Answer:
6 squared
Step-by-step explanation:
The square root of a perfect square is a rational number.
Answer:
Mean = 86
Median = 86
Mode = 93
Range = 20
Step-by-step explanation:
Mean is the average of a set of numbers. To find the average, you add all the numbers together and divide the product by how many numbers are in the set so:
93 + 86 + 93 + 85 + 73 = 430
430/5 = 86
Median is the middle of a set of numbers.
First put the numbers in order of smallest to biggest
73, 85, 86, 93, 93.
The middle number is 86 so the median is 86.
A mode or modes are numbers that appear most frequently in a number of sets. They’re can be multiple modes.
The most frequent number is 93 so the mode is 93
Range is the difference of the biggest number and the smallest number. The biggest is 93 and the smallest is 73.
93 - 73 = 20
The range is 20
Find the critical points of
:


All three points lie within
, and
takes on values of

Now check for extrema on the boundary of
. Convert to polar coordinates:

Find the critical points of
:



where
is any integer. There are some redundant critical points, so we'll just consider
, which gives

which gives values of

So altogether,
has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).
To find what the answer is for this problem, we need to find out whether each of them have infinite, no, or single solutions. We can do this individually.
Starting with the first one, we need to convert both of the equations into slope-intercept form. y = -2x + 5 is already in that form, now we just need to do it to 4x + 2y = 10.
2y = -4x + 10
y = -2x +5
Since both equations give the same line, the first one has infinite solutions.
Now onto the second one. Once again, the first step is to convert both of the equations into slope-intercept form.
x = 26 - 3y becomes
3y = -x + 26
y = -1/3x + 26/3
2x + 6y = 22 becomes
6y = -2x + 22
y = -1/3 x + 22/6
Since the slopes of these two lines are the same, that means that they are parallel, meaning that this one has no solutions.
Now the third one. We do the same steps.
5x + 4y = 6 becomes
4y = -5x + 6
y = -5/4x + 1.5
10x - 2y = 7 becomes
2y = 10x - 7
y = 5x - 3.5
Since these two equations are completely different, that means that this system has one solution.
Now the fourth one. We do the same steps again.
x + 2y = 3 becomes
2y = -x + 3
y = -0.5x + 1.5
4x + 8y = 15 becomes
8y = -4x + 15
y = -1/2x + 15/8
Once again, since these two lines have the same slopes, that means that they are parallel, meaning that this one has no solutions.
Now the fifth one.
3x + 4y = 17 becomes
4y = -3x + 17
y = -3/4x + 17/4
-6x = 10y - 39 becomes
10y = -6x + 39
y = -3/5x + 3.9
Since these equations are completely different, there is a single solution.
Last one!
x + 5y = 24 becomes
5y = -x + 24
y = -1/5x + 24/5
5x = 12 - y becomes
y = -5x +12
Since these equations are completely different, this system has a single solution.