The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
<h3>What is the equation of the ellipse associated with the coordinates of the foci?</h3>
By <em>analytical</em> geometry we know that foci are along the <em>major</em> axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the <em>standard</em> form of the equation of the ellipse is of the following form:
(x - h)² / a² + (y - k)² / b² = 1, where a > b (1)
Where:
- a - Length of the major semiaxis.
- b - Length of the minor semiaxis.
Now, we proceed to find the vertex and the lengths of the semiaxes:
a = 10 units.
b = 8 units.
Vertex
V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)
V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)
V(x, y) = (1.5, 1) + (- 4.5, 1)
V(x, y) = (- 3, 2)
The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
To learn more on ellipses: brainly.com/question/14281133
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Answer:
150 square feet
Step-by-step explanation:
It is half of the yard, because it extends from the corners. To find the area of the triangle of grass, you have to find the product of the legs divided by two.
30*10=300
300/2=150
150 square feet of Mr. West's backyard is covered in grass
FACTOR ALL OF THE EQUATIONS INTO "y = (x-h)^2 + k," AND THE EQUATION'S VERTEX IS (h,k)
10. y = (x+2)^2 - 11 --> (-2, -11)
11. y = -(x-4)^2 + 32 --> (4, 32)
12. y = 3(x-1)^2 - 5 --> (1, -5)
13. y = -2(x+2)^2 + 5 --> (-2, 5)
14. y = 2(x+1)^2 - 1 --> (-1, -1)
15. y = -5(x-1)^2 + 8 --> (1, 8)
16. y = 3(x-3)^2 - 26 --> (3, -26)
17. y = (x+5)^2 - 32 --> (-5, -32)
18. y = -(x-3)^2 + 10 --> (3, -10)
Answer:
I think 7
Step-by-step explanation:
4 , 8 , 9 and 12 has factors.
7 has no factor.
4= 2×2
8= 2×4
9= 3×3
12= 3×4
Step-by-step explanation:
÷6
First, simplify the 6 to an improper fraction, which is:
Next rewrite the equation using the improper fraction:
÷
Now, in order to divide the fraction, we will need to flip the second fraction over, and then multiply the two fractions together. A great way to remember this is the phrase <em>Copy Dot Flip - </em>Copy the first fraction, put a dot for multiplication, and flip the second fraction.
·
Finally, multiply together and simplify/reduce if needed:
<u>The final answer is </u>
<u> and no simplification or reduction is needed</u>
