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2 years ago

How are algebraic properties applied in the steps to solving equations?

1 answer:

6 0

<u>An algebraic equation can be solved by isolating the variable on one side of the equation using the properties of equality. To check the solution of an algebraic equation, substitute the value of the variable into the original equation.</u>

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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

What is Janelle’s position relative to sea level while swimming? What should the altimeter read at this position?

kondor19780726 [428]

Answer: Janelle is 1/2 below sea level, the altimeter should read -1/2 feet

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

If hoan was asked to drow a right angke how miny right agnkes are in a right angle

krek1111 [17]

I might not understand this correctly because of the misspellings, but if you draw a right angle. There is only 1 right angle... in a right angle.

4 0

3 years ago

Please answer this i dont understnad

serg [7]

The answer would be 6fg^3+5f^2g^2+f^3g-7

7 0

3 years ago

Help please, I need it

Helen [10]

Partial Answer:

For #10 the solutions are 2 and 5

Step-by-step explanation:

Solutions for an equation can be x-intercepts, or where it touches the x or horizontal line. The equation in #10 touches the x line at 2 and 5.

5 0

2 years ago