The figure is a diagram of a wall. Lengths are given in feet. Diagram of a wall.

a. How many square feet of wallpaper would be needed to cover the wall? Type the answer in the box below.

square feet

Explain your reasoning.

b. Wallpaper is sold in rolls that are 2 feet wide. What is the minimum length you would need to purchase to cover the wall? Type the answer in the box below.

feet

a. The area of the wall is 60 ft.²

b. The minimum length of wallpaper to be purchased is 30 ft

Step-by-step explanation:

a. The given diagram is a pentagon, with the two vertical sides equal in length and the  two slant sides equal in length and one horizontal

The length of the vertical sides = 6 feet each

The length of the horizontal side = 8 feet

The height of the pentagon = 9 feet

The pentagon can be split into a rectangle with a triangular cap by an horizontal line drawn at point of intersection of the vertical sides and the horizontal sides

The area of the formed rectangle = Base  × Height of rectangle

∴ The area of the formed rectangle = 6 × 8 = 48 ft.²

The area of the triangular part of the figure = 1/2 × base × Height of triangle

a = 9 - 6 = 3 feet

∴ The area of the triangular part of the figure = 1/2 × 8 × 3 = 12 ft.²

The area of the wall = The area of the formed rectangle + The area of the triangular part of the figure

∴ The area of the wall = 48 ft.² + 12 ft.² = 60 ft.²

The area of the wall = 60 ft.²

b. The width of the sold wallpaper = 2 feet wide

The area of wallpaper = Length of wallpaper × The width of the sold wallpaper

The area of wallpaper required = The area of the wall = 60 ft.²

∴ 60 ft.² = Length of wallpaper × 2 ft.

Length of wallpaper = 60 ft.²/2 ft. = 30 ft.

The minimum length of wallpaper to be purchased = 30 ft.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x