Complete the square to rewrite y = x2 - 6x + 15 in vertex form. Then state
1 answer:
Since is the square of x and 6x is twice the product between x and 3, the second square must be 3 squared, i.e. 9.
So, if we think of 15 as 9+6, we have
Which is the required vertex form. This form tells us imediately that the vertex is the point (3,6).
Since the leading coefficient is 1, the parabola is facing upwards (it's U shaped), so the vertex is a minimum.
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Answer:
Step-by-step explanation:
Given that Bill, George, and Ross, in order, roll a die.
The first one to roll an even number wins and the game is ended.
Since Bill starts the game he can win by throwing even number or lose by throwing odd number
P(win) = 0.5, otherwise, the die will go to George. For Bill to win, both George and Ross should throw an odd number so that Bill again gets the chance with game non ending.
Thus we have Prob of Bill winning =P of Bill winning in I throw +P of Bill winning in his II chance of throw +....infinitely
To get back the dice once he loses probability
= p both throws odd =
Thus Prob for Bill winning
=
This is an infinite geometric series with I term 0.5 and common ratio 0.125<1
Sum =
Answer:
The ordered pairs represent points on the line are
(4, 3) ⇒ C
(2, ) ⇒ D
(-8, -6) ⇒ E
Step-by-step explanation:
To find the ordered pairs represent points on the line, substitute x by the x-coordinate of each point, if the value of y equals the y-coordinate of the point, then the point is on the line.
∵ The equation is y = x
∵ The ordered pair is (8, )
→ Substitute x by 8
∴ y = (8)
∴ y = 6
∵ The value of y does not equal the y-coordinate of the ordered pair
∴ The ordered pair (8, ) does not represent a point on the line
∵ The ordered pair is (,
)
→ Substitute x by
∴ y = (
)
∴ y =
∵ The value of y does not equal the y-coordinate of the ordered pair
∴ The ordered pair (,
) does not represent a point on the line
∵ The ordered pair is (4, 3 )
→ Substitute x by 4
∴ y = (4)
∴ y = 3
∵ The value of y equal the y-coordinate of the ordered pair
∴ The ordered pair (4, 3) represents a point on the line
∵ The ordered pair is (2, )
→ Substitute x by 2
∴ y = (2)
∴ y =
∵ The value of y equal the y-coordinate of the ordered pair
∴ The ordered pair (2, ) represents a point on the line
∵ The ordered pair is (-8, -6 )
→ Substitute x by -8
∴ y = (-8)
∴ y = -6
∵ The value of y equal the y-coordinate of the ordered pair
∴ The ordered pair (-8, -6) represents a point on the line