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miv72 [106K]
3 years ago
7

For which of the following compound inequalities is there no solution? Select one: a. 8m+5>=5 and -4m+6<=-10 b. 6m<=-36

and m+24>20 c. -2m< 6 and 3m>24 d. m+9<8 and -2m>=10
Mathematics
1 answer:
enyata [817]3 years ago
6 0

<span>a.\\8m+5\geq5\&#10;\ \ |-5\\8m\geq0\ \ \ |:8\\m\geq0\to m\in\left

b.\\6m\leq-36\ \ \ |:6\\m\leq-6\to m\in\left(-\infty;\&#10;-6\right>\\\\m+24 > 20\ \ \ |-24\\m > -4\to m\in(-4;\&#10;\infty)\\\\solution:\ m\in\left(-\infty;\ -6\right>\ \cap\ (-4;\ \infty)\to&#10;m\in\O\to NO\ SOLUTION

c.\\-2m < 6\ \ \ |:(-2)\\m > -3\to m\in(-3;\ \infty)\\\\3m > 24\&#10;\ \ |:3\\m > 8\to m\in(8;\ \infty)\\\\solution:\ m\in(-3;\ \infty)\ \cap\&#10;(8;\ \infty)\to m\in(8;\ \infty)

d.\\m+9 < 8\ \ \ |-9\\m < -1\to m\in(-\infty;\ -1)\\\\-2m \geq10\ \&#10;\ |:(-2)\\m\leq-5\to m\in\left(-\infty;-5\right>\\\\solution:\&#10;m\in(-\infty;\ -1)\ \cap\ \left(-\infty;-5\right>\to&#10;m\in\left(-\infty;-5\right></span>


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The parts that are missing in the proof are:

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<h3>What is the Converse of Alternate Exterior Angles Theorem?</h3>

The theorem states that, if two exterior alternate angles are congruent, then the lines cut by the transversal are parallel.

∠1 ≅ ∠3 and l║m because we are: given

By the transitive property,

∠2 and ∠3 are alternate interior angles, therefore, they are congruent to each other by the alternate interior angles theorem.

Based on the converse alternate exterior angles theorem, lines p and q are proven to be parallel.

Therefore, the missing parts pf the paragraph proof are:

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