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Over [174]
3 years ago
15

Two friends are reading the same book. Amy can read 3 pages per minute, and she has already read 9 pages. Sam, who has a reading

speed of 2 pages per minute, has read 47 pages so far. The two friends decide to sit and read together. How long will it take Amy to catch up with Sam? By the time Amy catches up to Sam, how many pages will each one have read?
Mathematics
1 answer:
Daniel [21]3 years ago
5 0
Amy:  (3 pages/min)(x min) + 9 pages
Sam:  (2 pages/min)(x min)  + 47 pages

Equate these:  3x+9 = 2x + 47

Then x = 38.  The two friends will have covered the same number of pages after 38 minutes.  How many pages would that be?  3(38)+9 = 123 pages.
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The true statements are:

m∠ 3 + m∠ 4 = 180° ⇒ 1st

m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ 2nd

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Step-by-step explanation:

* Look to the attached diagram to answer the question

# m∠ 3 + m∠ 4 = 180°

∵ ∠ 3 and ∠ 4 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠ 3 + m∠ 4 = 180° ⇒ <em>true</em>

# m∠ 2 + m∠ 4 + m∠ 6 = 180°

∵ ∠ 2 , ∠ 4 , ∠ 6 are the interior angles of the triangle

∵ The sum of the measures of interior angles of any Δ is 180°

∴ m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ <em>true</em>

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∵ In any Δ, the measure of the exterior angle at one vertex of the

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∵ ∠ 5 is the exterior angle of the vertex of ∠ 6

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∴ m∠ 2 + m∠ 4 = m∠ 5 ⇒ <em>true </em>

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∵ ∠ 1 and ∠ 2 formed a straight angle

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# m∠4 + m∠6 = m∠2

∵ ∠ 4 , ∠ 6 , ∠ 2 are the interior angles of a triangle

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∴ m∠4 + m∠6 = m∠2 ⇒ <em>Not true</em>

<em></em>

# m∠2 + m∠6 = m∠5

∵ ∠ 5 is the exterior angle at the vertex of ∠ 6

∴ m∠ 2 + m∠ 6 = m∠ 5 ⇒ <em>Not true</em>

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