Mathematics, 15.12.2020 22:20 Anliz0179

Solve 0.2(4x+10)−0.9x=0.2(x−6)+12.2 . Justify each step.

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Answer from: faithbar0911p5p68a

x = -30

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

0.2(4x + 10) - 0.9x = 0.2(x - 6) + 12.2

Step 2: Solve for x

Distribute 0.2: 0.8x + 2 - 0.9x = 0.2x - 1.2 + 12.2Combine like terms: -0.1x + 2 = 0.2x + 11Add 0.1x on both sides: 2 = 0.3x + 11Isolate x term: -9 = 0.3xIsolate x: -30 = xRewrite: x = -30

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: 0.2(4(-30) + 10) - 0.9(-30) = 0.2(-30 - 6) + 12.2Multiply: 0.2(-120 + 10) + 27 = 0.2(-30 - 6) + 12.2Add/Subtract: 0.2(-110) + 27 = 0.2(-36) + 12.2Multiply: -22 + 27 = -7.2 + 12.2Add: 5 = 5

Here we see that 5 does indeed equal 5.

∴ x = -30 is the solution to the equation.

Answer from: Quest

5050 i think

step-by-step explanation:

Answer from: Quest

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

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Solve 0.2(4x+10)−0.9x=0.2(x−6)+12.2 . Justify each step....