Answer:
S₁₅ = 645
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
= [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Using the nth term formula = 5n + 3 , then
a₁ = 5(1) + 3 = 5 + 3 = 8
a₂ = 5(2) + 3 = 10 + 3 = 13 , then
d = a₂ - a₁ = 13 - 8 = 5
Thus
S₁₅ = [ (2 × 8) + (14 × 5) ]
= 7.5( 16 + 70)
= 7.5 × 86
= 645
Answer:
6
Step-by-step explanation:
3! = 3 x 2 x 1 = 6
Answer:
2) no change to the graphs
3) x = 1.47, y = 4.71
coordinates at intersection = (1.47, 4.71)
Step-by-step explanation:
4x + 3y = 20
3x - 2y = -5
2) Declan's way:
8x + 6y = 40
9x - 6y = -15
No change in graphs
4x + 3y = 20, 3y = 20 - 4x multiply by 2: 6y = 40 - 8x
3x - 2y = -5, 2y = 3x + 5 multiply by 3: 6y = 9x + 15
then:
40 - 8x = 9x + 15
simplify:
add 8x to each side:
17x + 15 = 40
subtract 15 from each side:
17x = 25
x = 1.47
3y = 20 - 4x
substitute for x:
3y = 20 - 4(1.47)
reduce:
3y = 14.12
y = 4.71
Answer:
32 = 8y
or
y = 32/8
Step-by-step explanation:
Each raft can hold 8 people.
If x = 8y, where "x" is the number of people and "y" is the number raft.
Given: The number of people 32
32 = 8y
y = 32/8
When we solve, we get y =4, 4 rafts needed.
Thank you.