10 and -4 can add up to give 6 and multiply to give -40
Answer:
The equation of the ellipse is ![\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D%7D%7B9%7D%20%2B%20%5Cfrac%7By%5E%7B2%7D%7D%7B5%7D%20%3D%201)
Step-by-step explanation:
Let the equation of the ellipse is
{As the center of the ellipse is at the origin}
Therefore, the vertices of the ellipse are (± a,0) and foci are (± ae,0)
Now, given that a = 3 and ae = 2
Now, eccentricity of a ellipse is given by b² = a² - a²e² = 3² - 2² = 5
Therefore, the equation of the ellipse is
(Answer)
Answer:
; minimum
Step-by-step explanation:
Given:
The function is, ![y=x^{2}+2](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D%2B2)
The given function represent a parabola and can be expressed in vertex form as:
![y=(x-0)^{2}+2](https://tex.z-dn.net/?f=y%3D%28x-0%29%5E%7B2%7D%2B2)
The vertex form of a parabola is
, where,
is the vertex.
So, the vertex is
.
In order to graph the given parabola, we find some points on it.
Let ![x=-2,y=(-2)^{2}+2=4+2=6](https://tex.z-dn.net/?f=x%3D-2%2Cy%3D%28-2%29%5E%7B2%7D%2B2%3D4%2B2%3D6)
![x=-1,y=(-1)^{2}+2=1+2=3](https://tex.z-dn.net/?f=x%3D-1%2Cy%3D%28-1%29%5E%7B2%7D%2B2%3D1%2B2%3D3)
![x=0,y=(0)^{2}+2=0+2=2](https://tex.z-dn.net/?f=x%3D0%2Cy%3D%280%29%5E%7B2%7D%2B2%3D0%2B2%3D2)
![x=2,y=(2)^{2}+2=4+2=6](https://tex.z-dn.net/?f=x%3D2%2Cy%3D%282%29%5E%7B2%7D%2B2%3D4%2B2%3D6)
![x=1,y=(1)^{2}+2=1+2=3](https://tex.z-dn.net/?f=x%3D1%2Cy%3D%281%29%5E%7B2%7D%2B2%3D1%2B2%3D3)
So, the points are
.
Mark these points on the graph and join them using a smooth curve.
The graph is shown below.
From the graph, we conclude that at the vertex
, it is minimum.
(30 days) * (12 h/day) * (0.040 kW) * ($0.08/kWh) = $1.152
It costs about $1.15 to keep the light on half the time for a month.
Answer:
a. No
b. 2.25 days
Step-by-step explanation:
0.75x + 3 = 0.25x + 5.25
a......................
Constants are $3 and $5.25 respectively
Topping costs $0.75 and $0.25 respectively
To have same cost the toppings number would be different as cost is different.
Suppose the number of toppings is x in one shop and y in the other, then the spending if same, we get this equation:
The answer is NO due to two different variables in the equation
b.......................
Constants are $3 and $5.25 respectively
Joseph adds $0.75 each day and Kelsey spends $0.25 each day
Number of days should be same in this case, so variable will be same and the result (amount left in bank) is same.
<u>So the equation for this case is:</u>
<u>Solving, we get:</u>
- 0.75x + 0.25x = 5.25 - 3
- x = 2.25
This is the solution to equation despite being a whole number.