Answer:
The last equation x2 - 2x -4 = 0
has solution (x - 1)^2 - 5 = 0, x = 1 + root(5) or x = 1 - root(5)
Step-by-step explanation:
If a quadratic function has roots 1 and 5
f(x) = (x -1)(x- 5)
f(x) = x^2 - 6x + 5
Unless you meant. -4 and 6 ?
g(x) = (x + 4)(x - 6)
g(x) = x^2 -2x -24
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Or did you mean x = 1 and x =4 ?...
x^2 + 2x + 4 = 0 : complete square x^2 + 2x + 1 + 3 = 0, (x+1)^2 + 3 = 0
x^2 - 2x + 4 = 0 : complete square: (x -1)^2 + 3 = 0
0x^2 + 2x - 4 = 0, 2x - 4 = 0, x = 2
x^2 - 2x - 4 = 0 becomes: x^2 - 2x + 1 - 1 -4 = 0 ; (x - 1)^2 - 5 = 0
Let a be the amount needed of 70% pure antifreeze, and let b be the amount needed of 95% pure antifreeze.
0.7a + 0.95b = 180 * 0.9 .........(1)
a + b = 180 .............................(2)
b = 180 - a ..............................(3)
Plugging the expression for b in equation (3) into equation (1), we get:
0.7a + 0.95(180 - a) = 162 ......(4)
Solving equation (4) gives the value a = 36, and plugging this value for a into equation (2) we get b = 144.
Amounts needed are therefore 36 gallons of 70% pure antifreeze and 144 gallons of 95% pure antifreeze.
Yo sup??
To find the turning point we have to differentiate the given function.
T(x)=(x-4)3+6
T'(x)=3
Therefore the turning point is at 3
Hope this helps.
Answer:
1/2
Step-by-step explanation:
Not sure but
I am assuming we have 8 integers :
All or (A) = {7,8,9,10,11,12,13,14} = n(A) = 8
Hence, the probability of any one outcome is 1/8.
Therefore, as you can detect, there are 4 numbers that are even numbers which means :
Even or (E) = {8, 10, 12, 14} = n(E) = 4
So, let E imply this occurrence
E x A
= 4 x 1/8
= 4/8
= 1/2