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3 years ago

Solve the inequality

Mathematics

2 answers:

Marianna [84]3 years ago

8 0

Answer:

The answer to your question is the letter A) x ≥ 0.5

Step-by-step explanation:

Inequality

2(4x - 3) ≥ -3(3x) + 5x

Process

1.- Expand

8x - 6 ≥ - 9x + 5x

2.- Simplify

8x - 6 ≥ - 4x

3.- Add 6 units in both sides

8x - 6 + 6 ≥ -4x + 6

4.- Simplify

8x ≥ -4x + 6

5.- Add 4x in both sides

8x + 4x ≥ -4x + 6 + 4x

6.- Simplify

12x ≥ 6

7.- Divide by 12 both sides

12x/12 ≥ 6/12

8.- Simplify

x ≥ 1/2 or 0.5

zubka84 [21]3 years ago

3 0

Answer:The answer is the letter A) x ≥ 0.5

Step-by-step explanation:

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$\sin^2\theta+\cos^2\theta=1\\\\\sin^2\theta=1-\cos^2\theta\\\\\sin^2\theta=1-\left(\dfrac{4}{5}\right)^2\\\\\\\sin^2\theta=1-\dfrac{16}{25}\\\\\\\sin^2\theta=\dfrac{9}{25}\quad|\sqrt{(\dots)}\\\\\\\sin\theta=\sqrt{\dfrac{9}{25}}\\\\\\\boxed{\sin\theta=\dfrac{3}{5}}$

We take positive value of sinθ because 0° < θ < 90°
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$\sin2\theta=2\sin\theta\cos\theta=2\cdot\dfrac{3}{5}\cdot\dfrac{4}{5}=\dfrac{2\cdot3\cdot4}{5\cdot5}=\dfrac{24}{25}\\\\\\\cos2\theta=\cos^2\theta-\sin^2\theta=\left(\dfrac{4}{5}\right)^2-\left(\dfrac{3}{5}\right)^2=\dfrac{16}{25}-\dfrac{9}{25}=\dfrac{7}{25}\\\\\\
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