List all of the number sets that contain the number –8.

a.) integers only
b.) integers and rational numbers
c.) integers and natural numbers
d.) integers, rational numbers, and natural numbers

The correct option is B.) integers and rational numbers.

Step-by-step explanation:

Consider the provided number –8.

Natural numbers: The natural numbers are 1, 2, 3, 4, 5,…

Whole number: Whole numbers are the set of natural numbers but starts with 0. i.e. 0, 1, 2, 3, 4, 5,…

Integers: Integers are the set of whole number and the negatives of the natural numbers, i.e, … ,-2, -1, 0, 1, 2, …

Rational number: A number is said to be rational, if it is in the form of p/q. Where p and q are integer and denominator is not equal to 0.

Irrational number: A number is irrational if it cannot be expressed be expressed by dividing two integers. The decimal expansion of Irrational numbers are neither terminate nor periodic.

Now consider the provided number –8.

From the above definitions the number –8 is neither natural number nor whole number.

But the number –8 is an integer.

The number –8 can be written as –8/1 which is the p/q form. Thus, it is a rational number.

–8 is a rational number so it can't be irrational. Thus –8 is not irrational.

Hence, the correct option is B.) integers and rational numbers.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: