now, let's recall the rational root test, check your textbook on it.
so p = 18 and q = 1
so all possible roots will come from the factors of ±p/q
now, to make it a bit short, the factors are loosely, ±3, ±2, ±9, ±1, ±6.
recall that, a root will give us a remainder of 0.
let us use +3.
![\bf x^4-7x^3+13x^2+3x-18 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{r|rrrrr} 3&1&-7&13&3&18\\ &&3&-12&3&18\\ \cline{1-6} &1&-4&1&6&0 \end{array}\qquad \implies (x-3)(x^3-4x^2+x+6)](https://tex.z-dn.net/?f=%5Cbf%20x%5E4-7x%5E3%2B13x%5E2%2B3x-18%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Br%7Crrrrr%7D%203%261%26-7%2613%263%2618%5C%5C%20%26%263%26-12%263%2618%5C%5C%20%5Ccline%7B1-6%7D%20%261%26-4%261%266%260%20%5Cend%7Barray%7D%5Cqquad%20%5Cimplies%20%28x-3%29%28x%5E3-4x%5E2%2Bx%2B6%29)
well, that one worked... now, using the rational root test, our p = 6, q = 1.
so the factors from ±p/q are ±3, ±2, ±1
let's use 3 again
![\bf \begin{array}{r|rrrrr} 3&1&4&1&6\\ &&3&-3&-6\\ \cline{1-5} &1&-1&-2&0 \end{array}\qquad \implies (x-3)(x-3)(x^2-x-2)](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Br%7Crrrrr%7D%203%261%264%261%266%5C%5C%20%26%263%26-3%26-6%5C%5C%20%5Ccline%7B1-5%7D%20%261%26-1%26-2%260%20%5Cend%7Barray%7D%5Cqquad%20%5Cimplies%20%28x-3%29%28x-3%29%28x%5E2-x-2%29)
and of course, we can factor x²-x-2 to (x-2)(x+1).
(x-3)(x-3)(x-2)(x+1).
Answer: -6(n - 3) = 18, n = 0
Step-by-step explanation:
The equation "The difference between a number and three is multiplied by negative six. The result is eighteen." can be expressed as -6(n - 3) = 18. To find n, you solve algebraically to get n = 0.
I hope this helps!
the simplest form of the ratio is 1/2
Answer:
<h3>
The answer is <u><em>
four</em></u>
.</h3>
Step-by-step explanation:
Each family gets four kilograms of apples because 16 divided by 4 is four. To show this, you can get 16 dots, draw 4 circles and add a dot into each circle representing 1 kilogram, once you've run out of dots in each circle, you will see the total of 4 dots in each circle.
Answer:
CI = ( 36,6 ; 41,4 )
Step-by-step explanation:
CI = 99,9 % α = 0,1 % α = 0,001
We find z scre for α = 0,001 in z -table
z(s) = - 3,08
CI = μ₀ ± MOE where μ₀ = 39 min and MOE = z(s) * σ/√n
CI = 39 ± 3,08 * 4,8 / √37
CI = 39 ± 2,4315
CI = ( 36,6 ; 41,4 )