Amir is starting a stamp collection. After 3 weeks he has collected 35 different stamps, and after 9 weeks he has collected 105 different stamps. Which equation represents this direct variation?

6y=70x or 6y-70x=0;

Step-by-step explanation:

System of equations:

35=3k+b；  

105=9k+b;

Equation 2 minus 1 is 6k is equal to 70, k is equal to 70/6, plug in to equation 1 and b is equal to 0, so the original equation is y is equal to 70/6x.

6 meters

step-by-step explanation:

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.