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AlexFokin [52]
2 years ago
6

A square orange rug has a green square in the center. The side length of the green square is x inches. The width of the orange b

and that surrounds the green square is 12 in. What is the area of the orange ​band?

Mathematics
1 answer:
Annette [7]2 years ago
3 0

Answer:

The area of the orange ​band is 576 + 48x square inches

Step-by-step explanation:

Step 1: Area of the green square

The area of the green square =side^2

The area of the green square  =  x^2 square inches

Step 2: Area of the orange square

The area of the orange square =side^2

The side of the orange square  =  12+12 + x = 24 +x

Now the area of the orange square  =(x+24)^2

Step 3: The area of the orange ​band

Area of the orange ​band =  area of the orange square - area of the green square

Area of the orange ​band =   (x+24)^2 - x^2

expanding and solving the equation we get

x^2 + 24^2 +48x - x^2

576 + 48 x square inches

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Answer:

\boxed {\boxed {\sf 2 \ real \ solutions }}

Step-by-step explanation:

The quadratic formula is:

{x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}

The discriminant of a quadratic is just the expression under the square root, or b^2-4ac. This can tell us the number of solutions a quadratic has.

If the discriminant is:

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Our quadratic equation has a discriminant of 5, which is positive. Therefore, it has 2 real solutions.

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2 years ago
The post office is now calculating the volume of packages to determine the shipping cost. If a box measure 8 1/2 inches long, 5
sladkih [1.3K]
Answer:
volume of box = 312.375 in²

Explanation:
The volume of a rectangular box can be measured as follows:
volume = length* width * height

From the givens we have:
length = 8.5 in
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3 0
3 years ago
N(17+x)=34x−r<br> Solve for x
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N(17+x)=34x−r
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7 0
3 years ago
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fgiga [73]
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4 0
2 years ago
Please help will mark brainliest for the right answer
hodyreva [135]

Answer:

a).  x + y + 90° = 180°

b).  x = 67°

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Step-by-step explanation:

The sum of all angles in a triangle is 180°.

One of the angles in the figure is a right angle, or 90°.  Therefore the sum of the three angles in the figure is:

x + y + 90 = 180

We are also told that x + 2 = 3y.  

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x = 3y - 2

Thake the first equation and substitute the above expression of in place of x:

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(3y-2) + y + 90° = 180°

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