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Naily [24]
3 years ago
15

Find the distance and midpoints of the following points:

Mathematics
1 answer:
timofeeve [1]3 years ago
4 0
1.) (2, 4) and (10, 8)
Distance: 4√5
Midpoint: (6, 6)

2.) (3, 8) and (7, 3)
Distance: √41
Midpoint: (5, 11/2)

3.) (4, 9) and (9, 5)
Distance: √41
Midpoint: (13/2, 7)
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Solve 0 = (x – 4)2 – 1 by graphing the related function.
fomenos

Answer:

Therefore, the solutions of the quadratic equations are:

x=5,\:x=3

The graph is also attached.

Step-by-step explanation:

The solution of the graph could be obtained by finding the x-intercept.

y=\left(x-\:4\right)^2-1

Finding the x-intercept by substituting the value y = 0

so

y=\left(x-\:4\right)^2-1

\:0\:=\:\left(x\:-\:4\right)^2\:-\:1        ∵ y = 0

\left(x-4\right)^2-1=0

\left(x-4\right)^2-1+1=0+1

\left(x-4\right)^2=1

\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

\mathrm{Solve\:}\:x-4=\sqrt{1}

\mathrm{Apply\:rule}\:\sqrt{1}=1

x-4=1

x=5

\mathrm{Solve\:}\:x-4=-\sqrt{1}

\mathrm{Apply\:rule}\:\sqrt{1}=1

x-4=-1

x=3

So, when y = 0, then x values are 3, and 5.

Therefore, the solutions of the quadratic equations are:

x=5,\:x=3

The graph is also attached. As the graph is a Parabola. It is visible from the graph that the values of y = 0 at x = 5 and x = 3. As the graph is a Parabola.

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