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2 years ago

Solve the equation.

Mathematics

1 answer:

aksik [14]2 years ago

8 0

Answer:

x = -1

Step-by-step explanation:

$\frac{2}{3} - 4x + \frac{7}{2} = -9x + \frac{5}{6}$

Add 4x to each side of the equation

$\frac{2}{3} - 4x + \frac{7}{2} + 4x = -9x + \frac{5}{6} + 4x$

$\frac{2}{3} + \frac{7}{2} = -9x + \frac{5}{6} + 4x$

Subtract ⅚ from each side

$\frac{2}{3} + \frac{7}{2} - \frac{5}{6} = -9x + \frac{5}{6} + 4x - \frac{5}{6}$

$\frac{2}{3} + \frac{7}{2} - \frac{5}{6} = -9x + 4x$

$\frac{4 + 21 + 5}{6} = -5x$

$\frac{30}{6} = -5x$

$5 = -5x$

Divide both sides by -5

$\frac{5}{-5} = \frac{-5x}{-5}$

$-1 = x$

$x = -1$

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Qual é a raiz quadrada de 841?

olga_2 [115]

Answer:

Step-by-step explanation:

Convert 189 To A Decimal And Then Round Your Answer To The Nearest Whole Number (29) Is Already Rounded To The Nearest Whole Number So Your Answer Is 29

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2 years ago

How solve step by step -5р - 9 + 8р = 36

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3 years ago

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In how many ways can a gymnastics team of 4 be chosen from 9 gymnasts?

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3 years ago

Rationalize the denominator and simplify.

cestrela7 [59]

If you're using the app, try seeing this answer through your browser: brainly.com/question/3151018

——————————

$\mathsf{\dfrac{3\sqrt{6}+5\sqrt{2}}{4\sqrt{6}-3\sqrt{2}}}$

Multiply and divide by the conjugate of the denominator, which is $\mathsf{4\sqrt{6}+3\sqrt{2}:}$

$\mathsf{=\dfrac{\big(3\sqrt{6}+5\sqrt{2}\big)\cdot \big(4\sqrt{6}+3\sqrt{2}\big)}{\big(4\sqrt{6}-3\sqrt{2}\big)\cdot \big(4\sqrt{6}+3\sqrt{2}\big)}}$

Expand those products and eliminate the brackets:

$\mathsf{=\dfrac{\big(3\sqrt{6}+5\sqrt{2}\big)\cdot 4\sqrt{6}+ \big(3\sqrt{6}+5\sqrt{2}\big)\cdot 3\sqrt{2}}{\big(4\sqrt{6}-3\sqrt{2}\big)\cdot 4\sqrt{6}+ \big(4\sqrt{6}-3\sqrt{2}\big)\cdot 3\sqrt{2}}}\\\\\\ \mathsf{=\dfrac{12\cdot \big(\sqrt{6}\big)^2+20\sqrt{2}\cdot \sqrt{6}+9\cdot \sqrt{6}\cdot \sqrt{2}+15\cdot \big(\sqrt{2}\big)^2}{16\cdot \big(\sqrt{6}\big)^2-12\cdot \sqrt{2}\cdot \sqrt{6}+ 12\cdot \sqrt{6}\cdot \sqrt{2}-9\cdot \big(\sqrt{2}\big)^2}}\\\\\\ \mathsf{=\dfrac{12\cdot 6+20\sqrt{2\cdot 6}+9\sqrt{6\cdot 2}+15\cdot 2}{16\cdot 6-12\sqrt{2\cdot 6}+ 12\sqrt{6\cdot 2}-9\cdot 2}}\\\\\\ \mathsf{=\dfrac{72+20\sqrt{12}+9\sqrt{12}+30}{96-12\sqrt{12}+12\sqrt{12}-18}}$

$\mathsf{=\dfrac{72+29\sqrt{12}+30}{96-18}}\\\\\\ \mathsf{=\dfrac{102+29\sqrt{2^2\cdot 3}}{78}}\\\\\\ \mathsf{=\dfrac{102+29\cdot \sqrt{2^2}\cdot \sqrt{3}}{78}}\\\\\\ \mathsf{=\dfrac{102+29\cdot 2\sqrt{3}}{78}}$

$\mathsf{=\dfrac{102+58\sqrt{3}}{78}}\\\\\\ \mathsf{=\dfrac{\,\diagup\!\!\!\! 2\cdot \big(51+29\sqrt{3}\big)}{\diagup\!\!\!\! 2\cdot 39}}$

$\mathsf{=\dfrac{51+29\sqrt{3}}{39}}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps. =)

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2 years ago

Solve the following system. x2 + y 2= 25 2x + y = 10 The solution set

anzhelika [568]

Answer: {(5,0), (3,4)}

Step-by-step explanation:

You can apply the Substitution method:

- Solve for y from the second equation.

- Substitute into the first equation and solve for x.

Then:

$y=10-2x$