What are the coordinates of the point on the directed line segment from (-10, -3) to (-3, -3) that partitions the segment into a ratio of 3 to 4?

9514 1404 393

  (-7, -3)

Step-by-step explanation:

The point is the weighted sum of the end point coordinates. The weights are the reverse of the adjacent segment proportions.

  P = (4(-10, -3) +3(-3, -3))/7 = (-40-9, -12-9)/7 = (-49, -21)/7

  P = (-7, -3)

The point that partitions the segment in the desired fashion is (-7, -3).

Alternate solution

The given segment can be recognized as a horizontal segment of length 7. Then the desired point is 3 units from the first end, so at (-10+3, -3) = (-7, -3).

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.