What is most likely the correlation coefficient for the set of data shown shown

C) 0.19

Step-by-step explanation:

A correlation coefficient is a measure of how well the line of best fit fits the data.  The higher the correlation coefficient, up to 1.0 or -1.0, the better the fit. A positive correlation coefficient means an increasing data set, while a negative correlation coefficient means a decreasing data set.

We can see that this line of best fit is increasing, so our correlation coefficient will be positive.

However we can also see that the points are fairly scattered; this means this is not a very good fit.  This means that 0.19 is the better fit.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15