Will mark as ! pls a point h on a segment with endpoints b(3, -1) and z(12,5) partitions the segment in a 5: 1 ratio. find h. show all work! i got (10.5, 5)

  (10.5, 4)

Step-by-step explanation:

You want H such that ...

  (H -B)/(Z -H) = 5/1

Solving for H, we get ...

  H -B = 5(Z -H) . . . . . . cross multiply

  H - B = 5Z -5H . . . . . eliminate parentheses

  6H = B + 5Z . . . . . . . . Add 5H+B

  H = (B +5Z)/6 . . . . . . . divide by the coefficient of H

Filling in the given values, we have ...

  H = ((3, -1) + 5(12, 5))/6 = (3+60, -1 +25)/6

  H = (10.5, 4)

stop cheating

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1