Question

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

Answer 1

Answer:

15. $x = 15$

17. $c = 13.2$

19. $x = 25.8$; $y = 12.4$

Step-by-step explanation:

15. $20*6 = 8*x$ (intersecting chord theorem)

Solve for x

$120 = 8x$

Divide both sides by 8

$15 = x$

$x = 15$

17. $(11 + 20)*11 = (13 + c)*13$ (two secants intersecting theorem)

Solve for c

$31*11 = 169 + 13c$

$341 = 169 + 13c$

Subtract 169 from each side

$341 - 169 = 169 + 13c - 169$

$172 = 13c$

Divide both sides by 13

$\frac{172}{13} = \frac{13c}{13}$

$13.2 = c$ (nearest tenth)

19. $(x + 5)*5 = (15 + 7)*7$ (two secants intersecting theorem)

Solve for x

$5x + 25 = 22*7$

$5x + 25 = 154$

Subtract 25 from each side

$5x + 25 - 25 = 154 - 25$

$5x = 129$

Divide both sides by 5

$\frac{5x}{5} = \frac{129}{5}$

$x = 25.8$ (nearest tenth)

$y^2 = 7*(15 + 7)$ (tangent and secant theorem)

Solve for y

$y^2 = 7*22$

$y^2 = 154$

Take the Square root of both sides

$\sqrt{y^2} = \sqrt{154}$

$y = \sqrt{154}$

$y = 12.4$ (nearest tenth)