Find an equation of the line. Write the equation in function notation. Through (6,-1); perpendicular to 9y=x-18
1 answer:
The first step is to find the slope of the given line by putting its equation in the form y = mx + b.
9y = x - 18
Dividing both sides by 9, gives:
y = (x/9) - 2
The slope of the given line is therefore 1/9.
Let the slope of the perpendicular line be m.
The product of the two slopes must equal -1 for the lines to be perpendicular.
Therefore m = -9.
At this stage the equation of the required line is y = -9x + b.
Now we need to find the value of b.
Plugging the given values of a point on the line (6, -1) into the equation gives:
-1 = -54 + b; from which b = 53.
The required equation for the line is:
f(x) = -9x + 53.
9y = x - 18
Dividing both sides by 9, gives:
y = (x/9) - 2
The slope of the given line is therefore 1/9.
Let the slope of the perpendicular line be m.
The product of the two slopes must equal -1 for the lines to be perpendicular.
Therefore m = -9.
At this stage the equation of the required line is y = -9x + b.
Now we need to find the value of b.
Plugging the given values of a point on the line (6, -1) into the equation gives:
-1 = -54 + b; from which b = 53.
The required equation for the line is:
f(x) = -9x + 53.
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Answer:
0.006% probability that the final vote count is unanimous.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Random voting:
So 50% of voting yes, 50% no, so
15 members:
This means that
What is the probability that the final vote count is unanimous?
Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So
In which
So
0.006% probability that the final vote count is unanimous.
See attached image
First, we must know this: Complementary angles are two angles whose sum is equal to 90°, while supplementary angles are two angles whose sum is equal to 180°. That been said, the only statement which is true is the second statement, <span>MNL is complementary to KNL
Reasons why others are False
</span>GNJ is supplementary to JNK, not complementary
MNG is supplementary to GNJ, not complementary
LNJ (not KNJ) <span>is supplementary to MNL
</span>GNM is equal to JNK, not supplementary
First, we must know this: Complementary angles are two angles whose sum is equal to 90°, while supplementary angles are two angles whose sum is equal to 180°. That been said, the only statement which is true is the second statement, <span>MNL is complementary to KNL
Reasons why others are False
</span>GNJ is supplementary to JNK, not complementary
MNG is supplementary to GNJ, not complementary
LNJ (not KNJ) <span>is supplementary to MNL
</span>GNM is equal to JNK, not supplementary