There are
total ways to draw any 6 numbers from the range 1 to 51, regardless of order.
Given 6 selected numbers that match those drawn by the lottery, there are
ways of rearranging them. So the probability of winning 1st prize is
Next, given 6 selected numbers of which 5 match those drawn by the lottery, there are
ways of rearranging those 5 matching numbers. There are 46 remaining numbers that didn't get drawn, so the probability of winning 2nd prize is
Answer:
x = 4
Step-by-step explanation:
You want x when ...
g(x) = f(2)
2x -3 = 3(2) -1
2x = 8 . . . . . . . . add 3, simplify
x = 4 . . . . . . . . . divide by 2
The vertex form of the given quadratic equation is
.
According to the given question.
We have a quadratic equation
Since, for the standard quadratic form is , the vertex form of a quadratic equation is
where (h, k) is the vertex.
And h and k can be calculated as
h = -b/2a and y = k
So, for the given equation the vertex (h, k) is given by
h = -(-8)/2(4) = 8/8 = 1 (X coordinate of vertex)
and,
substitute x = 1 in the above equation for the value of k
Y = 4(1)(1) - 8(1) + 20
⇒ Y = 4 - 8 + 20
⇒ Y = -4 + 20
⇒ Y = 16
so, k = 16 (Y coordinate of vertex)
Now, substitute the value of a, k and h in .
⇒
Therefore, the vertex form of the given quadratic equation is
.
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