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tester [92]
3 years ago
11

What is the value of x?

Mathematics
1 answer:
Nikolay [14]3 years ago
8 0
Answer: 7 centimeters 

Explanation:

Let triangle ABC and triangle CDE form a bow tie such that 
     - triangle ABC is smaller than triangle CDE
     - Segment AC and segment CD are the north sides
     - Segment BC and segment CE are the bottom sides
     - AC = 6, CD = 42, CE = 36, BC = x

Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent. 

Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure. 

Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent. 

Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:

- angle BAC and angle CED
- angle ACB and angle ECD

By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.

In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So, 

\frac{BC}{CD}  =  \frac{AC}{CE} 


    (1)

Since AC = 6, CD = 42, CE = 36, BC = x, we can substitute these values to equation (1). So, equation (1) becomes

\frac{x}{42} = \frac{6}{36}
\frac{x}{42} = \frac{1}{6}  (2)

SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that

x = 42(1/6)
x = 7 centimeters

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Curtis plays a trivia game he earns 2 points for each correct answer and loses 0.25 points for each incorrect answer he get 21 c
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Answer:

41

Step-by-step explanation:

Curtis is playing a trivia game.

Number of points earned for each correct answer = 2

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Given that:

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Solution:

First of all, let us find the points earned by correct answers.

Points earned by correct answers = Number of correct answers multiplied by Points earned on one correct answer.

Points earned by correct answers = 21 \times 2 = 42

Now, let us find the points to be lost by wrong answers.

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The score of the game can be calculated by subtracting the points lost from the points earned.

Score = 42 - 1 = <em>41</em>

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2 years ago
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Answer:

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Step-by-step explanation:

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