Answer:
see explanation
Step-by-step explanation:
Given
9n² - n - 
= 0 ← multiply through by 3 to clear the fraction
27n² - 3n - 2 = 0 ← factoring
Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term
product = 27 × - 2 = - 54 and sum = - 3
The factors are - 9 and + 6
Use these factors to split the n- term
27n² - 9n + 6n - 2 = 0 ( factor the first/second and third/fourth terms )
9n(3n - 1) + 2(3n - 1) = 0 ← factor out (3n - 1) from each term
(3n - 1)(9n + 2) = 0
Equate each factor to zero and solve for n
3n - 1 = 0 ⇒ 3n = 1 ⇒ n = 
9n + 2 = 0 ⇒ 9n = - 2 ⇒ n = - 
Answer:
Step-by-step explanation:
If the 4th lies opposite the 11th, then you know the 3rd lies opposite the 10th, the 2nd opposite the 9th, and the 1st opposite the 8th; meanwhile, in the reverse direction you'd find that the 5th lies opposite the 12th, the 6th opposite the 13th, and the 7th opposite the 14th. Move up one more bead and you're back at the 1st, which you already know lies opposite the 8th. Therefore there are 14 total bead
In 8, 9, 10, all the triangles are similar, meaning corresponding sides have the same ratio.
8. hypotenuse / (short side) = 25/x = x/9
x² = 25*9 = 5²×3²
x = √(5²×3²) = 5*3 = 15
9. (long side) / (short side) = x/7 = 9/x
x² = 7*9
x = √(9*7) = 3√7
10. (short side) / (long side) = x/48 = 48/64
x = 48²/64 = 36
Jen has 46 more than Jay, “Jen has 46 more than Jay.” You answered your own question.
