51. I checked the comments but I still didn't understand it, sorry :/
54.
(43+45+47+49)=184
They are all odd and they are in consecutive order (one after another)
The volume of a sphere is:
V=(4πr^3)/3, and you are told that r=5in so
V=(4π125)/3
V=500π/3 in^3
V≈523.60 in^3
The sum of the given sequence is -6384.
<u>Step-by-step explanation:</u>
The given Arithmetic sequence is 14 + 8 + 2+ ... + ( 274) + (-280).
- The first term of the sequence = 14
- The last term of the sequence = -280
- The common difference ⇒ 14 - 8 = 6
<u>To find the number of terms in the sequence :</u>
The formula used is 
where,
- n is the number of terms.
is the late term which is -280.
is the first term which is 14.- d is the common difference which is 6.
Therefore, 
⇒ 
⇒ 
⇒ 
⇒ n = 48, since n cannot be negative.
∴ The number of terms, n = 48.
<u>To find the sum of the arithmetic progression :</u>
The formula used is 
where,
- S is the sum of the sequence.
- is the first term which is 14.
- is the late term which is -280.
Therefore, 
⇒ 
⇒ 
⇒ 
∴ The sum of the given sequence is -6384.
14/9 reciprocal is a reverse of the number so it should be opposite
i hope it helps
Answer:
2(4x + 1)(x + 1)
Step-by-step explanation:
Given
8x² + 10x + 2 ← factor out 2 from each term
= 2(4x² + 5x + 1)
To factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × 1 = 4 and sum = + 5
The factors are + 1 and + 4
Use these factors to split the x - term
4x² + x + 4x + 1 ( factor the first/second and third/fourth terms )
= x(4x + 1) + 1 (4x + 1) ← factor out (4x + 1)
= (4x + 1)(x + 1), thus
4x² + 5x + 1 = (4x + 1)(x + 1) and
8x² + 10x + 2 = 2(4x + 1)(x + 1) ← in factored form
