymous
  • anonymous
10x + 31
anonymous
  • anonymous
ok good so C or D
anonymous
  • anonymous
yup but i think its with team work so C?
anonymous
  • anonymous
not sure if bob works 3 hours alone he makes \[f(3)=6\times 3+13=18+13=31\]
anonymous
  • anonymous
oh so D
anonymous
  • anonymous
don't jump the gun
anonymous
  • anonymous
if they both work 3 hours they make a total of \pg(3)=10\times 3+31=61\]
anonymous
  • anonymous
oh
anonymous
  • anonymous
\[h(3)=10\times 3+31=61\]\]
anonymous
  • anonymous
if he has to split it, then yes he is better off working alone
anonymous
  • anonymous
so is its C then?
anonymous
  • anonymous
i think D not really clear, but i think D
anonymous
  • anonymous
ok
anonymous
  • anonymous
next?
anonymous
  • anonymous
What is the equation of the quadratic graph with a focus of (3, 6) and a directrix of y = 4?
anonymous
  • anonymous
this takes a second
anonymous
  • anonymous
k
anonymous
  • anonymous
half way between 6 and 4 is 5, so the vertex is \((3,5)\)
anonymous
  • anonymous
therefore it will look like \[4p(y-5)=(x-3)^2\] we need \(p\)
anonymous
  • anonymous
the distance between 4 and 5 is 1, so p = 1 and one answer is \[4(y-5)=(x-3)^2\] now sure what your answer choices look like
anonymous
  • anonymous
f(x) = one fourth (x − 3)2 + 1 f(x) = one fourth (x − 3)2 + 5 f(x) = −one fourth (x − 2)2 + 5 f(x) = −one fourth (x − 2)2
anonymous
  • anonymous
\[4(y-5)=(x-3)^2\\ y-5=\frac{1}{4}(x-3)^2\\ y=\frac{1}{4}(x-3)^2+5\]
anonymous
  • anonymous
thnx Which of the following is a solution of x2 + 2x + 8? 4 + i times the square root of 7 −1 + i times the square root of 7 2 + i times the square root of 7 −4 + i times the square root of 7
anonymous
  • anonymous
x^2 + 2x +8
anonymous
  • anonymous
you want do step by step? or wolfram it?
anonymous
  • anonymous
step by step so i can learn
anonymous
  • anonymous
ok a) subtract 8 from both sides, what do you get?
anonymous
  • anonymous
if that is not clear say so i will tell you
anonymous
  • anonymous
oh note that you are starting with \[x^2+2x+8=0\]
anonymous
  • anonymous
x^2 + 2x = 8
anonymous
  • anonymous
i meaN -8
anonymous
  • anonymous
ok good
anonymous
  • anonymous
SO X^2 + 2X = -8
anonymous
  • anonymous
\[x^2+2x=8\] now what is half of 2?`
anonymous
  • anonymous
oops \[x^2+2x=-8\] what is half of two?
anonymous
  • anonymous
1
anonymous
  • anonymous
so x^2 + x = -8/2?
anonymous
  • anonymous
no slow
anonymous
  • anonymous
oh sorry
anonymous
  • anonymous
half of 2 is 1, so we go right to \[(x+1)^2=-8+1^2\] or \[(x+1)^2=-7\]
anonymous
  • anonymous
ok
anonymous
  • anonymous
take the square root, get \[x+1=\pm\sqrt{-7}\] or \[x+1=\pm\sqrt{7}i\]
anonymous
  • anonymous
subtract 1, get \[x=-1\pm\sqrt{7}i\]
anonymous
  • anonymous
thnx
anonymous
  • anonymous
What are the possible numbers of positive, negative, and complex zeros of f(x) = -3x4 - 5x3 - x2 - 8x + 4? Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0 Positive: 1; negative: 3 or 1; complex: 2 or 0 Positive: 3 or 1; negative: 1; complex: 2 or 0 Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
anonymous
  • anonymous
ok we do this, then i gotta split
anonymous
  • anonymous
\[f f(x) = -3x^4 - 5x^3 - x^2 - 8x + 4\]
anonymous
  • anonymous
it is a polynomial of degree 4, so it has 4 zeros for sure
anonymous
  • anonymous
there is one change in sign of the coefficients, which is a fancy way of saying that the go "minus, minus, minus, minus , PLUS" only once change in sign therefore there is one positive zero there cannot be no positive zeros because you count down by twos
anonymous
  • anonymous
\[f(x) = -3x^4 - 5x^3 - x^2 - 8x + 4\] \[f(-x) = -3x^4 + 5x^3 - x^2 + 8x + 4\]
anonymous
  • anonymous
here there are 3 changes in sign from -3 to +5, from +5 to -1 and from -1 tp +8 so there are either 3 negative zeros, or one negative zero
anonymous
  • anonymous
possibilities therefore are 1 positive, 3 negative (total of 4) or 1 positive, 1 negative 2 complex (total of 4)
anonymous
  • anonymous
now i really have to bolt ask your sister how to do the rest good luck!
anonymous
  • anonymous
thnx and ok bye
anonymous
  • anonymous
bye !

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