Solution:
Equation of line I J is given as :
y = - 3 x -8
The equation of line parallel to , y= m x + c is given by
y = m x + k.
Because if two lines are parallel , then their slopes are equal.
So, equation of line parallel to , y = - 3 x -8 is given by
y = - 3 x + K
Where , K = y - intercept.
Answer:
Step-by-step explanation:
- Firstly, plug in the point and slope into the slope-intercept equation format:
When lines are parallel to one another, their slopes are the same. But they have different y-intercepts. To explain further, slope is the angle of measure of a line from a horizontal standpoint and knowing that parallel angles must have the same angle, it can be concluded that parallel lines would have the same slope or in other words, an equal slope.
Now solving, use algebraic concepts:
11 = -8(-1) +b (Now solve for b)
11 = 8 + b (Subtract 8 from both sides) (Use the "Right" to "Left")
-8 -8
3 = b (Switch terms)
b = 3
Now let's write the equation with only slope and y-intercept.
Getting the result of:
y = -8x + 3
If Lines AC and ED intersect at point B, then ∠ABD and ∠EBC are vertically opposite angles
The point where two lines meet is known as an angle.
If line Lines AC and ED intersect at point B, then ∠ABD and ∠EBC will be vertically opposite to each other (They will be equal).
To show that the are equal
Given the angles
m∠ABD = 5x - 5
m∠EBC = 3x + 15
m∠ABD = m∠EBC (vertical angles)
5x - 5 = 3x + 15
5x - 3x = 15 + 5
2x = 20
x = 10
Substitute x = 10 into m∠ABD and m∠EBC
m∠ABD = 5x - 5
m∠ABD = 5(10)-5
m∠ABD = 50 - 5
m∠ABD = 45
Get m∠EBC
m∠EBC = 3x+15
m∠EBC = 3(10)+15
m∠EBC = 30+15
m∠EBC = 45 degrees
We can see that both angles are equal. Hence we can also conclude that they are vertically opposite angles
Learn more here: brainly.com/question/23466343
Answer:
60.9 mi
Step-by-step explanation:
Circumference of circle:
diameter = 19.4 mi
Circumference of circle = πd
= 3.14 * 19.4
= 60.9 mi
The average rate of change of the function over the given interval is 9
Here, we want to calculate the average rate of change of the function within the given interval
Mathematically, given a function f(x) , the average rate of change of the function within the interval a ≤ x ≤ b is given below;
withe respect to this question;
a = 1
b = 4
f(a) = f(1) = 12
f(b) = f(4) = 39
The average rate of change within the given interval is thus;