Which of the following statements is false? (5 points) a. the sum of two rational numbers is always rational. b. the sum of a rational number and an irrational number is always rational. c. the product of a nonzero rational number and an irrational number is always irrational. d. the product of two irrational numbers is either rational or irrational.

A: The sum of two rational numbers is always rational. I just took the test.

Step-by-step explanation:

Rational numbers are numbers that can be written as a fraction or ratio where irrational number cannot be written as a fraction or ratio.So the product or sum of two rational number is rational. Since your needed to find the false statement then the first one was the correct one.

d

gimmee one of those gold crowns!

~coco

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