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ira [324]
3 years ago
6

Sergei buys a rectangular rug for his living room. He measures the diagonal of the rug to be 18 feet. The length of the rug is 3

feet longer than the width. What are the approximate dimensions of the rug? Round each dimension to the nearest tenth of a foot.
A) 10.4 feet by 7.4 feet
B) 11.1 feet by 8.1 feet
C) 13.4 feet by 10.4 feet
D) 14.1 feet by 11.1 feet
Mathematics
1 answer:
kvv77 [185]3 years ago
5 0
The correct answer is d. Please give me brainlest I hope this helps let me know if it’s correct or not okay
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Composite numbers are numbers that are not prime.
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How do i find the volume in a 3d shape
IrinaVladis [17]

It depends on the shape

Use this:

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I've been stuck on this for a long time. I would greatly appreciate help.
choli [55]
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7 0
4 years ago
Evaluate Dx / ^ 9-8x - x2^
Solnce55 [7]
It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for \sqrt x.

In that case, you want to find the antiderivative,

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}

Complete the square in the denominator:

9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2

Now substitute x+4=5\sin y, so that \mathrm dx=5\cos y\,\mathrm dy. Then

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy

which simplifies to

\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy

Now, recall that \sqrt{x^2}=|x|. But we want the substitution we made to be reversible, so that

x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)

which implies that -\dfrac\pi2\le y\le\dfrac\pi2. (This is the range of the inverse sine function.)

Under these conditions, we have \cos y\ge0, which lets us reduce \sqrt{\cos^2y}=|\cos y|=\cos y. Finally,

\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C

and back-substituting to get this in terms of x yields

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C
4 0
3 years ago
Sue uses 1/5 cup of flour for 2 cups of milk to make a cake. how many cakes can she make with 15 cups of flour
Rasek [7]
She can make 75 cakes with 15 cups of flour
4 0
3 years ago
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