The first three terms of an arithmetic sequence are 2k+1, 5k, 7k+2. What is the value of k?

Step-by-step explanation:

In an arithmetic sequence, we keep adding/subtracting to get the next term in the sequence.

Therefore, we can make an equation that looks like this:

5k-(2k+1) = 7k+2-5k

We can subtract 2k+1 from 5k, and 5k from 7k+2, because from subtracting the difference would be the same. (common difference of sequence is what we would find)

Now, we just need to simplify.

5k-2k-1 = 2k+2

3k-1=2k+2

Now let's combine like terms, and we get:

k=3

Hope this helped!

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

a

step-by-step explanation: