The coefficient of x in the equation of the given line, 3, is its slope. The slope of the perpendicular line is the negatve reciprocal of that, -1/3. You now have the slope and a point on the perpendicular line, so you can write its equation using the point-slope form:
y = m(x -x₁) +y₁
where m is the slope and (x₁, y₁) is the point.
An equation for your perpendicular line is
y = (-1/3)(x -(-1)) -3
y = (-1/3)x -10/3
The slope-intercept form of the equation of the perpendicular line is ...
y = (-1/3)x -10/3
Answer:
71.3°
Step-by-step explanation:
A building 62 feet tall casts a shadow 21 meters long . At what angle is the sun shining on the building?
We solve this question using the Trigonometric function of Tangent
tan x = Opposite/Adjacent
Where
Opposite = 62ft
Adjacent = 21 ft
x = Angle
Hence,
tan x = 62/21
x = arc tan (62/21)
x = 71.288262125°
Approximately = 71.3°
Answer: The required probability that a randomly selected day in November will be snowy if it is cloudy is 86.79%.
Step-by-step explanation: Given that for the month of November in a certain city, 53% of the days are cloudy. Also in the month of November in the same city, 46% of the days are cloudy and snowy.
We are to find the probability that a randomly selected day in November will be snowy if it is cloudy.
Let A denote the event that the day is cloudy and B denote the event that the day is snowy.
Then, according to the given information, we have
![P(A)=53\%=0.53,\\\\P(A\cap B)=46\%=0.46.](https://tex.z-dn.net/?f=P%28A%29%3D53%5C%25%3D0.53%2C%5C%5C%5C%5CP%28A%5Ccap%20B%29%3D46%5C%25%3D0.46.)
Now, we need to find the conditional probability of event B given that the event A has already happened.
That is, P(B/A).
We know that
![P(B/A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{0.46}{0.53}=0.87=87.79\%.](https://tex.z-dn.net/?f=P%28B%2FA%29%3D%5Cdfrac%7BP%28B%5Ccap%20A%29%7D%7BP%28A%29%7D%3D%5Cdfrac%7B0.46%7D%7B0.53%7D%3D0.87%3D87.79%5C%25.)
Thus, the required probability that a randomly selected day in November will be snowy if it is cloudy is 87.79%.
This problem can be solved easily. The equation states that
y is a function of x. Since this is the case, then we can get the initial value
of the function when x = 0. Therefore by substitution:
y = - 2 x -5
y = - 2 (0) – 5
y = -5 (ANSWER)
Answer: x=-4
Step-by-step explanation:
See attachment