Joey is running an experiment with a mass on a spring. Joey models the height of the mass above the table he is working on using the equation h(t)=6.85cos(3.42t)+9, where the height is in inches and the time, t, is in seconds since he let the mass free. How many seconds, to the nearest tenth, will it take for the mass to return to its original position?

Write an equation for the function that includes the points (1,4/5) and (2,2/3)

Girardo is using the model below to solve the equation . girardo uses the following steps: step 1 add 4 negative x-tiles to both sides step 2 add 1 negative unit tile to both sides step 3 the solution is which step could be adjusted so that gerardo's final step results in a positive x-value? in step 1, he should have added 4 positive x-tiles to both sides. in step 1, he should have added 3 negative x-tiles to both sides. in step 2, he should have added 4 negative unit tiles to both sides. in step 2, he should have added 1 positive unit tile to both sides.

Every weekday, mr. jones bikes from his home to his job. sometimes he rides along two roads, the long route that is shown by the solid lines. other times, he takes the shortcut shown by the dashed line. how many fewer kilometers does mr. jones bike when he takes the shortcut instead of the long route?