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4 years ago

Simplify the expression: 3x (4x-6) ————— 2x(3x)

Mathematics

1 answer:

Marina86 [1]4 years ago

7 0

Answer:

$=\frac{2x-3}{x}$

Step-by-step explanation:

$=6x^2\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=\frac{3x\left(4x-6\right)}{2x\cdot \:3x}\\2x\cdot \:3x=6x^2\\=\frac{3x\left(4x-6\right)}{6x^2}\\\mathrm{Cancel\:}\frac{3x\left(4x-6\right)}{6x^2}:\quad \frac{4x-6}{2x}\\=\frac{4x-6}{2x}\\\mathrm{Factor}\:4x-6:\quad 2\left(2x-3\right)\\=\frac{2\left(2x-3\right)}{2x}\\\mathrm{Divide\:the\:numbers:}\:\frac{2}{2}=1\\=\frac{2x-3}{x}$

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What is the value of x and y of this problem X-3y=10

Eduardwww [97]

Y=-1
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3 years ago

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A 2x + 5 3x - 2 B+ X = [? ]

WITCHER [35]

Answer: 7

Step-by-step explanation:

They are alternate interior angle

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3 years ago

A certain drug is made from only two ingredients, there are five milliliters of part a and four milliliters of part b. If a chem

patriot [66]

You will have to divide 353 millimeters by 4:

353 ÷ 4 = 88.25

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(If you should round 88.25 to 88, the answer would be 88 x 9 = 792)

3 0

3 years ago

Solve the equation: 45n+60=285

Alex17521 [72]

Answer:

n = 5

Step-by-step explanation:

45n + 60 = 285

45n = 225

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3 years ago

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Find all solutions to the equation in the interval [0,2n) cos x = sin 2x

Serggg [28]

Answer:

$\huge\boxed{x\in\left\{\dfrac{\pi}{6};\ \dfrac{\pi}{2}\ \dfrac{3\pi}{2};\ \dfrac{5\pi}{6}\right\}}$

Step-by-step explanation:

$\cos x=\sin2x\qquad|\text{use}\ \sin\theta=2\sin\theta\cos\theta\\\\\cos x=2\sin x\cos x\qquad|\text{subtract}\ \cos x\ \text{from both sides}\\\\0=2\sin x\cos x-\cos x\\\\2\sin x\cos x-\cos x=0\qquad|\text{distribute}\\\\\cos x(2\sin x-1)=0\iff\underbrace{\cos x=0}_{(1)}\ \vee\ \underbrace{2\sin x-1=0}_{(2)}$

$(1)\\\cos x=0\Rightarrow x=\dfrac{\pi}{2}+k\pi;\ k\in\mathbb{Z}$

$(2)\\2\sin x-1=0\qquad|\text{add 1 to both sides}\\\\2\sin x=1\qquad|\text{divide sides by 2}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi$

$\text{From}\ (1)\ \text{and}\ (2)\ \text{we have}\\\\x=\dfrac{\pi}{2}+k\pi\ \vee\ x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi\\\\\text{We have the interval}\ x\in[0;2\pi).\ \text{Therefore the solution is:}\\\\x\in\left\{\dfrac{\pi}{6};\ \dfrac{\pi}{2}\ \dfrac{3\pi}{2};\ \dfrac{5\pi}{6}\right\}$

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3 years ago