Answer:
The center is located at (2, –1).
The major axis is 8 units long.
The vertices are 4 units above and below the centre.
The foci are √7 units above and below the centre.
Step-by-step explanation:
Assume the ellipse looks like the one below.
The properties of a vertical ellipse are
![\textbf{Vertical ellipse}\\\dfrac{ (x - h)^{2} }{b^{2}} + \dfrac{(y - k)^{2}}{a^{2}} = 1\begin{cases}\text{Centre} = (h,k)\\\text{Dist. between vertices} = 2a\\\text{Vertices} = (h, k\pm a)\\\text{Dist. between covertices} = 2b\\ \text{Covertices}= (h\pm b, k)\\c = \sqrt{a^{2} - b^{2}}\\\text{Dist. of foci from centre} = c\\\text{Foci} = (h, k\pm c)\\\end{cases}](https://tex.z-dn.net/?f=%5Ctextbf%7BVertical%20ellipse%7D%5C%5C%5Cdfrac%7B%20%28x%20-%20h%29%5E%7B2%7D%20%7D%7Bb%5E%7B2%7D%7D%20%2B%20%5Cdfrac%7B%28y%20-%20k%29%5E%7B2%7D%7D%7Ba%5E%7B2%7D%7D%20%3D%201%5Cbegin%7Bcases%7D%5Ctext%7BCentre%7D%20%3D%20%28h%2Ck%29%5C%5C%5Ctext%7BDist.%20between%20vertices%7D%20%3D%202a%5C%5C%5Ctext%7BVertices%7D%20%3D%20%28h%2C%20k%5Cpm%20a%29%5C%5C%5Ctext%7BDist.%20between%20covertices%7D%20%3D%202b%5C%5C%20%5Ctext%7BCovertices%7D%3D%20%28h%5Cpm%20b%2C%20k%29%5C%5Cc%20%3D%20%5Csqrt%7Ba%5E%7B2%7D%20-%20b%5E%7B2%7D%7D%5C%5C%5Ctext%7BDist.%20of%20foci%20from%20centre%7D%20%3D%20c%5C%5C%5Ctext%7BFoci%7D%20%3D%20%28h%2C%20k%5Cpm%20c%29%5C%5C%5Cend%7Bcases%7D)
A. Centre
TRUE. The centre is at (2,-1).
B. Major axis
TRUE
Length of major axis = 3 - (-5) = 3 + 5 = 8
C. Minor axis
False
Length of minor axis = 5 - (-1) = 5 + 1 = 6
D. Vertices
TRUE
Distance between vertices = 8 = 2a
a - 8/2 = 4
Vertices at (h, k ± a) = (2, -1 ± 4)
E. Foci
TRUE
c² = a² - b² = 4² - 3² = 16 - 9 = 7
c = √7
The foci are √7 above and below the centre.
F. Foci
False.
The foci are on a vertical line.
Answer:
13x^2 - 18x + 9
Step-by-step explanation:
<u>Step 1: Distribute the plus and minus signs</u>
(4x^2 - 5x + 6) + (9x^2 - 2x) - (11x - 3)
4x^2 - 5x + 6 + 9x^2 - 2x - 11x + 3
<u>Step 2: Combine like terms</u>
4x^2 <u>- 5x</u> <em>+ 6</em> + 9x^2 <u>- 2x</u> <u>- 11x</u> <em>+ 3</em>
13x^2 - 18x + 9
Answer: 13x^2 - 18x + 9
Answer:
![25\le AC\le 121](https://tex.z-dn.net/?f=25%5Cle%20AC%5Cle%20121)
Step-by-step explanation:
The key to this question is that the length of a side of a triangle is larger than the difference of the other 2 sides and is smaller than the sum of the other 2 sides. Hence the length of AC is larger than (or equal to, in case A, C, D do not form a triangle but are on the same line)
and is smaller than (or equal to)
.
Answer:
32,400
Step-by-step explanation:
180 * 180 + calculator = 32,400
Since he did not put the first card back, the events are dependent