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raketka [301]
3 years ago
5

Which expression is equivalent to 3x + 6

Mathematics
1 answer:
Ksju [112]3 years ago
8 0

Answer:

3(x+2)

High Hopes

                       Barry-

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A water storage tank has the shape of a cylinder with diameter 14 ft. It is mounted so that the circular cross-sections are vert
4vir4ik [10]

Check the picture below.

neverminding for a few seconds the volume of the cylinder, the percentage in the height used by the water will be the same as the percentage of its volume.  We know the total amount or 100% of the height is 14, so what is 11 in percentage?

\begin{array}{ccll} amount&\%\\ \cline{1-2} 14&100\\ 11&x \end{array}\implies \cfrac{14}{11}=\cfrac{100}{x}\implies 14x=1100 \\\\\\ x = \cfrac{1100}{14}\implies x = \cfrac{550}{7}\implies \boxed{x \approx 78.6}

7 0
3 years ago
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
At a store, notebooks are on sale for 78% off the regular price. The cost of a notebook is represented by n. Which of the
zlopas [31]

Answer:

C

Step-by-step explanation:

If the cost is represented by n, why would you subtract the cost of the notebook by 0.78 while multiping it witht the cost?

5 0
3 years ago
Read 2 more answers
T f(x) = x 5 - 3x 3 24 is
kolezko [41]
This question is not correct
8 0
3 years ago
Amy wants to save up money for a prom dress. Her dress costs $238. She only has $45. How much money does she need to get her dre
Vitek1552 [10]

Answer:

193

Step-by-step explanation:

All you do is 238 - 45 and its 193

4 0
2 years ago
Read 2 more answers
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