The volume v of a rectangular pyramid varies jointly as the area of the base b and the height h. v = 56 m3, when b = 24 m2 and h = 7 m. identify b when v = 81 m3 and h = 9 m.

B=27 m²

Step-by-step explanation:

Based on the information in the problem, if the volume V of a rectangular pyramid varies jointly as the area of the base B and the height h, you can write the following equation:

Where k is a constant.

You can calculate k as following:

When you solve for k you obtain:

Then, when V=81 m³ and h=9m m, B is:

B = 27 m² is the answer.

Step-by-step explanation:

Volume of a rectangular pyramid is = V

Area of the base is B and the height of pyramid is h.

We have to find the value of B

If V = 56 m³ then B was = 24 m²and h = 7 m

Now if V = 81 m³ and h = 9 m then from the formula of volume of a pyramid is V = 1/3(B×h) = 81 m³

81 = 1/3(B×9)

B = (81×3)/9 = 81/3 = 27 m

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.