Find the distance between the two points. Enter the number that goes beneath the radical symbol. (PICTURE ABOVE]

Mathematics

1 answer:

Alika [10]3 years ago

6 0

For this case we have that by definition, the distance between two points is given by:

$d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}$

We have the following points:

$(x_ {1}, y_ {1}) :( 1,4)\\(x_ {2}, y_ {2}): (- 2, -3)$

Substituting we have:

$d = \sqrt {(- 2-1) ^ 2 + (- 3-4) ^ 2}\\d = \sqrt {(- 3) ^ 2 + (- 7) ^ 2}\\d = \sqrt {9 + 49}\\d = \sqrt {58}$

Thus, the distance between the points is $\sqrt {58}$

ANswer:

$d = \sqrt {58}$

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HACTEHA [7]

Answer:

25*pi or

78.5 square units.

Step-by-step explanation:

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r = 10

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Area = 100 * pi

Since there is a shaded area, the shaded part looks to be 1/4 of the whole. There's no indication of what it actually is, but 1/4 should be close enough.

Area_shade = 1/4 (100*pi)

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That's one answer.

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3 years ago

What is the equation of the quadratic graph with a focus of (1 ,3) and a directrix of y=1?

zimovet [89]

Check the picture below.

now, we know the directrix is at y = 1, and the focus point is at 1,3, well, notice the picture, the distance between those fellows is just 2 units.

the vertex is half-way between those fellows, therefore, the vertex will be at 1,2.

the distance "p", from the vertex to either the directrix or focus, is really just 1 unit. Since the focus point is above the directrix, is a vertical parabola, and it opens upwards, like in the picture, and since it opens up, the "p" value is positive, or +1.

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
4p(x- h)=(y- k)^2
\\\\
\boxed{4p(y- k)=(x- h)^2}
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ( h, k)\\\\
 p=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
h=1\\
k=2\\
p=1
\end{cases}\implies 4(1)(y-2)=(x-1)^2\implies 4(y-2)=(x-1)^2
\\\\\\
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3 years ago

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Shkiper50 [21]

Hi there!

Pauline simplified the expression correctly.

Pauline made sure she used the distributive property and combined like terms after doing so.

Hope this helps !

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3 years ago

I need help please?!):

motikmotik

Answer:

Option C: $\sqrt{\textbf{121}}$