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12345 [234]
3 years ago
6

The length of a rectangle is 3 inches more than its width. If the perimeter is 42 inches, find the dimensions of the rectangle.​

Mathematics
1 answer:
aalyn [17]3 years ago
8 0

P = 2w + 2l where w is the width, and l is the length. We know the length (l) is 3 inches longer than it's width (or l = w+3). Substitute w +3 into Perimeter equation. P = 2w + 2(w+3).

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Step-by-step explanation:

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lesya692 [45]

Answer:

\displaystyle f(x) = -2(x-2)(x^2+4)

Step-by-step explanation:

We want to find a third degree polynomial with zeros <em>x </em>= 2 and <em>x</em> = 2i and f(-1) = 30.

First, note that by the Complex Root Theorem, since <em>x</em> = 2i is a root, <em>x</em> = -2i must also be a root.

Hence, we will have the three factors:

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Where <em>a</em> is the leading coefficient.

Expand and simplify the second and third factors:

\displaystyle \begin{aligned} (x-(2i))(x-(-2i)) &= (x-2i)(x+2i) \\ \\ &= x(x-2i)+2i(x-2i) \\ \\ &= (x^2 - 2ix) + (2ix - 4i^2) \\ \\ &=x^2 + 4\end{aligned}

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\displaystyle f(x) = a(x-2)(x^2+4)

Since f(-1) = 30:

\displaystyle \begin{aligned}  f(x) &= a(x-2)(x^2+4) \\ \\ (30) &= a((-1)-2)((-1)^2+4) \\ \\ 30 &= -15a \\ \\ a&= -2\end{aligned}

In conclusion, third degree polynomial function is:

\displaystyle f(x) = -2(x-2)(x^2+4)

5 0
3 years ago
The new club sticker is in the shape of a triangle. It has a height of 8 inches and a base of 10 inches. The area of the club st
rusak2 [61]

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2

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