Is 9, 5, 12, 11 solutions to 2w > 18?

All solutions are larger than 9

Explanation:

Divide both sides by 2 and we get

2w > 18

2w/2 > 18/2 dividing both sides by 2

w > 9

Any number larger than 9 can replace w, and we'll get a true statement.

For instance, if we tried w = 12, then,

2w > 18

2*12 > 18

24 > 18

Which is true since 24 is indeed larger than 18.

On the flip side, if we tried w = 5, then,

2w > 18

2*5 > 18

10 > 18

which is not true because 10 is actually smaller than 18.

So again, the inequality 2w > 18 solves to w > 9

This shows all solutions are larger than 9.

If we can only pick values from the set {9,5,12,11}, then the solutions are 11 and 12 since they are larger than 9.

any options?

step-by-step explanation:

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