10. Solve the proportion.

Question

(Image: 4 over x = square root 11 – 1 over 3) (1 point)
(Image: 6 over 5 square root 11 – 6 over 5)
(Image: 5 over 6 square root 11 – 6 over 5)
(Image: 5 over 6 square root 11 + 6 over 5)
(Image: 6 over 5 square root 11 + 6 over 5)

Answer 1

Cross-multiplying, we get:

4(3) = x(sqrt(11) - 1)

12 = x(sqrt(11) - 1)

12 = xsqrt(11) - x

x = (12 + x)/sqrt(11)

x(sqrt(11)) = 12 + x

x(sqrt(11) - 1) = 12

x = 12/(sqrt(11) - 1)

Multiplying the numerator and denominator by the conjugate of the denominator, we get:

x = 12(sqrt(11) + 1)/(11 - 1)

x = 6(sqrt(11) + 1)/5

Therefore, the answer is (B) 6 over 5 square root 11 – 6 over 5.