The answer is the first one; it is an arithmetic sequence with a common difference of -40.
Observe the figure below.
Statement Reason
1. AC and BD bisect each other Given
2. AE = EC and BE = ED Definition of bisection
3.
Vertical angle theorem
Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".
4.
SAS criterion for congruence
5.
Corresponding angles of congruent triangles are congruent
6.
Converse of alternate interior angle theorem
7.
Vertical angle theorem
8.
SAS criterion for congruence
9.
Converse of alternate interior angle theorem
As,
, so
as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by "Converse of alternate interior angle theorem".
Answer:
Yes. It is a vector space over the field of rational numbers 
Step-by-step explanation:
An element
of the set
has the form

where
are rational coefficients.
The operations of addition and scalar multiplication are defined as follows:


The properties that
, together the operations of vector addition and scalar multiplication, must satisfy are:
- Conmutativity
- Associativity of addition and scalar multiplication
- Additive Identity
- Additive inverse
- Multiplicative Identity
- Distributive properties.
This is not difficult with the definitions given. The most important part is to show that
has a additive identity, which is the zero polynomial, that is closed under vector addition and scalar multiplication. This last properties comes from the fact that
is a field, then it is closed under sum and multiplication.
Answer: 15
Explanation: the triangle to the right is a dial action of the smaller triangle, therefore the triangles are similar. Since the sides of both triangles are corresponding if the corresponding side to JI is 5, and JI is 25 then it is a dialation by a multiple of 5. So since the corresponding side to HI is 3, HI is 15