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vlabodo [156]
3 years ago
8

Given 14 – 2(x + 8) = 5x – (3x – 34), prove x = -9 what are the steps to be able to prove x=-9

Mathematics
1 answer:
Veronika [31]3 years ago
7 0

Answer: x = -9

steps

Simplifying

14 + -2(x + 8) = 5x + -1(3x + -34)

Reorder the terms:

14 + -2(8 + x) = 5x + -1(3x + -34)

14 + (8 * -2 + x * -2) = 5x + -1(3x + -34)

14 + (-16 + -2x) = 5x + -1(3x + -34)

Combine like terms: 14 + -16 = -2

-2 + -2x = 5x + -1(3x + -34)

Reorder the terms:

-2 + -2x = 5x + -1(-34 + 3x)

-2 + -2x = 5x + (-34 * -1 + 3x * -1)

-2 + -2x = 5x + (34 + -3x)

Reorder the terms:

-2 + -2x = 34 + 5x + -3x

Combine like terms: 5x + -3x = 2x

-2 + -2x = 34 + 2x

Solving

-2 + -2x = 34 + 2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.

-2 + -2x + -2x = 34 + 2x + -2x

Combine like terms: -2x + -2x = -4x

-2 + -4x = 34 + 2x + -2x

Combine like terms: 2x + -2x = 0

-2 + -4x = 34 + 0

-2 + -4x = 34

Add '2' to each side of the equation.

-2 + 2 + -4x = 34 + 2

Combine like terms: -2 + 2 = 0

0 + -4x = 34 + 2

-4x = 34 + 2

Combine like terms: 34 + 2 = 36

-4x = 36

Divide each side by '-4'.

x = -9

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3 years ago
Two sides of a triangle have measures 3 ft and 6 ft. Also, these sides form a vertex whose angle measures 60 degrees. Calculate
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Answer:

A. The length of the third side is approximately 5 feet.

B. A = 88^{o}, B = 60^{o} and C = 32^{o}.

Step-by-step explanation:

Let the triangle be ABC. Given two sides and an included angle, let us apply the cosine rule to determine the third length.

A. Let side a = 6 feet and c = 3 feet, thus;

b^{2} = a^{2} + c^{2} - 2ac Cos B

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b^{2} = 27

b = \sqrt{27}

  = 5.1962

b  = 5.2 feet

b ≅ 5 feet

The length of the third side is approximately 5 feet.

B. Given that B = 60^{o}, then let us apply the Sine rule to determined the measure of A.

\frac{a}{SinA} = \frac{b}{SinB}

So that,

\frac{6}{Sin A} = \frac{5.2}{Sin60^{o} }

Sin A = \frac{0.886*6}{5.2}

Sin A = 0.99923

A = Sin^{-1} 0.99923

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A ≅ 88^{o}

Since the sum of angle in a triangle = 180^{o}.

Then,

A + B + C = 180^{o}

88^{o} + 60^{o} + C = 180^{o}

148^{o} + C = 180^{o}

C = 180^{o} - 148^{o}

     = 32^{o}

C = 32^{o}

Thus,

A = 88^{o}, B = 60^{o} and C = 32^{o}.

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