Answer:
The recursive rule is 
= first term; 
= 
+ d
f(1) = 55; 
= 
+ 10
The explicit rule is f(n) = f(1) + (n - 1)d
f(20) = 245
Step-by-step explanation:
The recursive rule of the arithmetic sequence is
= first term; 
= 
+ d
Where:
- is the first term in the sequence
- is the nth term in the sequence
- is the term before the nth term
- d is the common difference.
The explicit rule of the arithmetic sequence is
where:
- is the first term in the sequence
- is the nth term in the sequence
- d is the common difference
∵ The first 4 terms of the sequence are 55, 65, 75, 85
∴ = 55
∵ d = 65 - 55
∴ d = 10
∵ We need to find the 20th term
∴ n = 20
∵ The recursive rule is = first term; = + d
→ Substitute the values of , n, and d in recursive rule
∴ f(1) = 55; = + 10
∵ The explicit rule is f(n) = f(1) + (n - 1)d
→ Substitute the values of n and d to find it
∴ f(20) = 55 + 19(10) = 245
∴ f(20) = 245
Answer:
6, - 36 )
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
x = - 
f(x) = x² + 12x ← is in standard form
with a = 1, b = 12, c = 0 , then
x = - 
= - 6
Substitute x = 6 into f(x) for corresponding value of y
f(6) = 6² + 12(- 6) = 36 - 72 = - 36
vertex = (6, - 36 )
Answer:
y = 5√3
x = 10√3
Step-by-step explanation:
From the given sides
Adjacent = 15
Opposite = y
Hypotenuse = x
Angle of depression = 30degree
Using the SOH CAH TOA identity
tan theta = opp/adj
tan 30 = y/15
y = 15tan30
y = 15(1/√3)
y = 15√3/3
y = 5√3
Similarly
cos theta = adj/hyp
cos 30 = 15/x
x = 15/cos30
x = 15 /√3/2
x = 30/√3
x = 30√3/3
x = 10√3
Answer:
- 3/8
Step-by-step explanation:
−9/24 −3/8= 3/8−3/4
=(3×4)−(3×8) = 8×4 = 12−24= -12/32 =−3/8
32
Hope it helps
The answer is 45 because you do parenthesis first which is 13.5-4.5=9 then you multiply 9×5=45 therefore the answer is 45.
