Chords XY and ZW intersect in a circle at P. If
XP = 7, PY=12, and WP= 14, find PZ.

Length of segment PZ = 6 units

Step-by-step explanation:

As per theorem of intersecting chords in a circle ;

"Product of lengths of line segments on each chord are equal".

From the figure attached,

Chords XY and WZ are intersecting at point P in a circle.

By theorem;  XP × PY = WP × PZ

7 × 12 = 14 × PZ

PZ =

PZ = 6 units

Therefore, length of the segment PZ = 6 units.

{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