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aleksandrvk [35]
3 years ago
11

Which expression is equivalent to...? Screenshots attached. Please help! Thank you.

Mathematics
1 answer:
Studentka2010 [4]3 years ago
4 0

Answer:

4x^{3} y^{2} (\sqrt[3]{4 x y})

Step-by-step explanation:

Another complex expression, let's simplify it step by step...

We'll start by re-writing 256 as 4^4

\sqrt[3]{256 x^{10} y^{7} } = \sqrt[3]{4^{4} x^{10} y^{7} }

Then we'll extract the 4 from the cubic root.  We will then subtract 3 from the exponent (4) to get to a simple 4 inside, and a 4 outside.

\sqrt[3]{4^{4} x^{10} y^{7} } = 4 \sqrt[3]{4 x^{10} y^{7} }

Now, we have x^10, so if we divide the exponent by the root factor, we get 10/3 = 3 1/3, which means we will extract x^9 that will become x^3 outside and x will remain inside.

4 \sqrt[3]{4 x^{10} y^{7} } = 4x^{3} \sqrt[3]{4 x y^{7} }

For the y's we have y^7 inside the cubic root, that means the true exponent is y^(7/3)... so we can extract y^2 and 1 y will remain inside.

4x^{3} \sqrt[3]{4 x y^{7} } = 4x^{3} y^{2} \sqrt[3]{4 x y}

The answer is then:

4x^{3} y^{2} \sqrt[3]{4 x y} = 4x^{3} y^{2} (\sqrt[3]{4 x y})

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The slope-intercept form of the equation of the line containing the points (−2, 4) and (6, 0) will be y =0.5 x+ 5.

<h3>What is the slope?</h3>

A numerical assessment of a line's angle relative to the ground is known as the slope.

The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.

The slope of the line is found as;

\rm m = \frac{y_2-y_1}{x_2-x_1} \\\\ m = \frac{0-4}{6-(-2)} \\\\ m = \frac{-4}{8} \\\\ m = \frac{-1}{2}

The standard line equation is;

y-y₁=m(x-x₁)

\rm y-4= \frac{-1}{2}(x-(-2)) \\\\ 2y-8 = x+2 \\\\ 2y =x+10 \\\\ y = 0.5 x + 5

Hence, the slope-intercept form of the equation of the line containing the points (−2, 4) and (6, 0) will be y =0.5 x+ 5.

To learn more about the slope, refer to the link;

brainly.com/question/3605446

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Step-by-step explanation:

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A particular beach is eroding at a rate of 4 centimeters per year. A realtor converts this rate to millimeters per day. Which
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Answer:

\frac{4cm}{1year}*\frac{10mm}{1cm}*\frac{1year}{365days}

Step-by-step explanation:

Whenever we are doing unit conversions, we have to remember to make the first ratio and then each successive ratio should be put <em>in such a way</em> that the top and bottom cancels out with each unit and whatever we want, remains.

A simple example would be if we were to just convert from cm to mm. Suppose we want to convert 5 centimeters to millimeters. We can write the ratios is 2 ways:

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Second:

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The first one is correct since we want mm, mm should be on top and cm should be on bottom form cm and cm to get canceled.

Now, for our problem, we want mm on top and day on bottom. So, cm and year should cancel. Looking at the first choice, the conversion factors are correct & skimming through, we see that

cm and cm cancels (top and bottom), also year and year cancels (top and bottom), it will leave us with mm on top and days on bottom, <em>which is what we want</em>.

First answer choice is right.

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