Hector earned $60 this week, which is 5 times the amount he earned last week. The model shows how much money he earned this week
1 answer:
You might be interested in
I don't know if we can find the foci of this ellipse, but we can find the centre and the vertices. First of all, let us state the standard equation of an ellipse.
(If there is a way to solve for the foci of this ellipse, please let me know! I am learning this stuff currently.)
Where
is the centre of the ellipse. Just by looking at your equation right away, we can tell that the centre of the ellipse is:
Now to find the vertices, we must first remember that the vertices of an ellipse are on the major axis.
The major axis in this case is that of the y-axis. In other words,
So we know that b=5 from your equation given. The vertices are 5 away from the centre, so we find that the vertices of your ellipse are:
&
I really hope this helped you! (Partially because I spent a lot of time on this lol)
Sincerely,
~Cam943, Junior Moderator
(If there is a way to solve for the foci of this ellipse, please let me know! I am learning this stuff currently.)
Where
Now to find the vertices, we must first remember that the vertices of an ellipse are on the major axis.
The major axis in this case is that of the y-axis. In other words,
So we know that b=5 from your equation given. The vertices are 5 away from the centre, so we find that the vertices of your ellipse are:
&
I really hope this helped you! (Partially because I spent a lot of time on this lol)
Sincerely,
~Cam943, Junior Moderator
Answer:
* The equation of the median of the trapezoid is 10x + 6y = 39
Step-by-step explanation:
* Lets explain how to solve the problem
- The slope of the line whose end points are (x1 , y1) , (x2 , y2) is
- The mid point of the line whose end point are (x1 , y1) , (x2 , y2) is
- The standard form of the linear equation is Ax + BC = C, where
A , B , C are integers and A , B ≠ 0
- The median of a trapezoid is a segment that joins the midpoints of
the nonparallel sides
- It has two properties:
# It is parallel to both bases
# Its length equals half the sum of the base lengths
* Lets solve the problem
- The trapezoid has vertices R (-1 , 5) , S (! , 8) , T (7 , -2) , U (2 , 0)
- Lets find the slope of the 4 sides two find which of them are the
parallel bases and which of them are the non-parallel bases
# The side RS
∵
# The side ST
∵
# The side TU
∵
# The side UR
∵
∵ The slope of ST = the slop UR
∴ ST// UR
∴ The parallel bases are ST and UR
∴ The nonparallel sides are RS and TU
- Lets find the midpoint of RS and TU to find the equation of the
median of the trapezoid
∵ The median of a trapezoid is a segment that joins the midpoints of
the nonparallel sides
∵ The midpoint of RS =
∵ The median is parallel to both bases
∴ The slope of the median equal the slopes of the parallel bases = -5/3
∵ The form of the equation of a line is y = mx + c
∴ The equation of the median is y = -5/3 x + c
- To find c substitute x , y in the equation by the coordinates of the
midpoint of RS
∵ The mid point of Rs is (0 , 13/2)
∴ 13/2 = -5/3 (0) + c
∴ 13/2 = c
∴ The equation of the median is y = -5/3 x + 13/2
- Multiply the two sides by 6 to cancel the denominator
∴ The equation of the median is 6y = -10x + 39
- Add 10x to both sides
∴ The equation of the median is 10x + 6y = 39
* The equation of the median of the trapezoid is 10x + 6y = 39