Ricky is building a ramp for his family's corner store to make it easier to receive deliveries. He wants to make the ramp 3 ft wide and 6 ft long. If the boards are 6 in wide, how many linear feet of lumber will he need?

9 linear feet of lumber will be needed.

Step-by-step explanation:

Since the ramp is going to be 3 ft wide and 6 ft long and we have 6 in wide boards, we are going to be stacking the boards side by side to cover the length and width of the ramp.

Let n boards cover the width of the ramp, then number of boards × width of one board = width of ramp.

So, n × 6 in = 3 ft

Since 12 in = 1 ft, we have

n × 6 in = 3 ft = 3 × 1 ft = 3 × 12 in

n × 6 in = 36 in

n = 36 in/6 in

n = 6

Let n' boards cover the length of the ramp, then number of boards × width of one board = length of ramp.

So, n' × 6 in = 6 ft

Since 12 in = 1 ft, we have

n' × 6 in = 6 ft = 6 × 1 ft = 6 × 12 in

n' × 6 in = 72 in

n' = 72 in/6 in

n' = 12

Thus, the total number of boards needed is n" = n + n' = 6 + 12 = 18

So, the number of inches of board needed is thus n" × width of one board = 18 × 6 in = 108 in

Now, since 12 in = 1 ft, 1 in = 1/12 ft

108 in = 108 × 1/12 ft = 108/12 ft = 9 ft

So, 9 linear feet of lumber will be needed.

d is the correct answer

step-by-step explanation:

x= 8 because 3x = 3 * 8, and 3*8 = 24

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'.