Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product p in 6 days. how many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product p in 4 days?

Danny draws a transversal, t, on two parallel lines ab and cd, as shown below: he makes the following table to prove that the alternate interior angles are equal: which is the missing justification? (6 points) corresponding angles formed by a transversal on parallel lines are supplementary. corresponding angles formed by a transversal on parallel lines are congruent. co-interior angles formed by a transversal on parallel lines are congruent. co-exterior angles formed by a transversal on parallel lines are congruent.

Drag each tile to the correct box. not all tiles will be used. consider the recursively defined function below. create the first five terms of the sequence defined by the given function

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth