1 ) Find the inverse of g(x) = 5x -2
2) the graph (x-2)^2 + 3(y-2)^2 = 25 is graph of a(an) ______
3) which equation has a vertex (5,- 4)
a) y= (x+4)^2 - 5 c) y = (x-5)^2 -4
b) y = (x-4)^2 +5 d) y=(x+5)^2 -4
4) solve 8^x less than or equal to 25
5) name the axis to which the major axis is parallel and find the center of 25(x+5)^2 + 4(y-3)^2 = 100
6) the vertex of the graph of y = -99(x-7)^2 -2 is a minimum value ?
a) true
b) false
7) there is no solution of x^2 - y^2 = 3 and y^2 - x^2 = 3
a) true
b) false
8) find the median of the set of data [9, 13, 8, 10, 11, 9, 12, 16, 10, 9]
can someone help me with these homework problems ASAP .. I'm stuck
No homework dumping please. Show your work.
As for question #7, how can both equations be true? Can x^2 - y^2 equal both 3 and -3?
I'll be happy to help you with your homework problems! Let's go through each question one by one and find the answers.
1) To find the inverse of g(x) = 5x - 2, we need to swap x and y and solve for y. The equation becomes x = 5y - 2. Now solve for y by isolating it.
x + 2 = 5y
(x + 2) / 5 = y
Therefore, the inverse function is g^(-1)(x) = (x + 2) / 5.
2) The equation (x-2)^2 + 3(y-2)^2 = 25 represents an ellipse. The general equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1. If a = b, it is a circle. Since the equation given has distinct values for a and b (a^2 = 25 and b^2 = 3), it is an ellipse.
3) The vertex form of a parabola is y = a(x-h)^2 + k, where (h, k) is the vertex. Using this, we can determine which equation has the vertex (5, -4).
Plugging in the vertex values into each equation will help us identify the correct one.
For option c: y = (x - 5)^2 - 4, the vertex is (5, -4).
Therefore, the correct equation is c) y = (x - 5)^2 - 4.
4) To solve 8^x ≤ 25, we can take the logarithm base 8 of both sides.
log base 8 of (8^x) ≤ log base 8 of 25
x ≤ log base 8 of 25
By evaluating the logarithm, x ≤ 1.4286.
Therefore, the solution is x ≤ 1.4286.
5) For the equation 25(x + 5)^2 + 4(y - 3)^2 = 100, let's rearrange it in standard form to identify the center and the axis to which the major axis is parallel.
Divide both sides by 100: (x + 5)^2 / 4 + (y - 3)^2 / 25 = 1.
Comparing it with the standard form: (x - h)^2 / a^2 + (y - k)^2 / b^2 = 1, we can identify the center (h, k) as (-5, 3) and the major axis parallel to the y-axis (vertical ellipse).
6) The vertex of the parabolic graph y = -99(x - 7)^2 - 2 represents the minimum point since the coefficient of the squared term is negative. Therefore, the answer is a) true.
7) By simplifying the equations x^2 - y^2 = 3 and y^2 - x^2 = 3, we can see that they are the same equation with the variables swapped. Since they are equivalent, they represent the same curve and intersect at all points. Therefore, there are infinite solutions, and the answer is b) false.
8) To find the median of the set of data [9, 13, 8, 10, 11, 9, 12, 16, 10, 9], first, sort the data in ascending order: 8, 9, 9, 9, 10, 10, 11, 12, 13, 16.
The median is the middle value of the sorted data set, which in this case is 10.
Therefore, the median of the given data set is 10.
I hope this helps! Let me know if you have any further questions or need additional assistance.