Rafael wrote the statements shown in the chart.
statement
description
1 if a point lies outside a line, then exactly one plane contains both the line and the point.
2 if two points lie in a plane, then the line joining them lies in that plane.

which option best classifies rafael’s statements?
a) statement 1 is a theorem because it can be proved and statement 2 is a postulate because it is a true fact.
b) statement 1 and statement 2 are postulates because they are true facts.
c) statement 1 is a postulate because it is a true fact and statement 2 is a theorem because it can be proved.

The correct option that best classifies Rafael's statement is:

a)Statement 1 is a theorem because it can be proved and Statement 2 is a postulate because it is a true fact.

" We know that a postulate also known as a axiom  is a  statement that is considered to be true and does not need any kind of proof "

" Whereas a theorem is a statement that need to be derived with the help of corollaries or axioms or some statements "

Hence, we are given two statements as:

statement 1: If a point lies outside a line, then exactly one plane contains both the line and the point.  

statement 2: If two points lie in a plane, then the line joining them lies in that plane.

So, statement 1 is a Theorem and statement 2 is a postulate.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places