Douglas has a segment with endpoints i(5, 2) and j(9, 10) that is divided by a point k such that ik and kj form a 2: 3 ratio. he knows that the distance between the x-coordinates is 4 units. which of the following fractions will let him find the x-coordinate for point k?
2/3, 2/5, 3/2, 3/5

The correct option is 2.

Step-by-step explanation:

It is given that the endpoints of the line segment are I(5, 2) and J(9, 10).

According to the section formula, if a point divide the line segment in m:n, then the coordinates of that point are

The x-coordinate is also written as

The distance between the x-coordinates is 4 units and . So, the  fractions that will let him find the x-coordinate for point K is

The required fraction is 2/5.

The x-coordinate of K is

Therefore the correct option is 2.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950