Convert 51 in base 10 into base 5

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

Zepler [3.9K]

Answer:

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.

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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.

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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.

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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.

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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.

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

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Step-by-step explanation:

7 0

3 years ago

HELP MATH WHIZZES!! TON OF FREE POINTS, EASY GEOMETRY QUESTION FOR THE RIGHT ANSWER! WHO WILL WIN THIS?! NEED HELP, NOT WRONG AN

Radda [10]

The area of the trapezoid is the product of the height and the average of the two bases:
30 (25 + 33)/2 = 30 (58)/2 = 30 (29) = 870 square yd. 

But we want to exclude the area of the fountain. 
Since it's circular its area is π times the square of its radius, or 16π square yd. 

So the area of the park, excluding the fountain, is 
870 - 16π square yd, 
or about 820 square yd.

5 0

4 years ago

Read 2 more answers

Work out the surface area of this cylinder. Radius= 12 cm Height= 35 cm

Ad libitum [116K]

3543.72 cm^2.

Hopefully it helped ya

7 0

3 years ago

Mrs. CADY CONSTRUCTS A CUBE WITH 512 MAGNETIC BLOCKS. STUDENTS IN HER TWO CLASSES WILL EACH MAKE AN IDENTICAL CUBE. THERE ARE 28

Lilit [14]

YOU DON"T HAVE TO YELL

512 PER STUDENT

BASICALLY,
CUBES NEEDED=CUBES PER STUDENT TIMES NUMBER OF STUDENTS

NUMBER OF STUDENTS=28+25=53

CUBES PER STUDENT=512

CUBES NEEDED=512 TIMES 53 EQUALS 27136 CUBES

SHE NEEDS 27136 CUBES FOR ALL HER STUDENTS

8 0

3 years ago

Describe the transformation of f(x) to g(x)

gulaghasi [49]

Answer:

D. f(x) is shifted up 1 unit to g(x).

Step-by-step explanation:

Just let's look at the y-intercept of each function.

f(0) = 0

g(0) = 1

Also remember that a vertical shift of N units is written as:

g(x) = f(x) + N

where if N is positive, the shift is upwards, and if N is negative, the shift is downwards.

then we can write, for the particular value x = 0

g(0) = f(0) + N

replacing the values

1 = 0 + N

1 = N

Then N is positive, so we have a shift up of one unit.

The correct option is:

D. f(x) is shifted up 1 unit to g(x).

6 0

3 years ago