Your answer would be -2/3 and that is in slope y-intercept is (0,2)
Answer:
Kenny is 18 years old Andrew is 10 years old Tim is 30 years old and Cameron is 5 years old
Step-by-step explanation:
Let a be Kenny's age , b be Andrew's age , c be Tim's age , d be Cameron's age
( b < a , b<c , d<b)
Kenny is 8 years older than Andrewn = > a = b + 8 (1)
Tim is 3 times as old as Andrew => c = 3 . b (2)
Cameron is 5 years younger than Andrew => d = b-5 (3)
The combined age of the four is 63 => a+b+c+d = 63 (4)
(1),(2),(3),(4) => b+8 + b + 3b + b-5 = 63 <=> 6b + 3 = 63 <=> b = 10
=> a= 10+8 =18, c = 3 . 10 = 30, d= 5
Answer:
I think the last one
Step-by-step explanation:
Answer:
Of the given geometric sequence, the first term a is 6 and its common ratio r is 2.
Step-by-step explanation:
Recall that the direct formula of a geometric sequence is given by:
![\displaystyle T_ n = ar^{n-1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20T_%20n%20%3D%20ar%5E%7Bn-1%7D)
Where <em>T</em>ₙ<em> </em>is the <em>n</em>th term, <em>a</em> is the initial term, and <em>r</em> is the common ratio.
We are given that the fifth term <em>T</em>₅ = 96 and the eighth term <em>T</em>₈ = 768. In other words:
![\displaystyle T_5 = a r^{(5) - 1} \text{ and } T_8 = ar^{(8)-1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20T_5%20%3D%20a%20r%5E%7B%285%29%20-%201%7D%20%5Ctext%7B%20and%20%7D%20T_8%20%3D%20ar%5E%7B%288%29-1%7D)
Substitute and simplify:
![\displaystyle 96 = ar^4 \text{ and } 768 = ar^7](https://tex.z-dn.net/?f=%5Cdisplaystyle%2096%20%3D%20ar%5E4%20%5Ctext%7B%20and%20%7D%20768%20%3D%20ar%5E7)
We can rewrite the second equation as:
![\displaystyle 768 = (ar^4) \cdot r^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20768%20%3D%20%28ar%5E4%29%20%5Ccdot%20r%5E3)
Substitute:
![\displaystyle 768 = (96) r^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20768%20%3D%20%2896%29%20r%5E3)
Hence:
![\displaystyle r = \sqrt[3]{\frac{768}{96}} = \sqrt[3]{8} = 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B768%7D%7B96%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B8%7D%20%3D%202)
So, the common ratio <em>r</em> is two.
Using the first equation, we can solve for the initial term:
![\displaystyle \begin{aligned} 96 &= ar^4 \\ ar^4 &= 96 \\ a(2)^4 &= 96 \\ 16a &= 96 \\ a &= 6 \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%2096%20%26%3D%20ar%5E4%20%5C%5C%20ar%5E4%20%26%3D%2096%20%5C%5C%20a%282%29%5E4%20%26%3D%2096%20%5C%5C%2016a%20%26%3D%2096%20%5C%5C%20a%20%26%3D%206%20%5Cend%7Baligned%7D)
In conclusion, of the given geometric sequence, the first term <em>a</em> is 6 and its common ratio <em>r</em> is 2.