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3 years ago

If 4x+5=13x+4-x-9 then x= ?

Mathematics

2 answers:

enyata [817]3 years ago

8 0

4x + 5 = 12x -5
10 = 8x
10/8 = x
5/4 = x

Llana [10]3 years ago

6 0

Answer:

x = 5/4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Combining Like Terms

Step-by-step explanation:

Step 1: Define Equation

4x + 5 = 13x + 4 - x - 9

Step 2: Solve for x

Combine like terms: 4x + 5 = 12x - 5
Subtract 4x on both sides: 5 = 8x - 5
Isolate x term: 10 = 8x
Isolate x: 5/4 = x
Rewrite: x = 5/4

Step 3: Check

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

Substitute in x: 4(5/4) + 5 = 13(5/4) + 4 - 5/4 - 9
Multiply: 5 + 5 = 65/4 + 4 - 5/4 - 9
Add: 10 = 81/4 - 5/4 - 9
Subtract: 10 = 19 - 9
Subtract: 10 = 10

Here we see that 10 does indeed equal 10.

∴ x = 5/4 is the solution to the equation.

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g 1.32 Two points on a sphere of radius 3 are given as P1(3,0,30) and P2(3,45,45): (a) Find the position vectors of P1 and P2. (

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Answer:

a) P.V of is OP₁ = [ 1.5i + 0j + 2.6k ], P.V of is OP₂ = [ 1.5i + 1.5j + 2.12k ]

b) Vector connecting P₁ to P₂ is [ 0i + 1.5j + 0.48k ]

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Step-by-step explanation:

Given that;

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y = rsin∅sin∅ = 3(sin0°) (sin30°) = (3 × 0 × 0.5) = 0

z = rcos∅ = 3(cos30°) = ( 3 × 0.866) = 2.6

∴ P.V of is OP₁ = [ 1.5i + 0j + 2.6k ]

P.V of P₂

x = rcos∅sin∅ = 3(cos45°) ( sin45°) = (3 × 0.7071 × 0.7071) = 1.5

y = rsin∅sin∅ = 3(sin45°) (sin45°) = (3 × 0.7071 × 0.7071) = 1.5

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∴ P.V of is OP₂ = [ 1.5i + 1.5j + 2.12k ]

Vector connecting P₁ to P₂ is given by

OP₂ - OP₁ = [ 1.5i + 1.5j + 2.12k ] - [ 1.5i + 0j + 2.6k ]

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