Answer:
a₁₂ = 16384
Step-by-step explanation:
The nth term of a geometric sequence is
= a₁ ![(r)^{n-1}](https://tex.z-dn.net/?f=%28r%29%5E%7Bn-1%7D)
where a₁ is the first term and r the common ratio
Here a₁ = 8 and r = a₂ ÷ a₁ = 16 ÷ 8 = 2 , then
a₁₂ = 8 ×
= 8 × 2048 = 16384
Answer: option 2 describes best
Step-by-step explanation:Given Marisol grouped the terms and factored the GCF out of the groups of the polynomial 6x3 – 22x2 – 9x + 33. Her work is shown.
Step 1: (6x3 – 22x2) – (9x + 33)
Step 2: 2x2(3x – 11) – 3(3x + 11)
Marisol noticed that she does not have a common factor. Which accurately describes what Marisol should do next?
Marisol should realize that her work shows that the polynomial is prime.
Marisol should go back and group the terms in Step 1 as (6x3 – 22x2) – (9x – 33).
Marisol should go back and group the terms in Step 1 as (6x3 – 22x2) + (9x – 33).
Marisol should refactor the expression in Step 2 as 2x2(3x + 11) – 3(3x + 11).
According to question Marisol grouped the terms and has done factorisation of the given polynomial 6x^3 – 22x^2 – 9x + 33.
In step 1 she has written as (6x^3 – 22x^2) – (9x + 33)
Marisol has to go to step 1 in order to correct her mistake. She has to group the expression as (6x^3 – 22x^2) – (9x – 33) so that she will be able to get the expression as
6x^3 – 22x^2 – 9x + 33 after opening the brackets.
equation of circle is given as
![{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\](https://tex.z-dn.net/?f=%20%7B%28x%20-%20h%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28y%20-%20k%29%7D%5E%7B2%7D%20%20%3D%20%20%7Br%7D%5E%7B2%7D%20%5C%5C%20)
where (h,k) is center of cirlce and r is radius.
so lets figure out it from graph.
as we can see in graph center is at ( -1, 1)
radius is 4 units as shown in graph but we can calculate it. take any point on circle and calculate its distance from center. lets take point (3, 1)
now distance = √((3+1)^2+(1-1)^2)
= √16 = 4
lets put it in equation
(x +1)^2 + (y-1)^2 = 4^2
Answer:
6.4 oz are left.
Step-by-step explanation:
Start with the bottle being half full.
A bottle that is half full when it started with 16 oz is 1/2 16 oz = 8 oz
If he drinks 1/5 of the remaining amount, it means that he has 4/5 left.
4/5 * 8 = 32/5 = 6.4 oz or 6 oz and 2/5 of an ounce.