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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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Answer:

P = 0,88          or       P  =  88 %

Step-by-step explanation:

The probability of having a married couple in nonadjacent desks is the total number of probabilities minus the probabilities of having them in adjacent places divide by total number of outcomes

The total possibilities (outcomes) of 9 elements in a row is:

P(₉) = 9!

P(₉) = 9*8*7*6*5*4*3*2*1

P(₉) = 362880

And the outcomes in which they are adjacent to each other is:

We consider them as one unit them we in this situation have 8 elements

P(₈) = 8!

P(₈) = 8*7*6*5*4*3*2*1

P(₈) = 40320

Then the probability that the married couple will have nonadjacent desks is:

P = P(₉)  -  P(₈) / P(₉)

P =  362880 - 40320 / 362880

P = 322560/ 362880

P = 0,88          or       P  =  88 %

6 0
3 years ago
Please help with the two problems on the top I’d really appreciate it please hurry thank you
Llana [10]
Can you explain it more ? I don’t know what I need to help you with
4 0
3 years ago
Please help and thank you!
lukranit [14]

9514 1404 393

Answer:

  • base area: 21 ft²
  • volume 105 ft³

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = (1/2)bh

The base and height of a right triangle can be taken to be the leg lengths, since each is perpendicular to the other.

  A = (1/2)(6 ft)(7 ft) = 21 ft² . . . . base area

__

The volume is the product of the base area and the height:

  V = Bh

  V = (21 ft²)(5 ft) = 105 ft³ . . . . volume

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3 years ago
Use the compound interest formulas to solve. A = P(1 + r/n)nt and A = Pert Suppose you have $3000 to invest. Which investment yi
cluponka [151]

Answer:

Account 1 yields greater return.

Step-by-step explanation:

Lets solve for the first formula:

A=P(1+\frac{r}{n} )^{nt}

First, change 6.5% into a decimal:

6.5% -> \frac{6.5}{100} -> 0.065

Now, plug in the values for Account 1:

A=3,000(1+\frac{0.065}{2})^{2(10)}

A=5,687.51

<u>Now solve for Account 2:</u>

Change 6% into a decimal:

6% -> \frac{6}{100} -> 0.06

Now plug in the values:

A=3,000e^{0.06(10)}

A=5,466.36

Account 1 yields better money after 10 years.

3 0
3 years ago
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Answer:

1, 2, and 6

Step-by-step explanation:

5*.25=1.25 7*.25=1.75 12*.25=3

3 0
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