Question

Algebra Find the value of each variable using the given chord, secant, and tangent lengths. If the answer is not

a whole number, round to the nearest tenth.

Answer 1

Answer/Step-by-step explanation:

15. Based on the intersecting Chords Theorem, thus,

`x * 8 = 20 * 6`

`8x = 120`

Divide both sides by 8

x = 15

17. Based on the two secants intersecting theorem,

`(c + 13) * 13 = (20 + 11) * 11`

Solve for c

`13c + 169 = (31) * 11`

`13c + 169 = 341`

Subtract 169 from each side

`13c = 172`

Divide both sides by 13

c = 13.2 (nearest tenth)

19. ✔️Based on the two secants intersecting theorem,

`(x + 5) * 5 = (15 + 7) * 7`

Solve for x

`5x + 25 = (22) * 7`

`5x + 25 = 154`

Subtract 25 from each side

`5x = 129`

Divide both sides by 5

x = 25.8

✔️according to the tangent and secant theorem, thus:

`y^2 = 7 * (15 + 7)`

Solve for y

`y^2 = 7 * (22)`

`y^2 = 154`

Square both sides

y = 12.4 (nearest tenth)