Answer:
![\displaystyle \boxed{8[x + 2][x^2 - 2x + 4]}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cboxed%7B8%5Bx%20%2B%202%5D%5Bx%5E2%20-%202x%20%2B%204%5D%7D)
Step-by-step explanation:
Use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] to figure this out:
![\displaystyle 8x^3 + 64 \\ 8[x^3 + 8] \\ \\ x + 2 = \sqrt[3]{x^3 + 8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%208x%5E3%20%2B%2064%20%5C%5C%208%5Bx%5E3%20%2B%208%5D%20%5C%5C%20%5C%5C%20x%20%2B%202%20%3D%20%5Csqrt%5B3%5D%7Bx%5E3%20%2B%208%7D)
Then, since the divisor\factor is in the form of <em>x - c</em>, use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
−2| 1 0 0 8
↓ −2 4 −8
___________
1 −2 4 0 → 
You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [x³ + 8]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², the −2x follows right behind it, then 4, giving you the other factor of 
, attaching this to the first two factors you started out your work on:
I am joyous to assist you anytime.
Answer:
y = 4x - 7
Step-by-step explanation:
m = 4
y - y1 = m(x - x1)
y - 5 = 4(x - 3)
y - 5 = 4x - 12
y = 4x - 7
Answer:
Step-by-step explanation:
It saids evaluate given the three different functions below: The graph f(x), the equation g(x) and the table h(x)
Answer:
B
Step-by-step explanation:
If you use the general equation for an arithmetic sequence,
,
where aₙ is the number of minutes for movie n,
a₁ is the length of the first movie in minutes, and
d is the difference between each movie, in minutes
Our sequence is this:
If we want the length of the second movie (we already know the length of the first), we fill in n with 2:
which gives us a length of 72. Now for the length of movie n = 3:
which gives us a length of 74. Now for the length of movie n = 4:
which gives us a length of 76. One more and I'm sure you'll notice the pattern:
which gives us a length of 78. Now we will find the length of the 14th movie and add up by 2's all the way up to that number of minutes:
which gives up a length of 96 minutes. We will add up by 2's from 70 to 96:
Step-by-step explanation:
1/2 represents every fraction, where the denominator (bottom part) is twice the numerator (top part).
like 4/8 or 6/12 or 128/256 or ...
what do we need in the denominator to calculate with 15/16 ?
the same : 16.
and what is half of 16 ? 8.
so, we need the 1/2 based on 16th = 8/16.
so, the dog ate 8/16 (1/2) of the original 15/16.
what was left was
15/16 - 8/16 = 7/16 pound
