Let a, b and c be in a geometric sequence, then ac = b^2
Hence, (2k + 1)(7k + 6) = (3k + 4)^2
14k^2 + 19k + 6 = 9k^2 + 24k + 16
5k^2 - 5k - 10 = 0
5k^2 + 5k - 10k - 10 = 0
5k(k + 1) - 10(k + 1) = 0
(5k - 10)(k + 1) = 0
5k - 10 = 0 or k + 1 = 0
5k = 10 or k = -1
k = 2 or k = -1
The geometric sequence formed is
2(2) + 1, 3(2) + 4, and 7(2) + 6
5, 10, and 20
OR
2(-1) + 1, 3(-1) + 4, and 7(-1) + 6
-1, 1, and -1
Answer:
12%
Step-by-step explanation:
Convert the fraction into a decimal and then multiply by 100
Answer:
A) 100 + 5x = y
10 + 20x = y
Step-by-step explanation:
100 is the amount Andre started with and 5x is the 5 he adds each week
10 is the amount Elena started with and 20x is the 20 she adds we week
The ratio of quarters to dimes is not still 5 : 3
<u>Solution:</u>
Given that ratio of quarters to dimes in a coin collection is 5:3 .
You add same number of new quarters as dimes to the collection .
Need to check if ratio of quarters to dimes is still 5 : 3
As ratio of dimes and quarters is 5 : 3
lets assume initially number of quarters = 5x and number of dimes = 3x.
Now add same number of new quarters as dimes to the collection
Let add "x" number of quarters and "x" number of dimes
So After adding,
Number of quarters = initially number of quarters + added number of quarters = 5x + x = 6x
Number of dimes = initially number of dimes + added number of dimes
= 3x + x = 4x
New ratio of quarters to dimes is 6x : 4x = 3 : 2
So we have seen here ratio get change when same number of new quarters and dimes is added to the collection
Ratio get change from 5 : 3 when same number of new quarters and dimes is added to the collection and new ratio will depend on number of quarters and dimes added to collection.
