Step-by-step explanation:
The simplest possible form of f(n) is:
f(n) = n² + bn + c
f(n) / (n + 1) has a remainder of -12, so:
n² + bn + c = (n + p) (n + 1) − 12
n² + bn + c = n² + (1 + p)n + p − 12
b = 1 + p and c = p − 12
f(n) / (n + 2) has a remainder of -24, so:
n² + bn + c = (n + q) (n + 2) − 24
n² + bn + c = n² + (2 + q)n + 2q − 24
b = 2 + q and c = 2q − 24
Setting the expressions equal:
1 + p = 2 + q and p − 12 = 2q − 24
1 = p − q and p = 2q − 12
Solving the system of equations:
1 = q − 12
q = 13
p = 14
b = 15, c = 2
Therefore, f(n) is:
f(n) = n² + 15n + 2
Using grouping:
f(n) = n² + 3n + 2 + 12n
f(n) = (n + 1) (n + 2) + 12n
f(n) / ((n + 1) (n + 2) = 1 + (12n) / ((n + 1) (n + 2))
The remainder is 12n.
7th graders prefer fiction is 0.75 = 75%
8th graders prefer fiction is 0.68 = 68%
7th graders is greater than 8 graders
answer
<span>A. greater than</span>
Answer:
Red: y=(x+6)^2-1
Blue: y=-(x+3)^2+1
Green: y=(x^2-1)
Orange: y=-(x-3)^2+1
Purple: y=(x-6)^2-1
Step-by-step explanation:
Use Desmos to check
So the answer is 14.04* 15.61 it gives an answer of product 224
Step-by-step explanation:
two sides of length =0.6 and 1.6
lengths for the third side,X =?
= 0.6+1.6=2.2
lengths for the third side of X=2.2