All the angles created by the transversal intersecting through a pair of parallel lines have got many names and connections with each other, like Alternate Angles, Corresponding angles, consecutive interior angles etc.
As per the question statement, We are given a pair of parallel lines which is cut by a transversal. We are supposed to mark the following angles.
Alternate Interior Angles, Alternate Exterior Angles, Corresponding Angles and Consecutive Interior Angles.
Here is an attached image of the same with angles marked on it.
Alternate Interior Angles: ∠
= ∠
and ∠
=∠
Alternate Exterior Angles: ∠
=∠
and ∠
=∠
Corresponding Angles: ∠=∠ , ∠=∠ , ∠=∠ and ∠=∠
Consecutive Interior Angles: ∠=∠ and ∠=∠
- Parallel Lines: Parallel lines are those straight lines that are, no matter how far they are extended, always the same distance apart from one another.
- Transversal Line: In geometry, a transversal line intersects two lines in the same plane at two different locations.
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Answer:
Step-by-step explanation:
p(A) = a^3 + 3a^2 + 9a + 27
put brackets around the 1st and second terms and another set around the 3rd and 4th
P(a)= (a^3 + 3a^2) + (9a + 27)
Using the distributive property, pull out the common factor for each of the 2 terms that contain the brackets.
P(a) = a^2 ( a + 3) + 9(a + 3)
Let a + 3 = x
P(a) = a^2x + 9x
Put brackets around these 2 terms
P(a)= x(a^2 + 9)
Substitute a + 3 for x
P(a) = (a + 3) ( a^2 + 9)
Answer:
Step-by-step explanation:
Given that the housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 38 bids from potential buyers to estimate the average loss in home value.
s = sample std deviation = 3000
Sample mean = 9379
Sample size n = 38
df = 37
Std error of sample mean = 
confidence interval 95% = Mean ± t critical * std error
=Mean ±1.687*486.66 = Mean ±821.003
=(8557.997, 10200.003)
a) If std deviation changes to 9000 instead of 3000, margin of error becomes 3 times
Hence 2463.008
b) The more the std deviation the more the width of confidence interval.
Equation of a line that is perpendicular to given line is 
.
Equation of a line that is parallel to given line is 
.
Solution:
Given line 
.
Slope of this line, 
= 
Slope of perpendicular line, 
Passes through the point (–7, 5). Here 
.
Point-slope formula:
Subtract 7 from both sides, we get
Equation of a line that is perpendicular to given line is .
To find the parallel line:
Slopes of parallel lines are equal.
Passes through the point (–7, 5). Here .
Point-slope formula:
Subtract 7 from both sides,
Equation of a line that is parallel to given line is .
X is 60, therefore, a = 120 and d = 60
