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3 years ago

5

What is the solution to the equation 5(x-3) = 2(x+3)?

1 answer:

VikaD [51]3 years ago

8 0

Answer:
x = 7

General Formulas and Concepts:
Order of Operations: BPEMDAS

Step-by-Step Explanation:
Step 1: Define
5(x - 3) = 2(x + 3)

Step 2: Solve for x
1. Distribute: 5x - 15 = 2x + 6
2. Subtract 2x on both sides: 3x - 15 = 6
3. Add 15 on both sides: 3x = 21
4. Divide both sides by 3: x = 7

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Answer:

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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

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substitute

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

step 2

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The volume of the cube is equal to

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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

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step 2

Find the lateral area of the pyramid

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step 3

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Step-by-step explanation

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