What is the answer in this question ? Macy is painting a design that contains two repeating patterns. One pattern repeats every 12 inches. If both patterns begin in the same place, in how many inches will they begin together again? The design is 19 feet long .Both pattern begin at the same place.

The correct answer is:

10 times.

Explanation:

We first find the LCM, or least common mulitple, of 8 and 12. To do this, we find the prime factorization of each:

8 = 2*4

4 = 2*2

8 = 2*2*2

12 = 4*3

4 = 2*2

12 = 2*2*3

To find the LCM, we take the common factors and multiply by the uncommon ones. The common factors are 2*2; the uncommon are 2 and 3:

2*2*2*3 = 24

The LCM is 24. This means that every 24 inches, both patterns will repeat.

The patterns are both at the beginning of the design. Then every 24 inches, or 2 feet, both patterns repeat.

19/2 = 9.5

There are an additional 9 times that the patterns repeat; this is 1+9 = 10 total times.

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:

step-by-step explanation:

what was your answer?