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nata0808 [166]

3 years ago

\frac{2}{3} = m - \frac{5}{3} " alt=" \frac{2}{3} = m - \frac{5}{3} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

EleoNora [17]3 years ago

4 0

7/3 or if you change it to a mixed number it will be 2 1/3

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A vertical number line is given.

Ad libitum [116K]

The absolute value of the number plotted on the number line is; 0.5

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2 years ago

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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,

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

The set {-x | inequality (1) holds ∀ y ∈ B} is [10, $\infty$ ) i.e.

10 ≤ -x ≤ $\infty$ .

Multiplying -1 throughout gives

-10 ≥ x ≥ - $\infty$ .

x, thus, lies in the range A = (- $\mathbf{\infty}$ , -10}.

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Disclaimer: The question was incomplete. Please find the full content below.

<h3>Question </h3>

Find the set A such that for x ∈ A

$\frac{5x - 2}{8} - \frac{3x - 5}{10} \ge x + y$

∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.

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4 0

2 years ago

PLEASE HELP!!! A.S.A.P!!

Ksivusya [100]

Answer:

142m

Step-by-step explanation:

This problem can be solved by simply using the pythagorean theorem, as you stated at the beginning of the problem, which is: $a^{2} +b^{2} =c^{2}$

You are given the <em>a</em> side and <em>b</em> side that are needed for this equation, so it's all a matter of plugging in the information you have:

$110^{2} +90^{2} =c^{2}$