Answer:
n = 10
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
Here a₁ = 12 and d = 5 and
= 345, thus
[ (2 × 12) + 5(n - 1) ] = 345 ( multiply both sides by 2 )
n( 24 + 5n - 5) = 690 ← distribute and simplify left side
n(19 + 5n) = 690
19n + 5n² = 690 ( subtract 690 from both sides )
5n² + 19n - 690 = 0 ← in standard form
(5n + 69)(n - 10) = 0 ← in factored form
Equate each factor to zero and solve for n
5n + 69 = 0 ⇒ 5n = - 69 ⇒ n = - 
n - 10 = 0 ⇒ n = 10
However, n > 0 , thus n = 10
Answer: 16
Step-by-step explanation:
Range is the largest number in the set minus the smalllest number in the set pf numbers or data.
9-(-7)
9+7
16
I think 12 minutes because if you take 9 divide it by 3/4 you get 12
5x + 2y = 13
x + 2y = 9
-------------------------subtract
4x = 4
x = 1
x + 2y = 9
1 + 2y = 9
2y = 8
y = 4
answer (1,4)
The sides of an equilateral triangle are equal length, so ...
GH = FH
3x-9 = 2x-2
x = 7 . . . . . . . . add 9-2x
Then the side lengths are
FG = x+5
FG = 7 +5 = 12
x = 7
FG = GH = FH = 12