Samuel and his brother were playing soccer in the basement, and one particularly strong kick punctured a hole in the wall. The hole can almost be hidden by a 4 in. by 6 in. unframed picture, so Samuel thinks it will be completely hidden by the picture after it’s framed. Samuel hasn’t purchased the frame yet. Write a polynomial to represent the total area of the picture after it is framed. With the frame, the sides are (2x + 4) and (2x + 6).

The polynomial representing the total area of the picture after it is framed is

Step-by-step explanation:

The area of the frame  can be found by using the area formula for the rectangle

we also have the sides of the framed picture

let (2x+6) be the length and (2x+4) be the width

Then area  of the framed  picture = length x breadth

On substituting the sides

Area  of the framed  picture =

Area  of the framed  picture =

Area  of the framed  picture =

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1