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Fantom [35]
3 years ago
8

The verticles of a triangle are A(1,2), B(3,4), and (4,1) What is the length of the shortest side

Mathematics
1 answer:
nirvana33 [79]3 years ago
4 0
Check the picture below.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&A&(~ 1 &,& 2~) 
%  (c,d)
&B&(~ 3 &,& 4~)
\end{array}~~~ 
%  distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AB=\sqrt{(3-1)^2+(4-2)^2}\implies AB=\sqrt{2^2+2^2}
\\\\\\
AB=\sqrt{2\cdot 2^2}\implies AB=2\sqrt{2}

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PLEASE HELP ME!!!!!!
Nata [24]

9514 1404 393

Answer:

  vertex: (2, -3.2)

  axis of symmetry: x = 2

  zeros: x=0, x=4

  formula for axis of symmetry:

  • x = <x-coordinate of vertex>
  • x = -b/(2a) . . . . . . . where the quadratic is ax^2 +bx +c
  • x = average of zeros, (z1 +z2)/2

Step-by-step explanation:

a) The vertex x-coordinate is halfway between the zeros, so is x = (0+4)/2 = 2. It is where the graph has a turning point.

The vertex y-coordinate is the low point of this graph. It is not on a grid line, so we can only guess at its value. I choose to call it -3.2.

The vertex is (2, -3.2).

__

b) The axis of symmetry is the vertical line through the vertex. The constant in its equation is the x-coordinate of the vertex:

  x = 2

__

c) The zeros of the function are where the function crosses the x-axis. These are marked on the graph with red dots. The zeros are x=0 and x=4.

__

d) When the quadratic is written in standard form, ax^2 +bx +c, the equation of the axis of symmetry is ...

  x = -b/(2a) . . . . . perhaps this is the formula you're being asked for (?)

When there is no equation, the axis of symmetry can be found from the graph a couple of ways. One is to identify the x-coordinate of the vertex.

  x = <x-coordinate of the vertex>

Another is to average the zeros, since they are symmetrical about the axis of symmetry.

  x = average of zeros = (z1 +z2)/2

If the quadratic is written in vertex form, the vertex coordinate is the constant in the equation for the axis of symmetry.

  y = a(x -h)^2 +k . . . . . quadratic with vertex (h, k)

  x = h . . . . . . equation of axis of symmetry

8 0
2 years ago
Thirty percent of the people refused to work and just sat around. if 1400 people worked, how many just sat around?
Nezavi [6.7K]
30% can also be written as .3, which is easier to use in this case.

To find how many just sat around, multiply the number of people by the percentage of how many just sat around.

1400*.3=420
5 0
3 years ago
Read 2 more answers
Eight less a number is less than or equal to 17​
Karolina [17]

Step-by-step explanation:

n-8≤17

add 8 on both sides to isolate the variable.

n is less than or equal to 25

6 0
3 years ago
How could you estimate the quotient 162 divided 19? i need help!!!
Ira Lisetskai [31]
It = 6.888888888 and you can round it to 7

6 0
3 years ago
B to the eighth power multiplied by b to the fourth power
scZoUnD [109]
U just add the exponents.

b^8 x b^4 = b^12

hope this helps :)





7 0
3 years ago
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