Y = 7x + b
2 = 7 + b, b = -5
Y = 7x - 5
The given plane has normal vector

Scaling <em>n</em> by a real number <em>t</em> gives a set of vectors that span an entire line through the origin. Translating this line by adding the vector <2, 1, 1> makes it so that this line passes through the point (2, 1, 1). So this line has equation

This line passes through (2, 1, 1) when <em>t</em> = 0, and the line intersects with the plane when

which corresponds the point (3, -1, 1) (simply plug <em>t</em> = 1 into the coordinates of
).
So the distance between the plane and the point is the distance between the points (2, 1, 1) and (3, -1, 1):

Answer:
The probability that the next two balls are blue is 
Step-by-step explanation:
There is a total number of 12 balls in the jar (7 Red and 5 blue), if the first marble drawn is a given, that is it is a Red marble, then following the instruction the Red marble and two more Red marbles are added. Therefore making the total number of marbles in the jar to be 14 marbles (9 red and 5 blue).
<u>FIRST EVENT:</u> So the probability of drawing the second marble to be a blue marble becomes = 5/14 [<em>this is the number of blue marbles/ total number of marbles in the jar</em>].
Thereafter the blue marble is returned and two more blue marbles are added to the jar making a total of 16 marbles (9 red and 7 blue}.
<u>SECOND EVENT: </u>So the probability of drawing the third marble to be a blue marble becomes = 7/16 [<em>this is the number of blue marbles/ total number of marbles in the jar</em>].
However, this is not the final answer because the first event and the second event must occur together, therefore, one has to multiply the first events probability and the second events probability to get the probability we are looking for.
So, the probability of picking the next two to be blue = 5/14*7/16 (seven can reduce the 14 to a 2 based on division)
Therefore the probability = 5/32 (the 2 multiplies the 16)
Answer:
84
Step-by-step explanation:
See the attached document.