Also, I belive that #4 is D. I drew out a graph and it is symmetrical to point A.
After looking over #3, I got B because axis of symmetry is -b/2a, so it would be 6/2(1)= 3.
I need help on how to do the following problems:
1. The graph of x^2 + y^2 = 100 will contain which of the following points?
A. (-6, -8)
B. (10, 1)
C. (10, -6)
D. (4, 6)
2. Write an equation for a circle whose center is at the origin and whose radius is square root of 7.
A. x^2 + y^2 = square root of 7
B. x^2/7 + y^2/7 = 1
C. x^2/5 + x^2/5 = 7
D. x^2/4 + y^2/3 = 1
3. Find the equation for the axis of symmetry for y= x^2-6x+5
A. y=0
B. x=3
C. y=5
D. x=1
4. Given A (4, -5), Find the coordinate of point B that is symmetric to A with respect to the x-axis.
A. (-4,-5)
B. (-4,5)
C. (-5,4)
D. (4,5)
5. There is a graph of a circle with points going through points (0,6),(0,-6), (8,0) and (-8,0).
The graph above would correspond to which of these equations?
A. x^2 - y^2 = 8
B. sq. rt. of 2x^2/4 + sq. rt. of 2x^2/4 = 1
C. x^2/64 + y^2/64 = 1
D. x^2 + y^2 = 8
We are not inclined to do work for students here. However, if you need your work or thinking critiqued, we will be happy to do that.
I just need to know how to find the answer, and I don't even know where to begin.
ok, i think i figured out how to do #1... because -6^2 is 36 and -8^2 is 64 and 36+64= 100, i think it is A.
To find the answer to these problems, let's go through each question step by step:
1. The equation x^2 + y^2 = 100 represents a circle with a radius of 10 (since 10^2 = 100). To determine which points lie on this circle, you can substitute the x and y coordinates of each option into the equation and check if the equation holds true.
For option A, (-6, -8):
(-6)^2 + (-8)^2 = 36 + 64 = 100
Since the equation holds true, option A is a point on the circle.
Similarly, you can check the other options. Substitute the coordinates and see if they satisfy the equation. The coordinates that satisfy the equation will be the points on the circle.
2. The equation of a circle with the center at the origin (0, 0) and a radius of √7 is given by x^2 + y^2 = r^2, where r is the radius.
Substituting the given radius, the equation becomes:
x^2 + y^2 = (√7)^2
x^2 + y^2 = 7
So the correct equation for the circle is option B: x^2/7 + y^2/7 = 1.
3. To find the equation for the axis of symmetry of the quadratic equation y = x^2 - 6x + 5, you can use the formula: axis of symmetry = -b/2a, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In this case, the equation is y = x^2 - 6x + 5, so a = 1 and b = -6. Plugging these values into the formula, we get:
axis of symmetry = -(-6) / (2 * 1) = 6 / 2 = 3
Therefore, the correct equation for the axis of symmetry is option B: x = 3.
4. To find the coordinate of point B that is symmetric to A (4, -5) with respect to the x-axis, you need to reflect the y-coordinate over the x-axis while keeping the x-coordinate the same.
In this case, the y-coordinate of A is -5. Reflecting it over the x-axis changes the sign, so the y-coordinate of point B will be 5. Since the x-coordinate remains the same, point B is (4, 5).
Therefore, the correct answer is option D: (4, 5).
5. To determine the equation of the graph that corresponds to the given points, you can use the general equation of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
From the given points, we can see that the center of the circle is (0, 0) and the radius is 8 (since it passes through points (0, 6), (0, -6), (8, 0), and (-8, 0)).
Substituting these values into the equation, we get:
(x - 0)^2 + (y - 0)^2 = 8^2
x^2 + y^2 = 64
Therefore, the correct equation for the graph is option C: x^2/64 + y^2/64 = 1.
I hope this helps you understand how to approach these problems and find the correct answers!