Rewrite the following statement using a number in scientific notation.
my new music player has a capacity of 310 gigabytes. (recall that giga means billion.)

3.1 x 10^11

Step-by-step explanation:

Since we know that giga means billion, we can piece together that 310 gigabytes = 310 billion

310 billion = 310,000,000,000

When writing in scientific notation, we move the decimal point over until there is only a single digit to the right of the decimal point.

Currently the decimal point is all the way at the end of the 310 billion.

310,000,000,000.

We need to move it over to the left, keeping count of how many times we do so, and stopping when there is only one digit to the right of the decimal.

We end up with: 3.10000000000 or 3.1

We moved the decimal over 11 times. This can be represented by the value 10^11 (pronounced as "10 to the 11th power")

Now, we combine these two to create 3.1 x 10^11

We must multiply the 3.1 by 10^11 in order to create the same amount as 310,000,000,000 (310 billion). If we were to leave 3.1 alone, it would not represent 310 billion.

Thus, we leave this as 3.1 x 10^11 which is scientific notation.

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)

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: