Carrie is finding the set of even numbers within the set of prime numbers. she starts by considering only positive numbers. of the sets described, which is the universal set? all real numbers positive numbers prime numbers even numbers

B positive numbers can be the universal set of the set of even numbers and set of prime numbers.

Step-by-step explanation:

Given: Carrie is finding the set of even numbers within the set of prime numbers. She starts by considering only positive numbers.

Set of even positive numbers = {0,2,4,6,8,10}

Set of prime numbers={2,3,5,7,11,}

Universal set is the collection of given sets and itself in a certain context.

So the universal set for the given sets can be positive numbers ={0,1,2,3,4,} which contains all the even positive number and all the prime number.

All real numbers can be universal set but in the given sets we talk only about positive numbers ,so there is no need for this.

Prime numbers cannot be the universal set of the given sets as it does not contains all the even numbers .

Even numbers cannot be universal set of the given sets as it doesn't contain all the prime numbers.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)