Which of the following numbers are rational, pie,0.7,and 0.

0.7 and 0.333... are rational.

Step-by-step explanation:

Given some numbers pie,0.7,and 0.333....

we have to find the numbers which are rational.

Rational numbers are the numbers which can be expressed in the form of , where q≠0.

Irrational numbers are those which cannot be expressed in the form of , where q≠0 and have an infinite non-repeating number of digits to right of decimal point.

The value of π is 3.14159265...

which is irrational as it is non-terminating without repetition.

which shows the above rational.

Now, 0.333... which is non-terminating but repeating.

Hence, rational.

Here, pi is irrational. 0.7  is rational. 0.3333... is rational because it cannot be expressed as a fraction.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

for the points

step-by-step explanation: