Answer:
see explanation
Step-by-step explanation:
(a)
A recursive formula allows any term in the sequence to be found by adding the common difference d to the previous term.
Here d = - 4 , then recursive formula is
= 
- 4 with a₁ = 2
(b)
The explicit formula for an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = - 4, thus
= 2 - 4(n - 1) = 2 - 4n + 4 = 6 - 4n ← explicit formula
(c)
Using the recursive formula
a₁ = 2
a₂ = 2 - 4 = - 2
a₃ = - 2 - 4 = - 6
Using the explicit formula
a₅ = 6 - 4(5) = 6 - 20 = - 14
a₁₀ = 6 - 4(10) = 6 - 40 = - 34
a₁₀₀ = 6 - 4(100) = 6 - 400 = - 394
Answer: x= -3
Step-by-step explanation:
Answer:53
Step-by-step explanation:
Answer: 10 minutes
Step-by-step explanation:
First you have to find out how big the tank is. You will have to you the formula Length x Width x Height. 20 x 18 x 10= 3,600 in. Then you would divide that by 360. 3,600/360= 10. It would have to take 10 minutes to empty the aquarium.
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (- 2, 3)
m = 
= 
= - 
, thus
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 2, 3) , then
3 = 
+ c ⇒ c = 3 - = 
y = - x + ← in slope- intercept form
Multiply through by 3 to clear the fractions
3y = - 2x + 5 ( add 2x to both sides )
2x + 3y = 5 ( subtract 5 from both sides )
2x + 3y - 5 = 0 ← in general form
