CAN YOU PLEASE HELP, I AM STUCK..THANKS
FIND THE DISTANCE BETWEEN (-3,2) AND (1,4)
DETERMINE WHETHER THE ROOT OF 77 AND THE ROOT OF 121 IS RATIONAL OR IRRATIONAL.
THANKS IN ADVANCE, I APPRECIATE ALL OF THE HELP....
The distance between a,b and c,d is
distance= sqrt ((a-c)^2 + (b-d)^2)
77 has the factors 7, and 11. The square root of both of these is not rational.
Sure, I'd be happy to help!
To find the distance between (-3,2) and (1,4), you can use the distance formula. The formula is:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the first point are (-3,2) and the coordinates of the second point are (1,4). Plugging those values into the formula, you get:
distance = sqrt((1 - (-3))^2 + (4 - 2)^2)
distance = sqrt((4)^2 + (2)^2)
distance = sqrt(16 + 4)
distance = sqrt(20)
So the distance between (-3,2) and (1,4) is sqrt(20), which simplifies to 2sqrt(5).
For the second question, we need to determine whether the square roots of 77 and 121 are rational or irrational.
The number 77 can be factored as 7 * 11. The square root of 7 and the square root of 11 are both irrational numbers. Therefore, the square root of 77 is also an irrational number.
The number 121 is a perfect square, and its square root is the whole number 11. Whole numbers are considered rational numbers.
In summary, the square root of 77 is irrational, while the square root of 121 is rational.