Answer:
x=5 twice
Step-by-step explanation:
x^2-10x+25=0
multiply the coefficient of x^2 and the last term
1X25=25
find two numbers you can multiply to get 25 and add to get -10
-5 + (-5)=-10 the middle term
replace -10x with -5x -5x and solve the equation
x^2-5x-5x+25=0
factorise by grouping
x(x-5)-5(x-5)=0
(x-5)(x-5)=0
Either x-5=0,x=5 or x-5=0,x=5
Therefore x=5 twice.
Answer:
y = -2x + 9
y= -1x + 10
Step-by-step explanation:
There is a way that you can figure it out but it’s complicated use desmos it makes it easy
2x + y = 3
3x - y = 12
Add both equations
5x = 15, x = 3
2(3) + y = 3
6 + y = 3, y = -3
Solution: x = 3, y = -3... or (3,-3)
Answer:
3 3/4
Step-by-step explanation: all that you have to do is add 1/3 +2/3+11/4 which gives you 3 3/4
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.
