In the floor plan for a house, one bed-
room was square with a square closet at-
tached. the sides of the bedroom were 8
| times as large as the sides of the closet,
and the sum of the areas of the two was
585 square feet. how long were the sides
of the bedroom and the closet?

the length of one side of the bedroom is 24 feet.

the length of one side of the closet is 3 feet

Step-by-step explanation:

Let x represent the length of one side of the bedroom.

Let y represent the length of one side of the closet.

The sides of the bedroom were 8

times as large as the sides of the closet. This means that

x = 8y

the sum of the areas of the two was

585 square feet. The area of the room is x^2 and the area of the closet is y^2. Therefore,

x^2 + y^2 = 585 - - - -- - - -1

Substituting x = 8y into equation 1, it becomes

(8y)^2 + y^2 = 585

64y^2 + y^2 = 585

65y^2 = 585

y^2 = 585/65 = 9

Take square root of both sides of the equation,

y = √9 = 3

x = 8y = 8×3 = 24

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2