Answer: -1
Step-by-step explanation:
slope formula: y=mx+b
m=slope
y=(-1)x+8
2/20 thats one i got for now
Answer:
See below
Step-by-step explanation:
We shall prove that for all
. This tells us that 3 divides 4^n+5 with a remainder of zero.
If we let
, then we have
, and evidently,
.
Assume that
is divisible by
for
. Then, by this assumption,
.
Now, let
. Then:

Since
, we may conclude, by the axiom of induction, that the property holds for all
.
Each of these roots can be expressed as a binomial:
(x+1)=0, which solves to -1
(x-3)=0, which solves to 3
(x-3i)=0 which solves to 3i
(x+3i)=0, which solves to -3i
There are four roots, so our final equation will have x^4 as the least degree
Multiply them together. I'll multiply the i binomials first:
(x-3i)(x+3i) = x²+3ix-3ix-9i²
x²-9i²
x²+9 [since i²=-1]
Now I'll multiply the first two binomials together:
(x+1)(x-3) = x²-3x+x-3
x²-2x-3
Lastly, we'll multiply the two derived terms together:
(x²+9)(x²-2x-3) [from the binomial, I'll distribute the first term, then the second term, and I'll stack them so we can simply add like terms together]
x^4 -2x³-3x²
<u> +9x²-18x-27</u>
x^4-2x³+6x²-18x-27