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3 years ago

Which is the simplified form of the expression 3 2 21 12 x y12 24

Mathematics

1 answer:

MakcuM [25]3 years ago

6 0

Answer:

the second option is solution

Step-by-step explanation:

exponents inside parentheses get multiplied by exponents outside them

so first: x^-9y^6 divided by x^12y^18

next, when dividing like terms, keep variable and subtract their exponents

-9 - 12 = -21

6 - 18 = -12

Don't leave negative exponents as answer, simplify by putting them into the denominator (where the exponents will now become positive) with 1 as numerator

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A glass paperweight has a composite shape: a square pyramid fitting exacty on top of an 8 centimeter cube. The pyramid has a hei

ArbitrLikvidat [17]

Answer:

Part 1) The volume of the paperweight is $576\ cm^{3}$

Part 2) The total surface area of the paperweight is $400\ cm^{2}$

Step-by-step explanation:

Part 1) what is the volume of the paperweight?

we know that

The volume of the paperweight is equal to the volume of the square pyramid plus the volume of the cube

step 1

Find the volume of the pyramid

The volume of the pyramid is equal to

$V=\frac{1}{3}BH$

where

B is the area of the square base

H is the height of the pyramid

$B=8^{2}=64\ cm^{2}$

$H=3\ cm$

substitute

$V=\frac{1}{3}(64)(3)=64\ cm^{3}$

step 2

Find the volume of the cube

The volume of the cube is equal to

$V=b^{3}$

$V=8^{3}=512\ cm^{3}$

step 3

Find the volume of the paperweight

$64\ cm^{3}+512\ cm^{3}=576\ cm^{3}$

Part 2) what is the total surface area of the paperweight?

we know that

The total surface area of the paperweight is equal to the surface area of 5 faces of the cube plus the lateral area of the pyramid

step 1

Find the surface area of 5 faces of the cube

$SA=5b^{2}$

$SA=5(8^{2})=320\ cm^{2}$

step 2

Find the lateral area of the pyramid

$LA=4[\frac{1}{2}bh]$

$LA=4[\frac{1}{2}(8)(5)]=80\ cm^{2}$

step 3

Find the total surface area of the paperweight

$320\ cm^{2}+80\ cm^{2}=400\ cm^{2}$

8 0

3 years ago

Which 2 organic compounds serve as energy sources? How do these 2 groups differ?

pav-90 [236]

Try glucose (C6H1206) and water (H2O)?

7 0

2 years ago

Which operation is NOT closed for polynomials?

MAXImum [283]

Answer:

Option D

Step-by-step explanation:

When you add, multiply or subtract polynomials, the operation results in another polynomial.

When dividing polynomials, the operation may not result in another polynomial. In this case you normally end up with rational expression in the fraction form.

This operation is said not closed.

In our case this is option D.

4 0

2 years ago

Read 2 more answers

Find the sum of partial fraction for x^4/(x-1)(x²-4)

Aneli [31]

Answer:

see attachment

Step-by-step explanation:

7 0

3 years ago

Find the quotient. x + 7 x ÷ 9 x

kicyunya [14]

The first step for solving this expression is to write the division as a fraction.
x + $\frac{7x}{9}$ × x
Calculate the product.
$\frac{7x X x}{9}$
Remember that if a term doesn't have an exponent,, it is considered that the exponent for that term is 1. This changes the expression to the following:
$\frac{7 x^{1}X x^{1} }{9}$
Now multiply the terms with the same base by adding their exponents.
$\frac{7 x^{1+1}}{9}$
Finally,, add the numbers together to get your final answer.
x + $\frac{7 x^{2}}{9}$
Let me know if you have any further questions.
:)

8 0

3 years ago