Ashley is stacking two boxes on a shelf the bottom box measures 6 in long x 5 in wide x 5 inches high the top box is a cube with one edge measuring 4 inches what is the volume of the stack explain how you found your answer

Volume_stack = 214 n^3

Step-by-step explanation:

The volume of the stack is the sum of the volume of the two boxes

The rectangular box has a volume of

V_rectbox = long*wide*height

V_rectbox  = 6 in * 5in * 5 in = 150 in^3

The volume of the cube is

V_cube = long*wide*height , but since all its sides are equal

V_cube  = side^3 = (4 in)^3 = 64 in^3

Volume_stack = V_rectbox  +  V_cube  = 150 in^3 + 64 in^3

Volume_stack = 214 n^3

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240