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3 years ago

5

A container was 1/2 filled with water. when 200 ml of water was poured out, it became 1/3 full. find the capacity of the contain

er in milliliters.

1 answer:

marusya05 [52]3 years ago

8 0

<span>the capacity of the container in milliliters would be </span>167ml all together

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Jada makes sparkling juice by mixing 2 cups of sparkling water with every 3 cups of apple juice.

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Step-by-step explanation:

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3 years ago

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I need help to fill in the blanks.. please

Murljashka [212]

Answer:

Part a) alternate interior angles theorem

Part b) vertical angles theorem

Part c) AA Similarity theorem

Part d) triangle ABC is similar with triangle EDC

Part e) The length side b is 3 cm

Step-by-step explanation:

Part a) we know that

The <u><em>Alternate Interior Angles Theorem</em></u> states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent. Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal.

In this problem

The transversal is the segment BD and the parallel lines are AB and DE

so

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Part b) we know that

<u><em>Vertical Angles Theorem</em></u> states that vertical angles are congruent. Vertical Angles are the angles opposite each other when two lines cross.

In this problem, the two lines that cross are BD and AE

so

$m\angle 5=m\angle 6$ ----> by vertical angles theorem

Part c) we know that

The <u><em>AA Similarity Theorem</em></u> states: If two angles of one triangle are congruent to two corresponding angles of another triangle, then the triangles are similar

In this problem

triangle ABC is similar with triangle EDC by AA Similarity Theorem

Because

$m\angle 1=m\angle 4$ ----> by alternate interior angles

$m\angle 5=m\angle 6$ ----> by vertical angles

Part d) triangle ABC is similar with triangle EDC by AA Similarity Theorem

see the explanation Part c)

Part e) Find the length of side b

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

we have that

triangle ABC is similar with triangle EDC

so

Applying proportion

$\frac{BC}{DC}=\frac{AC}{EC}$

substitute the given values

$\frac{2}{DC}=\frac{5}{7.5}$

solve for DC

$DC=2(7.5)/5=3\ cm$

therefore

The length side b is 3 cm

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