Are there any real number solutions to the system y=4 and x²+y²=2? support your findings both analytically and graphically.

The system has no real solution.

Step-by-step explanation:

Hi there!

We have the following equations system:

x² + y² = 2

y = 4

Let´s replace y = 4 in the first equation and solve it for x:

x ² + 4² = 2

x² + 16 = 2

Substract 16 from both sides of the equation

x² = 2 - 16

x² = -14

There is no real number that satisfies this equation, then, the system has no real solution. That means that both curves don´t intersect.

The expression x² + y² = 2 is a circumference of radius √2 with the center in the origin and y = 4 is a straight horizontal line at y = 4(see attached graphic).

Have a nice day!

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.