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KonstantinChe [14]
3 years ago
5

Need help please !!!!!!

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
5 0
A perfect square must be hidden within all of those radicands in order to simplify them down to what the answer is.  \sqrt{192}= \sqrt{64*3}= 8\sqrt{3}.  \sqrt{80}= \sqrt{16*5}=4 \sqrt{5}.  \sqrt{12288}= \sqrt{4096*3}=64 \sqrt{3}.  The rules for adding radicals is that the index has to be the same (all of our indexes are 2 since we have square roots), and the radicands have to be the same.  In other words, we cannot add the square root of 4 to the square root of 5.  They either both have to be 4 or they both have to be 5.  So here's what we have thus far: 8 \sqrt{3}+4 \sqrt{5}+64 \sqrt{3}.  We can add 8 \sqrt{3} and 64 \sqrt{3} to get 72 \sqrt{3}.  That means as far as our answer goes, A = 72 and B = 4, or (72, 4), choice a.
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The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 50 ft². Find the dimensions
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Answer

Length = 10 ft

Width = 5 ft

Explanation

Area of the rectangle given = 50 ft²

Let the width of the rectangle be x

So this means the length of the rectangle will be 3x - 5

What to find:

The dimensions of the rectangle.

Step-by-step solution:

Area of a rectangle = length x width

i.e A = L x W

Put A = 50, L = 3x - 5, W = x into the formula.

\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}

The quadratic equation can now be solve using factorization method:

\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}

Since the dimension can not be negative, hence the value of x will be = 5.

Therefore, the dimensions of the rectangle will be:

\begin{gathered} Length=3x-5=3(5)-5=15-5=10\text{ }ft \\  \\ Width=x=5\text{ }ft \end{gathered}

7 0
1 year ago
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Delvig [45]

Answer:

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