A point Q on a segment with endpoints A(2, −1) and C(4, 2) partitions the segment in a 3:1 ratio. Find Q. You must show all work to receive credit. (10 points)

The length of the segment is:

D= sqrt((4-2)^2 + (2- -1)^2 =

Sqrt( 2^2 + 3^2) =

Sqrt( 4 + 9) = sqrt(13) = 3.6055

The ratio is 3:1 so q is 3/4 of the way to point c

Q = 3/4 x sqrt(13)

Q = 3sqrt(13)/4 exact answer

Q = 2.7041 as a decimal answer

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt