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,

$x \times 8 = 20 \times 6$

$8x = 120$

Divide both sides by 8

x = 15

17. Based on the two secants intersecting theorem,

$(c + 13) \times 13 = (20 + 11) \times 11$

Solve for c

$13c + 169 = (31) \times 11$

$13c + 169 = 341$

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,

$(x + 5) \times 5 = (15 + 7) \times 7$

Solve for x

$5x + 25 = (22) \times 7$

$5x + 25 = 154$

Subtract 25 from each side

$5x = 129$

Divide both sides by 5

x = 25.8

✔️according to the tangent and secant theorem, thus:

$y^2 = 7 \times (15 + 7)$

Solve for y

$y^2 = 7 \times (22)$

$y^2 = 154$

Square both sides

y = 12.4 (nearest tenth)