Which is a possible turning point for the continuous

Mathematics

1 answer:

katrin2010 [14]2 years ago

5 0

Choice B: (-2,-1) is the answer

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Write an equation for the circle with endpoints of a diameter (9, 4) and (-3, -2)

inysia [295]

If the diameter is at (9,4) and (-3,-2), then the center of the circle is the midpoint of that segment.

and since we know that the radius of a circle is half of the diameter, whatever long that diameter segment is, the radius is half that.

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 9 &,& 4~) 
% (c,d)
&&(~ -3 &,& -2~)
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{-3+9}{2}~~,~~\cfrac{-2+4}{2} \right)\implies \stackrel{center}{(3~,~1)}$

$\bf -------------------------------\\\\
~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 9 &,& 4~) 
% (c,d)
&&(~ -3 &,& -2~)
\end{array}
\\\\\\
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{(-3-9)^2+(-2-4)^2}\implies d=\sqrt{(-12)^2+(-6)^2}
\\\\\\
d=\sqrt{180}\qquad \qquad \qquad radius=\cfrac{\sqrt{180}}{2}$

$\bf -------------------------------\\\\
\textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{3}{ h},\stackrel{1}{ k})\qquad \qquad 
radius=\stackrel{\frac{\sqrt{180}}{2}}{ r}
\\\\\\
(x-3)^2+(y-1)^2=\left( \frac{\sqrt{180}}{2} \right)^2\implies (x-3)^2+(y-1)^2=\cfrac{(\sqrt{180})^2}{2^2}
\\\\\\
(x-3)^2+(y-1)^2=\cfrac{180}{4}\implies (x-3)^2+(y-1)^2=45$

7 0

3 years ago

Find the perimeter of a regular pentagon with sides of (3x + 5).

kotegsom [21]

Answer:

5(3x + 5) or 15x + 25

Step-by-step explanation:

A regular pentagon has 5 sides of equal length. The perimeter is the sum of the lengths of those sides. We can use multiplication to find the sum of 5 of the same value:

P = 5(3x +5)

Perhaps you want it expanded. Using the distributive property, we multiply each term in parentheses by 5:

P = 15x + 25

4 0

3 years ago

Given the diagram below, what is the length of segment EF

bekas [8.4K]

Let x = length of segment EF.

Assume that
(a) line segments AD, EF, and BC are parallel, and
(b) the vertical distance between AD and EF is equal to the vertical distance between EF and BC.

Then from similarity between geometric shapes, we can write
$\frac{2.2}{x} = \frac{x}{4.8}$
$x^{2} =(2.2)(4.8)=10.56$
x=3.2 (nearest tenth)

Answer: B. 3.2

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2 years ago

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Are two cubes always similar

Ann [662]

Yes, because similar means same shape same angles different size!!

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2 years ago