Answer/Step-by-step explanation:
15. Based on the intersecting Chords Theorem, thus,
[tex] x \times 8 = 20 \times 6 [/tex]
[tex] 8x = 120 [/tex]
Divide both sides by 8
x = 15
17. Based on the two secants intersecting theorem,
[tex] (c + 13) \times 13 = (20 + 11) \times 11 [/tex]
Solve for c
[tex] 13c + 169 = (31) \times 11 [/tex]
[tex] 13c + 169 = 341 [/tex]
Subtract 169 from each side
[tex] 13c = 172 [/tex]
Divide both sides by 13
c = 13.2 (nearest tenth)
19. ✔️Based on the two secants intersecting theorem,
[tex] (x + 5) \times 5 = (15 + 7) \times 7 [/tex]
Solve for x
[tex] 5x + 25 = (22) \times 7 [/tex]
[tex] 5x + 25 = 154 [/tex]
Subtract 25 from each side
[tex] 5x = 129 [/tex]
Divide both sides by 5
x = 25.8
✔️according to the tangent and secant theorem, thus:
[tex] y^2 = 7 \times (15 + 7) [/tex]
Solve for y
[tex] y^2 = 7 \times (22) [/tex]
[tex] y^2 = 154 [/tex]
Square both sides
y = 12.4 (nearest tenth)