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sergij07 [2.7K]
1 year ago
8

Find the number of units in the length of diagonal $DA$ of the regular hexagon shown. Express your answer in simplest radical fo

rm.
Mathematics
1 answer:
LekaFEV [45]1 year ago
6 0

17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.

<h3>How do you find the length of the diagonal of a regular hexagon?</h3>

Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.

For a polygon, the SUM of the internal angles is:

(n-2) * 180 (n=6 for hexagon)

(6-2)*180 = 720   Thus EACH angle is :   720/6 = 120 degrees

Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.

There are 180 degrees in any triangle:  

(180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines:

10/sin30 = x/(sin120)

10/(.5)  × (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30  ×  sin 120  =  17.32

17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.

Learn more about hexagon here:

brainly.com/question/28016053

#SPJ4

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What fractional part of 84 is 14?
goldenfox [79]

Answer:

1/6

Step-by-step explanation:

14/84 = 7/42 = 1/6

8 0
3 years ago
Nicole has 16 nickels and dimes. If the value of her coins is 1.05, how many of each coin does she have?
earnstyle [38]

Answer:

  • 11 nickels
  • 5 dimes

Step-by-step explanation:

If all were dimes, she would have $1.60, which is $0.55 more than she actually has. Replacing a dime with a nickel reduces the total by .05, so there must be .55/.05 = 11 such replacements. This is the number of nickels. The number of dimes makes up the rest of the 16 coins.

Nicole has 11 nickels and 5 dimes.

_____

You can write equations for this several ways. My personal favorite is to use a single variable to represent the number of highest-value coin: d = number of dimes. Then the number of nickels is 16-d and the total value is ...

  0.10d + 0.05(16 -d) = 1.05

  0.05d + 0.80 = 1.05 . . . eliminate parentheses, collect terms

  0.05d = 0.25 . . . . . . . . . subtract 0.80

  d = 0.25/0.05 = 5 . . . . . number of dimes

  16-d = 16-5 = 11 . . . . . . . .number of nickels

__

If you let the variable match the number of nickels, the solution looks a lot like the one described in words, above.

  0.05n + 0.10(16 -n) = 1.05

  -0.05n +1.60 = 1.05

  -0.05n = -0.55 . . . . . . . subtract 1.60

  n = -0.55/-0.05 = 11 . . . number of nickels

  16-n = 16-11 = 5 . . . . . . . number of dimes

__

Comparing these two solutions, you see that we work with negative numbers in the second solution. The reason for choosing the variable to represent the higher-value coin is to keep the numbers positive, as they are in the first solution. (It's no big deal, if you're not bothered by negative number arithmetic.)

3 0
3 years ago
kendra is 3 times her duahters age plus 7myears kendra is 49 years old. write an equation to find her duaters age
natima [27]

Answer:

Kendra's daughter is 14 years old.

Step-by-step explanation:

If I'm reading this correctly, it says "plus 7 <em>more</em> years." I'm writing my equation based off that phrase being true.

Set up equation:

Variable x = daughter's age

x × 3 + 7 = Kendra

x × 3 + 7 = 49

3x + 7 = 49

3x = 42

x = 14

Check your work:

14 × 3 + 7 = 49

42 + 7 = 49

49 = 49

Correct!

5 0
2 years ago
Pls help me with this work sheet i will give brainliest and 50 points
Elden [556K]

1) y = 5

2) y = 34

3) y = -13

idek the rest :(

4 0
3 years ago
Marsha gave the cashier $20 to pay for 3 pairs of socks. The cashier gave her $5.03 in change. Each pair of socks cost the same
allochka39001 [22]

Answer:

$4.99

Step-by-step explanation:

If she pays with $20 and recieves $5.03 in change, her total cost was 20 - 5.03 or $14.97. If each pair of socks is the same amount, 14.97 / 3 will give you the amount per each pair. 14.97 / 3 = $4.99

7 0
2 years ago
Read 2 more answers
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