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VashaNatasha [74]
2 years ago
7

What is a formula for the nth term of the given sequence? 6, 12, 24...

Mathematics
1 answer:
Aleks04 [339]2 years ago
8 0

Answer:

the answer is 6n please do you get it

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find the equation of the circle where (-9,4),(-2,5),(-8,-3),(-1,-2) are the vertices of an inscribed square.
solniwko [45]
Check the picture below, so, that'd be the square inscribed in the circle.

so... hmm the diagonals for the square are the diameter of the circle, and keep in mind that the radius of a circle is half the diameter, so let's find the diameter.

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -2}}\quad ,&{{ 5}})\quad 
%  (c,d)
&({{ -8}}\quad ,&{{ -3}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
\stackrel{diameter}{d}=\sqrt{[-8-(-2)]^2+[-3-5]^2}
\\\\\\
d=\sqrt{(-8+2)^2+(-3-5)^2}\implies d=\sqrt{(-6)^2+(-8)^2}
\\\\\\
d=\sqrt{36+64}\implies d=\sqrt{100}\implies d=10

that means the radius r = 5.

now, what's the center?  well, the Midpoint of the diagonals, is really the center of the circle, let's check,

\bf \textit{middle point of 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -2}}\quad ,&{{ 5}})\quad 
%  (c,d)
&({{ -8}}\quad ,&{{ -3}})
\end{array}\qquad 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left( \cfrac{-8-2}{2}~,~\cfrac{-3+5}{2} \right)\implies (-5~,~1)

so, now we know the center coordinates and the radius, let's plug them in,

\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
\begin{array}{lllll}
center\ (&{{ h}},&{{ k}})\qquad 
radius=&{{ r}}\\
&-5&1&5
\end{array}
\\\\\\\
[x-(-5)]^2-[y-1]^2=5^2\implies (x+5)^2-(y-1)^2=25

8 0
3 years ago
Working in separately , three carpenters can make three chairs in three days. How many chairs can 7 carpenters working at the sa
tekilochka [14]
210chairs since the ratio is 3/3 which is 1/1 since 7 carpenters make 7 chairs every day for 30 days thats 7 * 30 which is 210
6 0
3 years ago
Sally needs 2 cups of flour to make her cake. She has 1 cups of flour. How much flour will she need to borrow to have enough to
bulgar [2K]
She needs one more cup of flower
7 0
3 years ago
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Natalija [7]

Answer:

The correct answer is A

Step-by-step explanation:

plz brainlyest (:

7 0
2 years ago
Warm up question, what is 5/6 + 5/6? Explain how you got the answer.
Helga [31]

Answer: 5/3

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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