Step-by-step explanation:
What is the equation of the parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
?
To solve this you need to use the vertex form of the equation of a parabola which is
y
=
a
(
x
−
h
)
2
+
k
, where
(
h
,
k
)
are the coordinates of the vertex.
Explanation:
The first step is to define your variables
h
=
−
4
k
=
2
And we know one set of points on the graph, so
x
=
−
7
y
=
−
34
Next solve the formula for
a
y
=
a
(
x
−
h
)
2
+
k
−
34
=
a
(
−
7
+
4
)
2
+
2
−
34
=
a
(
−
3
)
2
+
2
−
34
=
9
a
+
2
−
36
=
9
a
−
4
=
a
To create a general formula for the parabola you would put in the values for
a
,
h
, and
k
and then simplify.
y
=
a
(
x
−
h
)
2
+
k
y
=
−
4
(
x
+
4
)
2
+
2
y
=
−
4
(
x
2
+
8
x
+
16
)
+
2
y
=
−
4
x
2
−
32
x
−
64
+
2
So the equation of a parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
is:
y
=
−
4
x
2
−
32
x
−
62
Answer:
(-5,-37)
(-4,-34)
(-3,-31)
(-2,-28)
(-1,-25)
(0,-22)
(1,-19)
(2,-16)
(3,-13)
(4,-10)
(5,-7)
(6,-4)
Step-by-step explanation:
y - 10 = 3(x - 11)
y - 10 = 3x - 33
y = 3x -22
<span>2/3 or 0.66666
This is a sum of an infinite series problem.
A sequence of 1 will happen with a probability of 0.5
A sequence of 3 will happen with a probability of 1/2^3, 1/8, = 0.125
In general we have an infinite series of
1/2^1 + 1/2^3 + 1/2^5 + ... + 1/2^(2n-1) where n >= 1
The sum of such a series with a constant ratio between sequential terms is
S = s1/(1-r)
where
s1 = first term in the series
r = ratio between terms.
The value for s1 = 0.5 as shown above and the 2nd term is 0.125. So
r = 0.125 / 0.5 = 0.25
And the sum of the infinite series is
S = s1/(1-r)
S = 0.5/(1 - 0.25)
S = 0.5/0.75
S = 2/3
S = 0.666..66
So the probability of the first head coming up in an odd number of tosses is 2/3, or 66.6%</span>
Answer:
Expression: 3.5((12x18) + 13²)
Step-by-step explanation:
Since George is going to put carpeting in two different rooms, one rectangular and one square, you need to find the area of each room, add the sum and then multiply the total area needed by the cost per square foot of carpet. The area of a rectangle is: a = lw, where l=length and w = width. The area of a square is: a = s², where s = side of the square. Take the sum of these two areas would be (12 x 18) + 13² or 213 + 169 = 382. Since the cost of the carpet is the same per square foot, you can multiply the entire sum by the cost of $3.50 or: 3.5((12 x 18) + 13²) or 3.5(382) = $1,337.
