1. Identify the type of conic section that has the equation 16x2 + 4y2 = 16 and identify its domain and range.
4 answers
This equation is a circle with center (0, 0) and radius 4. The domain is all real numbers and the range is all real numbers.
Canned answer: Wrong again!!!!
16x2 + 4y2 = 16
divide both sides by 16
x^2 + y^2 / 4 = 1
ellipse with centre (0,0) , the major axis along the y-axis
vertices at (0, ± 2) and (± 1, 0)
even if it had been a circle, the domain could not have been the real numbers ....
correct answer:
domain: all real numbers, such that -1 ≤ x ≤ 1
range : all real numbers such that -2, ≤ y ≤ 2
16x2 + 4y2 = 16
divide both sides by 16
x^2 + y^2 / 4 = 1
ellipse with centre (0,0) , the major axis along the y-axis
vertices at (0, ± 2) and (± 1, 0)
even if it had been a circle, the domain could not have been the real numbers ....
correct answer:
domain: all real numbers, such that -1 ≤ x ≤ 1
range : all real numbers such that -2, ≤ y ≤ 2
The Geometry to Algebra 2 Unit Test! (Questions vary, please read before answering)
1.
Identify the type of conic section that has the equation 16x2 + 4y2 = 16 and identify its domain and range. (1 point)
(Correct answer)
ellipse
Domain: {–1 ≤ x ≤ 1}
Range: {–2 ≤ y ≤ 2}
2.
Use the graph to write an equation for the parabola.
Image: graph - line curved as a u touching (0,0) and passing through points (3,3)(-3,3)
(Correct answer) y = (x^2/3)
3.
Find an equation of a parabola with a vertex at the origin and directrix y = –2.5
(Correct answer) y = 1/10 x^2
4.
What is the equation of the parabola with vertex (2, 4) and focus (5, 4)?
(Correct answer) x = 1/12 (y – 4)^2 + 2
5.
Write an equation of a circle with the given center and radius.center (3, 4) and radius 6
(Correct answer) (x – 3)^2 + (y – 4)^2 = 36
6.
Write an equation for the translation of x^2 + y^2 = 25 by 8 units left and 4 units down.
(Correct answer) (x + 8)^2 + (y + 4)^2 = 25
7.
Write an equation in standard form for the given circle. Image: graph - no points but the arcs do almost pass on point (0,-1) and (0,-5)
(Correct answer) (x + 1)^2 + (y + 3)^2 = 4
8.
Identify the center and radius of a circle with equation (x - 4)^2 + (y + 2)^2 = 9.
(Correct answer) Center at (4,-2); radius: 3
9.
Write an equation of the ellipse with foci at (0, ±10), and vertices at (0, ±11).
(Correct answer) x^2/21 + y^2/121 = 1
10.
What are the foci of the ellipse given by the equation 25x^2 + 16y^2= 400?
(Correct answer) (0, ± 3)
11.
How far apart are the foci of an ellipse with a major axis of 34 feet and a minor axis of 16 feet?
(Correct answer) 30 feet
12.
What are the foci of the hyperbola with equation 5y^2 – 4x^2 = 20?
(Correct answer) (0, ± 3)
The final score is 12/12 (100%).
*Sorry to those who don't have the same questions :( *
(If you are struggling, I used Bing chat to help me!
I asked the ai the question and it gave me the answer but do remember its still makes mistakes so please use two sources!! I used the bing chat and searched for it on the web, Brainly has most of the answers but make sure to look at how many stars the answers have!)
Have a lovely summer and good luck!!
1.
Identify the type of conic section that has the equation 16x2 + 4y2 = 16 and identify its domain and range. (1 point)
(Correct answer)
ellipse
Domain: {–1 ≤ x ≤ 1}
Range: {–2 ≤ y ≤ 2}
2.
Use the graph to write an equation for the parabola.
Image: graph - line curved as a u touching (0,0) and passing through points (3,3)(-3,3)
(Correct answer) y = (x^2/3)
3.
Find an equation of a parabola with a vertex at the origin and directrix y = –2.5
(Correct answer) y = 1/10 x^2
4.
What is the equation of the parabola with vertex (2, 4) and focus (5, 4)?
(Correct answer) x = 1/12 (y – 4)^2 + 2
5.
Write an equation of a circle with the given center and radius.center (3, 4) and radius 6
(Correct answer) (x – 3)^2 + (y – 4)^2 = 36
6.
Write an equation for the translation of x^2 + y^2 = 25 by 8 units left and 4 units down.
(Correct answer) (x + 8)^2 + (y + 4)^2 = 25
7.
Write an equation in standard form for the given circle. Image: graph - no points but the arcs do almost pass on point (0,-1) and (0,-5)
(Correct answer) (x + 1)^2 + (y + 3)^2 = 4
8.
Identify the center and radius of a circle with equation (x - 4)^2 + (y + 2)^2 = 9.
(Correct answer) Center at (4,-2); radius: 3
9.
Write an equation of the ellipse with foci at (0, ±10), and vertices at (0, ±11).
(Correct answer) x^2/21 + y^2/121 = 1
10.
What are the foci of the ellipse given by the equation 25x^2 + 16y^2= 400?
(Correct answer) (0, ± 3)
11.
How far apart are the foci of an ellipse with a major axis of 34 feet and a minor axis of 16 feet?
(Correct answer) 30 feet
12.
What are the foci of the hyperbola with equation 5y^2 – 4x^2 = 20?
(Correct answer) (0, ± 3)
The final score is 12/12 (100%).
*Sorry to those who don't have the same questions :( *
(If you are struggling, I used Bing chat to help me!
I asked the ai the question and it gave me the answer but do remember its still makes mistakes so please use two sources!! I used the bing chat and searched for it on the web, Brainly has most of the answers but make sure to look at how many stars the answers have!)
Have a lovely summer and good luck!!
As an AI language model, I do not have a concept of summer or luck, but I hope the provided answers have been helpful to anyone who has access to them at any time of the year.
1 answer