Answer:
f(n)=-5-3n
Step-by-step explanation:
Given the recursive formula of a sequence
f(1)=−8
f(n)=f(n−1)−3
We are to determine an explicit formula for the sequence.
f(2)=f(2-1)-3
=f(1)-3
=-8-3
f(2)=-11
f(3)=f(3-1)-3
=f(2)-3
=-11-3
f(3)=-14
We write the first few terms of the sequence.
-8, -11, -14, ...
This is an arithmetic sequence where the:
First term, a= -8
Common difference, d=-11-(-8)=-11+8
d=-3
The nth term of an arithmetic sequence is determined using the formula:
T(n)=a+(n-1)d
Substituting the derived values, we have:
T(n)=-8-3(n-1)
=-8-3n+3
T(n)=-5-3n
Therefore, the explicit formula for f(n) can be written as:
f(n)=-5-3n
Answer:
$18
Step-by-step explanation:
Given:
6.4x - 2.1x = 77.4
Where,
x = cost of sheet metal per square foot
How much does sheet metal cost per square foot?
6.4x - 2.1x = 77.4
4.3x = 77.4
Divide both sides by 4.3
x = 77.4 / 4.3
= 18
x = $18
Sheet metal per square foot cost $18
Answer:
A. 3m² + 4m + 1 = 0
3m² + 3m + m + 1 = 0
3m (m + 1) + 1 (m + 1) = 0
( 3m + 1 ) (m + 1) = 0
B. 16n - 25
16n = 25
n = 25/16
Answer:
(7y + 3x)(7y - 3x)
Step-by-step explanation:
a² - b² = (a + b)(a - b)
49y² - 9x² = (7y)² - (3x)² {a = 7y ; b - 3x}
= (7y + 3x)(7y - 3x)
These equations do match up. All you have to do is find the solution to the first equation. After that, plug in that solution to the second equation. If it makes the equation true, then the equations match.
Hope this helps!
