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3 years ago

Claudia says that she used the GCF to factor the expression 20x + 100xy as 20(x + 5xy). Is she correct? Explain.

Mathematics

1 answer:

Keith_Richards [23]3 years ago

8 0

No, She is not correct.

Step-by-step explanation:

To find the greatest common factor of the expression 20x + 100xy.

Given expression 20x + 100xy.

Let us factor the expression 20x + 100xy.

Now take the common factor in the expression 20x + 100xy.

The common factor is 20x.

So, 20x + 100xy = 20x( 1+ 5y)

But Claudia says that the greatest common factor is 20(x+5xy).

The GCF is wrong.

So, she is not correct.

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Given that

Length of the rectangle in 34 miles less than 5 times its width

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Let assume width of the rectangle be represented by variable x.

So 5 times width of the rectangle =5x

34 inches less than 5 times width of the rectangle = 5x – 34

As Length of the rectangle in 34 miles less than 5 times its width

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The formula for rectangle is given as:

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As given that Area of rectangle = 867 square inches

$\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}$

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

In our case a = 5, b = -34 and c = -867

On substituting value of a, b and c in quadratic formula we get

$\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}$

Since x represents width, it cannot be negative, so x = 17

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Hence length of the rectangle is 51 inches

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