Line y=2x+3 is tangent to a circle with center (2,-3). Which of the length of the radius of the circle?

Step-by-step explanation:

Since it is tangent to the center, the perpendicular line passes through the center, (2,-3). We find the slope of the perpendicular line to be -1/2 (perpendicular to a slope of 2). We can use point slope form to find the line from the tangent line to the center:

y+3=-1/2(x-2)

We can simplify this to

y= -1/2x-2

We can then check the point of intersection:

-1/2x-2=2x+3

-5=2.5x

x=-2

we can plug this in to the first equation to get y=2(-2)+3=-1

So the point of intersection of the circle and the tangent line is (-2,-1)

Then we find the distance of this point to (2,-3) and we can use pythagorean theorem.

The radius of the circle is

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

answer: y = 3/2 x - 3

y = 1/8 x - 3/4 that would be your correct option

step-by-step explanation: w