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Galina-37 [17]
3 years ago
14

Find the area of an equilateral triangle (regular 3-gon) with the given measurement of 6 inch side

Mathematics
1 answer:
Anton [14]3 years ago
6 0

\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}~~ \begin{cases} s=length~of\\ \qquad a~side\\[-0.5em] \hrulefill\\ s=6 \end{cases}\implies A=\cfrac{6^2\sqrt{3}}{4}\implies A=9\sqrt{3}

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4x-35=9x<br><br>please help me i really need help
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4x-35=9x
     -4x
-35=5x
divide by 5
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5 0
3 years ago
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The sum of three numbers is 26. Twice the first minus the second is the third less 2. The third is the second minus 3 times the
Agata [3.3K]

Let a, b, c represent the three numbers. The problem statement gives rise to three equations:

  • a +b +c = 26
  • 2a -b = c -2
  • -3a +b = c

Adding the first two equations gives

... (a +b +c) +(2a -b) = (26) +(c -2)

... 3a +c = 24 +c . . . . . simplify

... 3a = 24 . . . . . . . . . . subtract c

... a = 8 . . . . . . . . . . . . divide by 3

Adding the second and third equations gives ...

... (2a -b) +(-3a +b) = (c -2) +(c)

... -a = 2c -2 . . . . simplify

... -6 = 2c . . . . . . add 2, substitute for a

... -3 = c . . . . . . . . divide by 2

Using the third equation we can find b.

... -3·8 +b = -3 . . . . substitute for a and c

... b = 21 . . . . . . . . .add 24

The numbers are 8, 21, -3.

_____

The method above is sort of "ad hoc", taking advantage of the numbers in this particular set of equations. You can use more formal methods of Gaussian elimination or Cramer's Rule to solve these by just following a procedure. Or, your graphing calculator can do it for you.

6 0
3 years ago
What is three fourth divided by four
kap26 [50]

3/4 divided by 4 is 0.1875

5 0
3 years ago
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What is the range of the function f(x) = |x| – 3?
Likurg_2 [28]
Why not draw the graph of y=|x|?  It has a v-shape, and the vertex is at (0,0).

The graph of f(x) = |x| - 3 looks exactly the same, EXCEPT that the whole graph of |x| is shifted 3 units downward.  The smallest value that y can have is therefore -3.

Can you now figure out the range of f(x)?
3 0
3 years ago
Please help .... Jeff is traveling from Atlanta to Columbia and then to Charleston. He decides to plot the cities on a coordinat
Crazy boy [7]

Answer:

The answer is C

Step-by-step explanation:

Use the Pythagoras theorem which states that a2 = b2 + c 2

For easier understanding imagine a straight line along the x axis. At (0,0) we have Atlanta. Moving 21 units to our right we have Columbia. This is represented on the coordinate system by (21, 0). To go from Colombia to Charleston, which is located at (24, -11), we need to travel 3 units right along the x- axis to reach ‘24’ and ‘11’ units down along the y- axis to reach (24, -11). Starting from Colombia we can make an imaginary triangle with its perpendicular being the y- component and its base being the x- component, which as we have stated above is ‘-11’ and ‘3’ respectively

Now applying the Pythagoras theorem to calculate the hypothesis and hence the distance between Colombia and Charleston.

a, which represents the distance between Colombia and Charleston would be

a² = b² + c²

a² = (3)² + (-11)²

a = √[(3)² + (-11)²]

Hence the answer is C

5 0
3 years ago
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