A roll of ribbon was 12 meters long. Diego cut 9 pieces of ribbon that were 0.4 meter each to tie some presents. He then used the remaining ribbon to make some wreaths. Each wreath required 0.6 meter. How many meters of ribbon were available for making wreaths?

8.4 meters

Step-by-step explanation:

From the question, we are informed that a roll of ribbon was 12 meters long and that Diego cut 9 pieces of ribbon that were 0.4 meter each to tie some presents. The length of ribbon used by Diego for the present would be:

= 9 × 0.4meter

= 3.6 meter.

Therefore, the meters of ribbon that were available for making wreaths would be:

= 12 meters - 3.6 meters

= 8.4 meters

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.