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svetoff [14.1K]
3 years ago
12

The sale price of a table is $472 it was 20% off what was the original price?

Mathematics
1 answer:
ira [324]3 years ago
5 0
To solve, set an equation:

472=0.8x

Divide both sides by 0.8

472/0.8=0.8x/0.8

x=590

Answer: The original price was $590
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Find the area of the shaded region. Round your answer to the nearest tenth.
Alex
Check the picture below on the left-side.

we know the central angle of the "empty" area is 120°, however the legs coming from the center of the circle, namely the radius, are always 6, therefore the legs stemming from the 120° angle, are both 6, making that triangle an isosceles.

now, using the "inscribed angle" theorem, check the picture on the right-side, we know that the inscribed angle there, in red, is 30°, that means the intercepted arc is twice as much, thus 60°, and since arcs get their angle measurement from the central angle they're in, the central angle making up that arc is also 60°, as in the picture.

so, the shaded area is really just the area of that circle's "sector" with 60°, PLUS the area of the circle's "segment" with 120°.

\bf \textit{area of a sector of a circle}\\\\
A_x=\cfrac{\theta \pi r^2}{360}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=6\\
\theta =60
\end{cases}\implies A_x=\cfrac{60\cdot \pi \cdot 6^2}{360}\implies \boxed{A_x=6\pi} \\\\
-------------------------------\\\\

\bf \textit{area of a segment of a circle}\\\\
A_y=\cfrac{r^2}{2}\left[\cfrac{\pi \theta }{180}~-~sin(\theta )  \right]
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=6\\
\theta =120
\end{cases}

\bf A_y=\cfrac{6^2}{2}\left[\cfrac{\pi\cdot 120 }{180}~-~sin(120^o )  \right]
\\\\\\
A_y=18\left[\cfrac{2\pi }{3}~-~\cfrac{\sqrt{3}}{2} \right]\implies \boxed{A_y=12\pi -9\sqrt{3}}\\\\
-------------------------------\\\\
\textit{shaded area}\qquad \stackrel{A_x}{6\pi }~~+~~\stackrel{A_y}{12\pi -9\sqrt{3}}\implies 18\pi -9\sqrt{3}

7 0
3 years ago
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the trar
Citrus2011 [14]

Answer:

(x, y) → (x - 3, y + 5 )

Step-by-step explanation:

A shift of 3 units to the left means subtract 3 from the original x- coordinate.

A shift of 5 units up means add 5 to the original y- coordinate.

Thus the rule representing the translation is

(x, y ) → (x - 3, y + 5 )

6 0
3 years ago
Read 2 more answers
Need help finding a constant k at which the function is continuous everywhere.
saveliy_v [14]

Answer:

k = -6/35

Step-by-step explanation:

To make the function continuous

kx^2 = x+k

These must be equal where the function is defined for two different intervals

This is at the point x=-6  so let x=-6

k(-6)^2 = -6+k

36k = -6+k

Subtract k from each side

36k-k = -6+k-k

35k = -6

Divide by 35

35k/35 = -6/35

k = -6/35


3 0
3 years ago
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If 2+3+6+9=21 then does 7x3=21?
Oxana [17]

Answer:

Yes

Step-by-step explanation:

If you do 7x3 it equals 21.

7 0
3 years ago
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The width of a rectangle is 1 foot less than the length. the area is 2ft squared what is the width
SVEN [57.7K]
 the answer is 1 ft is the width
5 0
3 years ago
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