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1 year ago

Which is a factor of 144 - 49x²? O 12-7x² O 72-7x² O 12-7x O 72 + 7x

Mathematics

1 answer:

lisabon 2012 [21]1 year ago

4 0

Answer: C: 12-7x

Step-by-step explanation:

This expression is a good example of the difference of two squares, as 144 is the square of 12, while 49x² is the square of 7x.

Any difference of two squares $a^2-b^2$ can be factored into the sum of their square roots times the difference of their square roots $(a+b)(a-b)$ .

Let's factor our expression.

$144-49x^2=(12+7x)(12-7x)$

Out of all the options given, only $12-7x$ is a factor. Hence, option C is correct.

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2 years ago

After being treated with chemotherapy, the radius of the tumor decreased by 23%. What is the corresponding percentage decrease i

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The volume of the tumor experimented a decrease of 54.34 percent.

Step-by-step explanation:

Let suppose that tumor has an spherical geometry, whose volume ( $V$ ) is calculated by:

$V = \frac{4\pi}{3}\cdot R^{3}$

Where $R$ is the radius of the tumor.

The percentage decrease in the volume of the tumor ( $\%V$ ) is expressed by:

$\%V = \frac{\Delta V}{V_{o}} \times 100\,\%$

Where:

$\Delta V$ - Absolute decrease in the volume of the tumor.

$V_{o}$ - Initial volume of the tumor.

The absolute decrease in the volume of the tumor is:

$\Delta V = V_{o}-V_{f}$

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The percentage decrease is finally simplified:

$\%V = \left[1-\left(\frac{R_{f}}{R_{o}}\right)^{3} \right]\times 100\,\%$

Given that $R_{o} = R$ and $R_{f} = 0.77\cdot R$ , the percentage decrease in the volume of tumor is:

$\%V = \left[1-\left(\frac{0.77\cdot R}{R}\right)^{3} \right]\times 100\,\%$

$\%V = 54.34\,\%$

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3 years ago