Answer:
The answer to your question is the letter b) y = -3x + 11
Step-by-step explanation:
Data
Original line y = 1/3x - 2
Point = (3, 2)
New line = ? (perpendicular)
Process
1.- Get the slope of the original line
The slope is the coefficient of the x in the line equation.
y = 1/3x - 2
slope = m = 1/3
2.- Find the slope of the new line
new slope = -3 (because the lines are perpendicular)
3.- Find the equation of the new line
y - y1 = m(x - x1)
x1 = 3 y1 = 2
-Substitution
y - 2 = -3(x - 3)
-Simplification
y - 2 = -3x + 9
y = -3x + 9 + 2
-Result
y = -3x + 11
Answer:
{-2, -1 , 3}
Step-by-step explanation:
When we have a set like:
{x₁, x₂, x₃}
The mode is the value that appears the most, so if there is no mode, then each value appears just one time.
The median is the middle value, here we know that the median is -1, then we can rewrite the set as:
{x₁, -1 , x₃}
The mean is computed as:
Mean = (x₁ + x₂ + x₃)/3
in this case we know that the mean is 0, then:
0 = (x₁ + x₂ + x₃)/3
then the numerator must be zero, so:
0 = (x₁ + x₂ + x₃)
replacing the value of x₂ = -1 we get:
0 = (x₁ - 1 + x₃)
where:
-5 < x₁ < -1 < x₃ ≤ 3
Now we can select the values of x₁ and x₃ such that the sum is equal to zero, and it meets the wanted restrictions.
here we can choose x₃ to be equal to 3 (the maximum allowed value), I do this because I noticed that the other values that are larger than -1 will not work (just with quick math).
then:
0 = x₁ - 1 + 3
Now we can solve this for x₁
0 = x₁ + 2
-2 = x₁
Then the set is:
{-2, -1 , 3}
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