The tree's grow rate is 1.1 per month
7.48/6.8
=1.1
The basic form of the equation is:
4p(x-h) = (y-k)2
(h,k) is the vertex
4(-0.5)(x-1.5) = (y-(-4))2
-2(x-1.5) = (y+4)2
-2(x-1.5) = y2 + 8y + 16
x - 1.5 = (-1/2)(y2 + 8y + 16)
x = (-1/2)y2 - 4y - 8 + 1.5
x = (-1/2)y2 - 4y - 6.5
Answer:
The probability of getting two of the same color is 61/121 or about 50.41%.
Step-by-step explanation:
The bag is filled with five blue marbles and six red marbles.
And we want to find the probability of getting two of the same color.
If we're getting two of the same color, this means that we are either getting Red - Red or Blue - Blue.
In other words, we can find the independent probability of each case and add the probabilities together*.
The probability of getting a red marble first is:

Since the marble is replaced, the probability of getting another red is: 
The probability of getting a blue marble first is:

And the probability of getting another blue is:

So, the probability of getting two of the same color is:

*Note:
We can only add the probabilities together because the event is mutually exclusive. That is, a red marble is a red marble and a blue marble is a blue marble: a marble cannot be both red and blue simultaneously.
Answer:
∠ BAC = 80°
Step-by-step explanation:
The sum of the interior angles of quadrilateral ACDB = 360°
DB and DC are tangents to the circle, thus
∠ DBA = ∠ ACD = 90° ( angle between tangent/ circle at point of contact )
Thus
∠ BAC + 90° + 90° + 100° = 360°
∠ BAC + 280° = 360° ( subtract 280° from both sides )
∠ BAC = 80°
We know that
if two lines are perpendicular
then
the slopes
m1*m2=-1
step 1
find the slope AB
A (0,2)
B (-3,-3)
m=(y2-y1)/(x2-x1)-----> m=(-3-2)/(-3-0)-----> m=-5/-3----> m1=5/3
step 2
find the slope CD
C (-4,1)
D (0,-2)
m=(y2-y1)/(x2-x1)-----> m=(-2-1)/(0+4)-----> m=--3/4----> m2=-3/4
step 3
multiply mi*m2
(5/3)*(-3/4)-----> -15/12
so
15/12 is not -1
therefore
AB is not perpendicular to CD