One line passes through the points (-2, 1) and (4,9). Another line passes through points (-3, 8) and (5,2).Are the lines parallel, perpendicular, or neither?
A.Parallel
B.Perpendicular
C.Neither
Answers
The given lines are perpendicular to each other because there slope are negative reciprocals of each other.
What is the point slope form of a line ?
Point slope form is used to represent a straight line using its slope and a point on the line.
The line passes through two points which are (-2,1) and (4,9). The other line passes through points which are (-3,8) and (5,2).
We know that the equation of a linein point slope form is given by :
(y - y1) = m (x - x1)
For the first line : (x , y) = (-2 , 1) and (x1 , y1) = (4 , 9)
So ,
(1 - 9) = m (-2 - 4)
-8 = m × -6
m = 8/6
For the other line : (x , y) = (-3 , 8) and (x1 , y1) = (5 , 2)
So,
(8 - 2) = m (-3 - 5)
6 = m × -8
m = -6 / 8
We know that if two lines are perpendicular then , there slopes are negative reciprocals of each other. i.e.,
8/6 can be written as :
= -1/(8/6) = -6/8
The lines are perpendicular to each other.
Therefore , the first line and second line are perpendicular to each other because there slope are negative reciprocals of each other.
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Answer:
Perpendicular
Step-by-step explanation:
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Option D:
Difference between g(x) and f(x) is 44.
Solution:
Let us first write the function of f(x).
Take any two points on the line (0, -1) and (-2, 0).
Here,
Equation of a line:
Do cross multiplication.
-2(y + 1) = x
-2y - 2 = x
Add 2 on both sides.
-2y = x + 2
Divide by -2 on both sides.
y = -0.5x - 1
f(x) = -0.5x - 1
At x = 20,
f(20) = -0.5(20) - 1 = -11
g(x) = 1.5x + 3
g(20) = 1.5(20) + 3 = 33
Difference between g(x) and f(x)
= g(20) - f(20)
= 33 - (-11)
= 33 + 11
= 44
Difference between g(x) and f(x) is 44.
Option D is the correct answer.
Answers
a - the constant of proportionality
We have the constant of proportionality a = 0.7.
Therefore the equation is:
y = 0.7x
Answer:
y= 0.7x ...................................................................................
Answers
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_________________________________
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The names of 25 employees that have taken 5 or more sick days in the last quarter are chosen out of a hat and asked their opinion about the working conditions.
The names of 25 employees are chosen out of a hat and asked their opinion about the working conditions.
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The first 25 employees that clock in on a Monday morning are chosen out of a hat and asked their opinion about the working conditions.
Answers
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What is random sample?
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A random sample ensures that the opinions gathered are representative of the entire employee population and can be used to make broad statements about working conditions.
Thus, the correct option is 2.
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Answer:
The names of 25 employees are chosen out of a hat and asked their opinion about the working conditions.
Answers
Replace X with the x value in the parenthesis and solve. If the answer equals the Y value inside the parenthesis, it is a solution.
A) (-2, 3), -2(-2) +7 = 4+7 = 11. 11 does not equal 3 so this is not a solution.
B) (-1,9), -2(-1) +7 = 2+7 = 9. 9 equals 9, this is a solution.
c) (3,1), -2(3)+7 = -6+7 = 1, 1 equals 1, this is a solution.
d) (4,-1) = -2(4) +7 = -8 +7 = -1. -1 equals -1, so this is a solution.
The only one that isn't a solution is A.
A.
11.3
B.
–3.5
C.
36.9
D.
–22.1
Answers
-12.8 + 7.4 + 16.7 Simply add all
= 11.3
A
-12.8 + 7.4 + 16.7 Minus Minus is Plus.
16.7 + 7.4 - 12.8
24.1 - 12.8
11.3
Option A.