Mathematics, 22.08.2019 12:50 carliehanson9908

The volume of a prism is the product of its height and area of its base, v = bh. a rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. which could be the base area and height of the prism?
a base area of 4y square units and height of 4y2 + 4y + 12 units
a base area of 8y2 square units and height of y2 + 2y + 4 units
a base area of 12y square units and height of 4y2 + 4y + 36 units
a base area of 16y2 square units and height of y2 + y + 3 units

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We have a prism with a volume of 16y⁴ + 16y³ + 48y² cubic units.
Its volume is equal to the area of its base times its height.
Of course, for those to be the base area and height of this prism, they would have to multiply to 16y⁴ + 16y³ + 48y² cubic units.
Let's test each of these answers to see which gives us the correct volume.

a base area of 4y square units and height of 4y² + 4y + 12 units
We find the volume by multiplying the base area by the height...
4y(4y² + 4y + 12)
Distribute the 4y to each term inside the parentheses.
16y³ + 16y² + 48y
This is not the right volume, so these can not be dimensions of our prism.

a base area of 8y² square units and height of y² + 2y + 4 units
We find the volume by multiplying the base area by the height...
8y²(y² + 2y + 4)
Distribute the 8y² to each term inside the parentheses.
8y⁴ + 16y³ + 32y²
This is not the right volume, so these can not be dimensions of our prism.

a base area of 12y square units and height of 4y² + 4y + 36 units
We find the volume by multiplying the base area by the height...
12y(4y² + 4y + 36)
Distribute the 12y to each term inside the parentheses.
48y³ + 48y² + 432y
This is not the right volume, so these can not be dimensions of our prism.

a base area of 16y² square units and height of y² + y + 3 units
We find the volume by multiplying the base area by the height...
16y²(y² + y + 3)
Distribute the 16y² to each term inside the parentheses.
16y⁴ + 16y³ + 48y²
The volume fits, so these could be the base area and height of our prism.

D. a base area of 16y² square units and height of y² + y + 3 units

Answer from: Quest

to plot points for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4) in the parenthesis on the left of the comma is x and the right is y.

Answer from: Quest

44% of 325 is 143hope this

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