Answer:
15. [tex] x = 15 [/tex]
17. [tex] c = 13.2 [/tex]
19. [tex] x = 25.8 [/tex]; [tex] y = 12.4 [/tex]
Step-by-step explanation:
15. [tex] 20*6 = 8*x [/tex] (intersecting chord theorem)
Solve for x
[tex] 120 = 8x [/tex]
Divide both sides by 8
[tex] 15 = x [/tex]
[tex] x = 15 [/tex]
17. [tex] (11 + 20)*11 = (13 + c)*13 [/tex] (two secants intersecting theorem)
Solve for c
[tex] 31*11 = 169 + 13c [/tex]
[tex] 341 = 169 + 13c [/tex]
Subtract 169 from each side
[tex] 341 - 169 = 169 + 13c - 169 [/tex]
[tex] 172 = 13c [/tex]
Divide both sides by 13
[tex] \frac{172}{13} = \frac{13c}{13} [/tex]
[tex] 13.2 = c [/tex] (nearest tenth)
19. [tex] (x + 5)*5 = (15 + 7)*7 [/tex] (two secants intersecting theorem)
Solve for x
[tex] 5x + 25 = 22*7 [/tex]
[tex] 5x + 25 = 154 [/tex]
Subtract 25 from each side
[tex] 5x + 25 - 25 = 154 - 25 [/tex]
[tex] 5x = 129 [/tex]
Divide both sides by 5
[tex] \frac{5x}{5} = \frac{129}{5} [/tex]
[tex] x = 25.8 [/tex] (nearest tenth)
[tex] y^2 = 7*(15 + 7) [/tex] (tangent and secant theorem)
Solve for y
[tex] y^2 = 7*22 [/tex]
[tex] y^2 = 154 [/tex]
Take the Square root of both sides
[tex] \sqrt{y^2} = \sqrt{154} [/tex]
[tex] y = \sqrt{154} [/tex]
[tex] y = 12.4 [/tex] (nearest tenth)
