<h2>Answer:</h2>
This is a theorem called Converse of Alternate Exterior Angles that states that <em>if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel</em>. Moreover, this theorem is based upon the corresponding Angles Converse Postulate that states that<em> if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. </em>We don't need to prove this postulate, it's assume to be true. So our goal is to get corresponding angles congruent in order to use the corresponding Angles Converse Postulate,
1.
Reason: Given
Statement: 
2.
Reason: Def of vertical 
Statement: 
3.
Reason: Def of vertical 
Statement: 
4.
Reason: Transitive Property
Statement: 
5.
Reason: corresponding Angles Converse Postulate
Statement: 
5sqrt(x+7)=-10
Dividing both sides by 5:
5sqrt(x+7)/5=-10/5
sqrt(x+7)=-2
Squaring both sides of the equation:
[sqrt(x+7)]^2=(-2)^2
x+7=4
x+7-7=4-7
x=-3
Replacing in the original equation:
5sqrt(x+7)=-10
5sqrt(-3+7)=-10
5sqrt(4)=-10
5(2)=-10
10=-10 It's not equal, then x=-3 is an extraneous solution
C - 0.15c is the same as 1c - 0.15c.
1 - 0.15 = 0.85.
Joe can also use 0.85c.
Answer:
The sum of the first 18 terms is 270.
Step-by-step explanation:
First the 18th term is calculated which is gotten using the following steps below:
an = a1 + d ( n - 1 )
Where, an =18th term
a1= first term (-2)
d = difference
n = 18
Therefore, 18th term
an= -2 + 2 (18 - 1)
= -2 + 2 (17)
= -2 + 34
18th term = 32
To calculate the sum of the first 18th terms the following steps are used,
Sn = n(a1 + an)/2
Where,
Sn = sum of 18th term
n = 18
a1 = -2
an = 18 term
Therefore,
Sn = 18 (- 2+ 32)/2
= 18 (30)/2
= 18 ×30 /2
= 540/2
= 270
