We have the operation:
(2n² + 1)/3
2n (n/3) + 1/3
Since we are to use the condition that 3 does not divide n, we have:
n/3 = q +r/3
n = 3q + r
where q is the quotient and r is the remainder and not divisible by 3 or equal to 0
both q and r are whole numbers
Substituting,
2(3q + r) (q + r/3) + 1/3
6q² + 4qr + 2r²/3 + 1/3
6q² + 4qr + (2r² + 1)/3
The term:
(2r² + 1)/3
will only be a whole number if r is not divisible by 3 or equal to 0, which means that
(2n² + 1)/3
is a whole number if and only if
n/3 is not a whole number
Answer:
0.5x - y = 1.5
Step-by-step explanation:
First, put the equation in point slope form:
y - y1 = m(x - x1)
y + 2 = 1/2(x + 1)
Distribute the 1/2:
y + 2 = 1/2x + 1/2
Change the fractions to decimals:
y + 2 = 0.5x + 0.5
Subtract y from both sides:
2 = 0.5x - y + 0.5
Subtract 0.5 from both sides:
1.5 = 0.5x - y
Rearrange the equation:
0.5x - y = 1.5
So, the equation of the line in standard form is 0.5x - y = 1.5
Answer:an expression to describe the total cost of a party is written as
y = 13.50p + 50
Step-by-step explanation:
The cost of renting the party room at a restaurant is $50.00. Snacks cost $13.50 per person. Assuming the total number of persons invited for the party is p, and the total cost of renting the party room is y. Therefore an expression to describe the total cost of a party is written as
y = 13.50p + 50
The $50 always remains constant
2838=total
Women = 3X +5
Men = 4(3x+5)-3
Children= x
Men= 12x+17
Total= 16X +23
16x + 23 = 2838
16x = 2815
X = 2815/16