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umka2103 [35]
3 years ago
5

Last question! I need help with showing my work! I already have the answer in the attached image below, thanks!

Mathematics
1 answer:
Rainbow [258]3 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

Given

\sqrt{\frac{4x^2}{3y} }

= \frac{\sqrt{4x^2} }{\sqrt{3y} }

= \frac{2x}{\sqrt{3y} }

Rationalise the denominator by multiplying the numerator/ denominator by \sqrt{3y}

Note that \sqrt{a} × \sqrt{a} = a

= \frac{2x}{\sqrt{3y} } × \frac{\sqrt{3y} }{\sqrt{3y} }

= \frac{2x\sqrt{3y} }{3y}

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After we graph each individual inequality, we then combine the two regions on one graph. See figure 3 below. The red and blue shaded areas in figure 3 overlap to get the purple shaded area you see in figure 4, which is the final answer. Any point in this purple region will satisfy both inequalities at the same time. The solution point cannot be on the dashed line but it can be on the solid line as long as the solid line is bordering the shaded purple region. Figure 4 matches up perfectly with the bottom right corner in your answer choices.

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