The probability of choosing a large red fish is 5/15 or 1/3
I assume you mean x squared in the first equation
Because both are equal to y, they are equal to each other so x + 5 = x^2 +3
If we then move everything over to one side, we get x^2 - x - 2 = 0
Then factorise it to (x-2)(x+1) = 0
And solve both parts separately
x + 1 = 0
x = -1
x-2 = 0
x = 2
Sub both values into the simplest equation in this case y=x+5
to get y = 4 and y = 7
<span>0.05 is 10 times greater than 0.005</span>
Answer:
I believe the answer is - they are the same shape but different sizes
Answer:
f
(
x
)
=
−
1
2
x
2
+
3
x
−
1
2
Explanation:
A quadratic function can be written in vertex form as:
f
(
x
)
=
a
(
x
−
h
)
2
+
k
where
(
h
,
k
)
is the vertex and
a
is a constant multiplier.
In our example the vertex
(
h
,
k
)
is
(
3
,
4
)
, so we can write:
f
(
x
)
=
a
(
x
−
3
)
2
+
4
Given that this passes through the point
(
1
,
2
)
, we must have:
2
=
a
(
1
−
3
)
2
+
4
=
4
a
+
4
Subtract
4
from both ends to get:
−
2
=
4
a
Divide both sides by
4
and transpose to find:
a
=
−
1
2
So our quadratic function can be written in vertex form as:
f
(
x
)
=
−
1
2
(
x
−
3
)
2
+
4
We can multiply this out and simplify as follows:
f
(
x
)
=
−
1
2
(
x
−
3
)
2
+
4
f
(
x
)
=
−
1
2
(
x
2
−
6
x
+
9
)
+
4
f
(
x
)
=
−
1
2
x
2
+
3
x
−
9
2
+
4
f
(
x
)
=
−
1
2
x
2
+
3
x
−
1
2
Step-by-step explanation:
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