You originally draw a design for an art contest on a 2 inch by 5 inch card. the second phrase of the contest requires the drawing to be transferred to an 8.5 inch by 11 inch standard sheet of paper and utilize as much of the space on the paper as possible. you determine the largest size one of the dimensions of your drawing can be is 10.5 inches. what is the length of the other dimension if two drawings are similar? type your exact answer in the blank without the units and round to the nearest tenth.

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: