If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by ~p → ~q? the original conditional statement the convif p is the hypothesis of a conditional statement and q is the conclusion, which is represented by ~p → ~q? the original conditional statement the converse of the original conditional statement the contrapositive of the original conditional statement the inverse of the original conditional statementerse of the original conditional statement the contrapositive of the original conditional statement the inverse of the original conditional statement

inverse

Explanation:

1) A conditional is a statement of the kind if p then q. Symbolically it can be written as p → q.

In such statement, p is the hypothesis and q is the conclusion.

It means that whenever p (the hypothesis) is true, then the conclusion is also true.

2) Starting from that form, three related statements may be build: the contrapositive, the converse and the inverse.

These are those forms:

Original conditional: p → q (if p then q)

Contrapositive:  ¬q → ¬p (if not q then not p)

Converse: q → p (if q then p)

Inverse: ¬p → ¬q (if not p then not q). This one is the given in the question (~p → ~q). Both signs ~ and ¬ are commonly used to represent the negation)

You should know that only the contrapositive (if not q then not p) may be validly derived from the original statement (if p then q), because both p → q and not p then not q have the same true values.

Hence, the congtrapositive is used as a valid demostration, but the converse and the inverse are not valid demostrations.

D

Step-by-step explanation:

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2