The points which represents the vertices of the given equation are; (15, −2) and (−1, −2).
<h3>Which points among the answer choices represents the vertices of the ellipse whose equation is given?</h3>
The complete question gives the equation of the ellipse as; (x-7)²/64+(y+2)²/9=1.
Since, It follows from convention that general equation of ellipse with centre as (h, k) takes the form;
(x-h)²/a² +(y-k)²/b² = 1.
Consequently, it follows from observation that the value of a and b in the given equation in the task content is; √64 = 8 and √9 = 3 respectively.
Since, 8 > 3, The vertices of the ellipse are given by; (h±a, k).
The vertices in this scenario are therefore;
(7+8, -2) and (7-8, -2).
= (15, -2) and (-1, -2).
Read more on vertices of an ellipse;
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Answer:
In other words: any of the prime numbers that can be multiplied to give the original number. ... Example: The prime factors of 15 are 3 and 5 (because 3×5=15, and 3 and 5 are prime numbers).
Class ratio of girls to boys is 3:5
So there are 3 girls and 5 boys in 8 students
If there are 32 students, then 3/(3+5) * 32 = 12 girls, and 5/(3+5) * 32 = 20 boys
Hope it helps you?
Answer:
y=2x-3
Explanation:
which equation represents the relationship between x and y shown in the table?
x | y
2 | 1
4 | 5
6 | 9
8 | 13
take a look at the values in the table one more,
we find the gradient of the line to be
G=y2-y1/(x2-x1)
G=13-1/(8-2)
slope/gradient=12/6
m=2
from equation of a line graph, we know
y=mx+c
m=gradient
c=intercept
y=vertical axis
x=a point on the horizontal axis
y=2x+c
when x=6, y=9
9=2(6)+C
c=-3
Therefore the equation becomes
y=2x-3
Step-by-step explanation:
Answer:
For x(θ) = 3cosθ + 2
y² = [9x²/(x - 2)²] - x²
For x(θ) = 3cosθ + 2
x² = [4y²/(y - 1)²] - y²
Step-by-step explanation:
Given the following equivalence:
x² + y² = r²
r = √(x² + y²)
x = rcosθ
cosθ = x/r
y = rsinθ
sinθ = y/r
Applying these to the given equations,
x(θ) = 3cosθ + 2
x = 3(x/r) + 2
xr = 3x + 2r
(x - 2)r = 3x
r = 3x/(x - 2)
Square both sides
r² = 9x²/(x - 2)²
(x - 2)²r² = 9x²
(x - 2)²(x² + y²) = 9x²
(x² + y²) = 9x²/(x - 2)²
y² = [9x²/(x - 2)²] - x²
y(θ) = 2sinθ - 1
y = 2y/r - 1
yr = 2y - r
(y - 1)r = 2y
r = 2y/(y - 1)
Square both sides
r² = 4y²/(y - 1)²
x² + y² = 4y²/(y - 1)²
x² = [4y²/(y - 1)²] - y²
