Answer:
f(x) = -(x-4)^2 + 5
Step-by-step explanation:
The function 
is a quadratic function. Its graph looks like a parabola. The graph has a vertex of (4,5) and opens up downward.
Proving that 
for all x:
Given
Brian's house: (-7, 9)
Sue's house: (-7, -2)
Find
The number of units between Brian's house and Sue's house.
Solution
Both Brian and Sue live on the "street" x=-7, so the distance between their houses is the distance between -2 on that street and +9 on that street. We always consider distance to be positive, so it doesn't matter whether we start at Brian's house and go -11 units to Sue's house, or start at Sue's house and go +11 units to Brian's house. Either way, we travel 11 units.
_____
"Displacement" is another matter. That has a sign associated with it and there is always a reference direction that is positive. Movement in the opposite direction results in a negative displacement. "Distance" is always positive.
Answer:
18/25
Step-by-step explanation:
Total number of students = 23+14+10+3 = 50.
14 out of 50 are playing sport and taking a foreign language.
So the answer is (50 - 14) / 50
= 36/50
= 18/25.
This is an arithmetic sequence because there is a common difference between terms, a constant found when subtracting the preceding term from any term in the sequence. In this case the common difference is 7.
Any arithmetic sequence can be expressed as:
a(n)=a+d(n-1), a=initial value, d=common difference, n=term number
Here we have a=44 and d=7 so
a(n)=44+7(n-1)
a(n)=44+7n-7
a(n)=7n+37, so the 39th term is:
a(37)=7(37)+7
a(37)=266
I am assuming that 44 is the first term, not the 5th term...if 44 was the fifth term let me know and I will edit to reflect that...
