We are dealing with monomial function so we just focus on end behavior.
5x¹⁰ has both ends going up so it would have minimum value
-4x¹¹ has one end going down and other end going up so no minimum value
-x¹² has both ends going down so it opens downward thus no minimum value. Just maximum.
6x⁷ has one ends going up and other going down so no minimum value.
So final answer is y = 5x¹⁰
Answer:
W'' = (2, -3)
Step-by-step explanation:
Reflection over the x-axis negates the y-coordinate and leaves the x-coordinate alone. The W becomes ...
... W' = (-2, -3)
Reflection over the y-axis negates the x-coordinate and leaves the y-coordinate alone. The W' becomes ...
... W'' = (2, -3)
Answer:
The sample mean is 
min.
The sample standard deviation is 
min.
Step-by-step explanation:
We have the following data set:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values.
The formula for the mean of a sample is
where, 
is the number of values in the data set.
The standard deviation measures how close the set of data is to the mean value of the data set. If data set have high standard deviation than the values are spread out very much. If data set have small standard deviation the data points are very close to the mean.
To find standard deviation we use the following formula
The mean of a sample is .
Create the below table.
Find the sum of numbers in the last column to get.
1/2 is a fraction so it is 5
Answer:
x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)
Step-by-step explanation:
Solve for x:
-8 + x^2 + (x^2 - 8)^2 = 20
Expand out terms of the left hand side:
x^4 - 15 x^2 + 56 = 20
Subtract 20 from both sides:
x^4 - 15 x^2 + 36 = 0
Substitute y = x^2:
y^2 - 15 y + 36 = 0
The left hand side factors into a product with two terms:
(y - 12) (y - 3) = 0
Split into two equations:
y - 12 = 0 or y - 3 = 0
Add 12 to both sides:
y = 12 or y - 3 = 0
Substitute back for y = x^2:
x^2 = 12 or y - 3 = 0
Take the square root of both sides:
x = 2 sqrt(3) or x = -2 sqrt(3) or y - 3 = 0
Add 3 to both sides:
x = 2 sqrt(3) or x = -2 sqrt(3) or y = 3
Substitute back for y = x^2:
x = 2 sqrt(3) or x = -2 sqrt(3) or x^2 = 3
Take the square root of both sides:
Answer: x = 2 sqrt(3) or x = -2 sqrt(3) or x = sqrt(3) or x = -sqrt(3)
