Answer:
k = 9
Step-by-step explanation:
Consider the pattern on the right side , that is
= k(k + 2) + 1 = k² + 2k + 1
Equating
k² + 2k + 1 = 100 ( subtract 100 from both sides )
k² + 2k - 99 = 0 ← in standard form
(k + 11)(k - 9) = 0 ← in factored form
Equate each factor to zero and solve for k
k + 11 = 0 ⇒ k = - 11
k - 9 = 0 ⇒ k = 9
But k > 0 , then k = 9
2/20 = 1/10 = 3/30 = 4/40
so 3 equivalent ratios can be 1/10 (or 1:10), 3/30 (or 3:30), 4/40 (or 4:40)
Answer:
k = -2
Step-by-step explanation:
If 
Then

So

From this follows k = -2