Mathematics, 29.09.2019 20:30 taytaycola223

With question 6, 7, 8, and 9 about rational and irrational numbers

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6. When we multiply two surdic integers, we can leave it into one big surd.
For instance, if we have:

$\sqrt{a} \cdot \sqrt{b}$ , we can simplify it down to one uniform square root sign, $\sqrt{ab}$ .

So, we can say: $3\sqrt{2} \cdot 8\sqrt{18} = 24\sqrt{36}$ , which is a rational root, because the square root of 36 can be converted into an integer, namely 6 and -6.

Hence, it is a rational root.

7. The summation, on the other hand, cannot be simplified any further, so it will stay as irrational. This is because √2 is already an irrational root, and adding it onto a number that is rational will stay as irrational.

8. Once again, the summation cannot be simplified. We can only simplify by factoring like terms. Hence, this must be irrational.

9. Even if it is in fractional notation, √5 can never be a rational number because no two integers when multiplied by itself will give 5. So, even if it is written in fractional form, they cannot be rational if there is an already irrational term in it.

Answer from: Quest

i am currently in the exact same situation rn. algebra2/adv algebra is killing

step-by-step explanation:

Answer from: Quest

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

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