A) zeroes
P(n) = -250 n^2 + 2500n - 5250
Extract common factor:
P(n)= -250 (n^2 - 10n + 21)
Factor (find two numbers that sum -10 and its product is 21)
P(n) = -250(n - 3)(n - 7)
Zeroes ==> n - 3 = 0 or n -7 = 0
Then n = 3 and n = 7 are the zeros.
They rerpesent that if the promoter sells tickets at 3 or 7 dollars the profit is zero.
B) Maximum profit
Completion of squares
n^2 - 10n + 21 = n^2 - 10n + 25 - 4 = (n^2 - 10n+ 25) - 4 = (n - 5)^2 - 4
P(n) = - 250[(n-5)^2 -4] = -250(n-5)^2 + 1000
Maximum ==> - 250 (n - 5)^2 = 0 ==> n = 5 and P(5) = 1000
Maximum profit =1000 at n = 5
C) Axis of symmetry
Vertex = (h,k) when the equation is in the form A(n-h)^2 + k
Comparing A(n-h)^2 + k with - 250(n - 5)^2 + 1000
Vertex = (5, 1000) and the symmetry axis is n = 5.
The two numbers that add to make twenty and have a difference of 4 are 12 and 8
Hello,
p=>q is equivalent to ~q → ~p
p-------q-------p=>q--~q ----- ~p----~q → ~p
0-------0-------1-------1 ------- 1------- 1
0-------1-------1-------0------- 1------- 1
1-------0-------0-------1------- 0-------0
1-------1-------1-------0------- 0-------1
Column 3= column 6 ==>equivalent
Answer B
Answer:
There is a free prize drawing in a shopping mall. There are some youngsters and older peoples. The result of the number of winning people is shown below.
Which grow had highest % of winning between youngster and older people? - 30 older people won washing machines out of the 60 older people. - 45 youngsters won washing machines out of the
Answer:
The center of the circle is midpoint of the diameter:
The radius is equal the distance between C and Q:
An equation of a circle:
(x - a)² + (y - b)² = r²
(a; b) - a coordinates of a center
r - a radius
r = √65; (-3; 2) ⇒ a = -3 and b = 2
subtitute
(x - (-3))² + (y - 2)² = (√65)²
Answer:
the center: (-3; 2)
the radius: √65
the equation of the circle: (x + 3)² + (y - 2)² = 65
