Outside Danny is building the base of a brick fireplace. He is using bricks that are 3.625 inches wide, 2.25 inches high, and 8 inches long. He
starts by laying 6 bricks end to end as shown in the diagram.

Danny lays another 6 bricks alongside the 6 bricks already in place, and repeats laying another 6 bricks alongside of the 6 bricks he just placed 4 more times.

Danny stacks more layers on top of the brick base. Each layer is the same size which creates a rectangular prism of bricks. The total
volume of the rectangular brick base is 11,745 cubic inches

How many layers of bricks is the rectangular base?

30 layers of bricks

Step-by-step explanation:

find the volume of the bricks first

3.625*2.25*8

65.25

multiply by 6

65.25*6

391.5

divide by the volume of the base

11,745/391.5

30 layers

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

3

step-by-step explanation:

because where the point where the 2 lines intersect is (3,-1) the x value is 3