Nate draws a map to show locations on a playground.

Mathematics

1 answer:

o-na [289]3 years ago

7 0

i think that it is 1 yard because they are 1 apart

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Answer the following

Amanda [17]

The set A satisfying the given inequality is A = (- $\infty$ , -10].

<h3>What are some properties of an inequality relation? </h3>

Following are some facts which are true for an inequality relation:

Equal numbers can be added or subtracted from both sides of an inequality without affecting the inequality sign.
The Inequality sign is unchanged if both sides are multiplied or divided by a positive number, but when multiplied or divided by a negative number the inequality sign is reversed.

$\frac{5x-2}{8} - \frac{3x-5}{10} &\ge& x+y\\\\\Rightarrow\;\; \frac{13}{40}x + \frac{1}{4}&\ge& x+y\\\\\Rightarrow\;\;\;\;\;\; -\frac{27}{40}x &\ge & y - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\;\; -x &\ge & \frac{40}{27}\left( y-\frac{1}{4} \right).\hspace{1cm}(1)$

Since y ∈ B, -2 ≤ y ≤ 7. So,

$\;\;\;\;\;\;\;\,-2 - \frac{1}{4}\; \le\; y - \frac{1}{4} \;\le\; 7 - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\; -\frac{9}{4}\; \le\; y - \frac{1}{4} \;\le\; \frac{27}{4}\\\\\Rightarrow\;\;\; -\frac{9}{4}\cdot \frac{40}{27} \;\le\; \frac{40}{27} \left( y-\frac{1}{4} \right) \;\le \;\frac{27}{4}\cdot \frac{40}{27}\\\\\Rightarrow\;\;\;\;\;\;\;\; -\frac{10}{3} \;\le\; \frac{40}{27}\left( y - \frac{1}{4} \right)\; \le\; 10.$