Please help.. several problems.

[j9vo2]

(1.) subtract: x/(x^2-16) minus 7/(x^2+5x+4): I figured out the denominators as being (x-4)(x+4) and (x+1)(x+4) consecutively.


(2.) Find the x-intercepts of this quadratic function: y+2x^2-10x-72. this is what I did so far.

2x^2/2 - 10x/2=72/2

x^2-5x^2 (25) = 36

x^2-10x+25+61 ???????


(3.) Simplify: [(64x^7y^8)/x^-8 y^2] everything to the 2/3 power

(4.) Simplify: (16x^4y^16z^12) all to the 1/4 power

this is the answer that I got. 2xy^4z^3

I divided all the powers by 4 and put 16 1/4 power.. which will be 2? right?

thanks so much!!

 

[stapel]

1) You have correctly done the first step: factoring the denominators. Clearly, the common denominator will be (x + 1)(x + 4)(x - 4). Convert the fractions to this denominator, combine, and simplify. Then remember to re-factor the numerator, to see if anything cancels with a factor in the denominator.

2) Is this actually "y = 2x² - 10x - 72"...?

I'm not sure what you're doing in the work you show. Why not just follow the usual "intercept" procedure: set the other variable equal to zero, and solve. Since you're looking for the x-intercepts, set y equal to zero and solve (by the Quadratic Formula or whatever).

3) Follow the usual exponent rules: negative exponents mean "move the base to the other side of the fraction line" and powers on exponential expressions get multiplied onto everything inside. For instance:

. . . . .x^-3 = 1/x³

. . . . .1/y^-2 = y²

. . . . .(x³)⁴ = x¹²

4) This works just like (3) and, yes, you have the correct answer.

Eliz.

 

[j9vo2]

Is the answer to the first one..(x^2-6x+28)/[(x-4)(x+4)(x+1)] Im not sure if I have that negative sign right for the numerator.. in front of the 6.

For the second one.. I tried doing the quadratic formula and it is not working out for me.. I just do not understand how to do this problem. Ive tried it several different ways. I even tried to look in my book and online for help and still cannot seem to get it.

 

[Gene]

(1.) Correct.

2) You didn't answer Stapl
Is this actually "y = 2x2 - 10x - 72".
If it is you can factor it into
y = 2(x+4)(x-9)
But the quadratic gives the same
(10+sqrt(100+4*2*72))/(2*2) =
(10+sqrt(676))/4 =
(10+(26))/4 =
(10+26)/4 and (10-26)/4

Where you went wrong is
2x^2/2 - 10x/2=72/2
x^2-5x^2 = 36
I don't see where you got the (25) from.

 

[j9vo2]

thank you.
I got 25 b/c my book said to take 1/2 and then times by two.. that is why I was getting so confused. I have the worst book in the world.

can you help with this one.. [(64x7y8))/x-8y2]2/3

I got this so far.. Since x-8 is a negative exponent, i moved it up to the top of the fraction..so.

64x7x8y8/y2 I added the x's 64x15y8/y2

now, do i multiply all by 2, just the exponents by 2?

If I multiply the exponents by 2.. then i get 64x30y16/y4

then I get stuck. not even sure if what i have is correct or not.



Also.. is this correct..

x2-7x-2=0 I used the quadratic formula..

so i got x= -(-7) +/- sqrt -7-4(1)(-2)/2(1)=

x= 7 +/- sqrt 49+8/2=

7 +/- sqrt 57/2+

7+/-(57)1/2 divided by 2.

 

[Gene]

It is sqrt(b squared...
You didnt square the -7
Also the 2a is under the whole thing so it would be
x= (-(-7) +/- sqrt (-7)²-4(1)(-2))/2(1)

 

[TchrQbic]

thank you.
I got 25 b/c my book said to take 1/2 and then times by two.. that is why I was getting so confused. I have the worst book in the world.

can you help with this one.. [(64x7y8))/x-8y2]2/3

I got this so far.. Since x-8 is a negative exponent, i moved it up to the top of the fraction..so.

64x7x8y8/y2 I added the x's 64x15y8/y2

now, do i multiply all by 2, just the exponents by 2?

If I multiply the exponents by 2.. then i get 64x30y16/y4

Please indicate exponents by ^. Here, it's not clear just what's happening. The 2/3 outside the brackets, if it is an exponent, will MULTIPLY all exponents inside the [ ]. Keep in mind that 64 = 64¹, so that it becomes 64^2/3.

A 2/3 exponent is equal to squaring the base, then taking the cube(3) root.

then I get stuck. not even sure if what i have is correct or not.



Also.. is this correct..

x2-7x-2=0 I used the quadratic formula..

so i got x= -(-7) +/- sqrt -7-4(1)(-2)/2(1)=

x= 7 +/- sqrt 49+8/2=

7 +/- sqrt 57/2+

7+/-(57)1/2 divided by 2.

 

[j9vo2]

ok.. i am still gettting the same answer for x2-7x-2=0 :

[7+/(57)^1/2]/2


Would the answer for the other problem: [(64x^7y^8))/x^-8y^2]^2/3

be 8x^10y^4 ?

 

[Denis]

ok.. i am still gettting the same answer for x2-7x-2=0 :
[7+/(57)^1/2]/2

Correct! be clearer: x = [7 +or- sqrt(57)] / 2


Would the answer for the other problem: [(64x^7y^8))/x^-8y^2]^2/3 be 8x^10y^4 ?

Close: 16 x^10 y^4

 

[j9vo2]

THANK YOU SOOO MUCH!!