Answer:
Step-by-step explanation:
Given
Required
Determine the equation
First, we need to determine the slope (m):
Next, we determine the line equation using:
Where
A friend tells you that he has a cubic equation with exactly three complex roots. Determine which explanation best explains why
2 answers:
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Answer:
(i). . Point
is at
.
(ii). Point is at
.
(iii). (slope-intercept form) or equivalently
(standard form.)
Step-by-step explanation:
<h3>Coordinates of the Extrema</h3>Note, that when is expanded, the expression would become
.
Compare this expression to the original . In particular, try to match the coefficients of the
terms and the
terms, as well as the constant terms.
- For the
coefficients:
.
- For the
coefficients:
. Since
gives
.
- For the constant terms:
. Since
gives
.
Hence, the original expression for the parabola is equivalent to .
For a parabola in the vertex form , the vertex (which, depending on
, can either be a minimum or a maximum,) would be
. For this parabola, that point would be
.
Assume is an intersection of the graphs of the two functions
and
. Setting
to
, and
to
should make sure that both equations still hold. That is:
.
Take the sum of these two equations to eliminate the variable :
.
Simplify and solve for :
.
.
There are two possible solutions: and
. For each possible
, substitute back to either of the two equations to find the value of
.
corresponds to
.
corresponds to
.
Hence, the two intersections are at and
, respectively.
The coordinates of point and point
each have two components.
- For point
, the
while the
-component is
.
- For point
, the
while the
.
Let denote the midpoint of segment
. The
-component of point
would be
, the average of the
-components of point
and point
.
Similarly, the -component of point
would be
, the average of the
-components of point
and point
.
Hence, the midpoint of segment would be at
.
The slope of the line joining (the coordinates of point
) and
(the midpoint of segment
) would be:
.
Point (the midpoint of segment
) is a point on that line. The point-slope form of this line would be:
.
Rearrange to obtain the slope-intercept form, as well as the standard form of this line:
.
.
The answer is nine pounds of grapes.
X=0
Y=9
X=0
Y=9
Answer:
here the order will be 104! =
Step-by-step explanation:
since the cards are to arranged in no particular order that is why we used combination to find the result.
Combination can simply be explained as the method of selecting items from a collection of items where the order of the selections does not matter.