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.
Each hour, the bus moves 50 km closer to their meeting point, while the car moves 70 km closer. That is, the distance between them is reduced by
50 km + 70 km = 120 km
each hour.
They are becoming 120 km closer to each other every hour.
1:8. 16oz in 1lb. 16x2 is 32. Simplify
First u need to know what distributive property is so Distributive Property<span> is an algebra </span>property<span> which is used to multiply a single term and two or more terms inside a set of parentheses. Take a look at this problem. 2(3 + 6)
thats distributive property so.... if u need more help then ask im happy to help</span>
Your answer is -1. hope this helps