Answer:
see explanation
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
= 
[2a + (n - 1)d ]
where d is the common difference and a is the first term
here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence
= [(2 × 5) + 2(n - 1) ]
= (10 + 2n - 2)
= (2n + 8)
= n² + 4n
When sum = 165, then
n² + 4n = 165 ← rearrange into standard form
n² + 4n - 165 = 0 ← in standard form
(n + 15)(n - 11) = 0 ← in factored form
equate each factor to zero and solve for n
n + 15 = 0 ⇒ n = - 15
n - 11 = 0 ⇒ n = 11
but n > 0 ⇒ n = 11
Answer:
<h2>45, 46, 47</h2>
Step-by-step explanation:
n, n + 1, n + 2 - three consecutive integers
The equation:
138 - n = (n + 1) + (n + 2)
138 - n = n + 1 + n + 2 <em>combile like terms</em>
138 - n = 2n + 3 <em>subtract 138 from both sides</em>
-n = 2n - 135 <em>subtract 2n from both sides</em>
-3n = -135 <em>divide both sides by (-3)</em>
n = 45
n + 1 = 46
n + 2 = 47
Answer:
1 7/12
Step-by-step explanation:
here you go :)
Answer:
D
Step-by-step explanation:
We can test each pair making each ratio into its simplest form.
For A 2/3 is already in its simplest form and 9/15=3/5. they are not equivalent.
For B, 5/8 is already in its simplest form and 15/21=5/7. they are not equivalent.
For C, 3/12=1/4, and 6/18=1/3. They are not equivalent.
For D, 4/10=2/5, and 12/30=2/5. They are equivalent.
I think $43.57 Bc 41.90 times .04 is 16.76 then move the decimal, and add 41.90+1.67=43.57
