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Over [174]
3 years ago
12

In trapezoid ABCD AC is a diagonal and ∠ABC ≅ ∠ACD. Find AC if the lengths of the bases BC and AD are 14m and 28m respectively.

Mathematics
1 answer:
krek1111 [17]3 years ago
8 0

Answer:

AC = 14 sqrt(2) = 19.80    

Step-by-step explanation:

Below is the diagram showing you how this has been set up. The figure is a trapezoid which means BC and AD are parallel. AC is a transversal of the parallel lines.

Givens

  • <ABC = <ACD                          
  • ABCD  is a trapezoid
  • BC = 14
  • AD = 28
  • AC is a transversal of BC and AD

Solution

  • <ABC = <ACD                Given
  • <DAC = <ACB                Alternate interior angles.
  • ΔACB ≅ΔDAC               AA
  • <BAC = <ADC                Angles of similar triangles are equal
  • AC /28 = 14/AC              Form a proportion from corresponding sides
  • AC*AC = 14 * 28             Cross multiply the proportion. Combine
  • AC^2 = 392                    Express as prime factors.
  • AC^2 = 7*7*2*2*2           Take the square root of both sides
  • sqrt(AC)^2 = sqrt(7*7*2*2*2)
  • AC = 7*2 * sqrt(2)
  • AC = 14 sqrt(2) = 19.80    

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bija089 [108]

Answer:

Sometimes the form factor can be determined without opening the case and the form factor can be predicted on the basis of the shape of the case.

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7 0
3 years ago
6.25t=5 please help I need this to finish my assignments
vazorg [7]

Answer:

t=0.8

Step-by-step explanation:

5/6.25

4 0
3 years ago
Read 2 more answers
This table shows the number of points two teams scored in five games
mezya [45]

Answer:

2.16

Step-by-step explanation:

The question is on mean absolute deviation

The general formula ,

Mean deviation = sum║x-μ║/N where  x is the each individual value, μ is the mean and N is number of values

<u>Team 1</u>

Finding the mean ;

mean= \frac{51+47+35+48+64}{5}  =49

Points     Absolute Deviation from mean

51                          2

47                         2

35                        14

48                         1

64                         15

<u>Sum    </u>                34          

Absolute mean deviation = 34/5= 6.8

<u>Team 2</u>

Finding the mean

mean=\frac{27+55+53+38+41}{5} = 42.8

Points                      Absolute deviation from the mean

27                                    15.8

55                                    12.2

53                                     10.2

38                                      4.8

41                                       1.8

<u>Sum                                 44.8        </u>

Absolute deviation from the mean = 44.8/5 =8.96

Solution

Difference in mean absolute deviation of the two teams = 8.96-6.8 = 2.16

5 0
3 years ago
iris charges a fee for her consulting services plus an hourly rate that is 1 1/5 times her fee on a 7 hour job and iris charged
Veronika [31]
Based on the given problem above, here is the solution.
Given: Iris's charge: 470
           1 1/5 times her fee: additional hourly rate
           ? = fee for an hourly rate
What we need to do first is divide 470 by 7 hours, so 470/7 = 67.143/hour.
So Iris's per hour is 67.143 without the additional rate.
Now, let's look for the 1 1/5 of 470. 1 1/5 is equal to 1.2. So 470 x 1.2 = 564.
To get the total fee of her hourly rate, we add 67.143 and 564, so Iris's hourly rate then is 631.143 or 631.14.
5 0
3 years ago
Write the phrase as an expression. 28 divided by 7
4vir4ik [10]
The answer would be 28/7

Hope this helps

Have a great day/night

Feel free to ask any questions
4 0
3 years ago
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