The two positive integer solutions of the equation $x^2 - mx + n = 0$ are $k$ and $t$, where $m$ and $n$ are both prime numbers and $k > t$. what is the value of $m^n + n^m + k^t + t^k$?

Since k and t are roots of x² - mx + n = 0,

0 = (x - k)(x - t) = x² - (k+t)x + kt = x² - mx + n

Equating respective coefficients,

m = k + t   and  n = kt

If n is prime we have one of k and t must be a unit ±1.  Since we're told they're positive, the smallest must be +1, so we conclude

t = 1

So

n = kt = k

We're told m is prime

m = k + t = n + 1

m and n are consecutive and prime.  The only consecutive primes are 2 and 3.  Our solution is

k = 2, n = 2, m = 3, t = 1

We're inexplicably asked for the symmetric quantity

We compute

3² + 2³ + 2 + 1² = 9 + 8 + 2 + 1 = 20

20

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

she would want to sell 10 full-year subscriptions and at least 9 half-year subscriptions to get a total of at least $300. 

i hope this answer you! if you have any further questions or concerns, feel free to ask! : )

step-by-step explanation:

mark brainliest!