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4 years ago

The length of a rectangle is 10m more than twice the width. The

Mathematics

1 answer:

ipn [44]4 years ago

3 0

Answer:

5.6, 21.3

Step-by-step explanation:

Let x be the width.

We know that the length is 10+2x. The area of a rectangle is length times width, so substitute the values.

x*(10+2x)=120

10x+2x^2=120

Divide both sides by 2.

x^2+5x=60

Add 25/4 to both sides so we can make a square.

x^2+5x+ 25/4= 60+25/4=265 /4

Factor the left side.

(x+ 5 /2 )^2= 265 /4

x+2.5=(positive or negative) sqrt(265/4)

x=(positive or negative) sqrt(265/4)-2.5

But, we know that if the equation is negative, the width of the rectangle would be negative. Therefore, x=positive sqrt(265/4)-2.5

Then, we will find the sides.

sqrt66.25-2.5=5.63941, or about 5.6

10+(2(sqrt66.25-2.5))= 21.278821, or about 21.3

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Darla found that the least common denominator needed to subtract \frac{x}{x^2+4x-12}-\frac{3}{x+6}is (x + 6)(x – 2). Which is th

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<h3>Answer: Choice B</h3>

$\frac{x}{(x+6)(x-2)} - \frac{3(x-2)}{(x+6)(x-2)}$

which is the same as x/((x+6)(x-2)) - 3(x-2)/((x+6)(x-2))

=====================================

Explanation:

The LCD is (x+6)(x-2) which is the factorization of x^2+4x-12, and that is the denominator of the first fraction. The first fraction has the LCD already. The second fraction does not. It has (x+6) but it is missing (x-2).

We multiply top and bottom of the second fraction by (x-2) to get the second fraction to have the LCD.

$\frac{3}{x+6}$ turns into $\frac{3}{x+6}*\frac{x-2}{x-2} = \frac{3(x-2)}{(x+6)(x-2)}$

------

So,

$\frac{x}{x^2+4x-12} - \frac{3}{x+6}$

$\frac{x}{(x+6)(x-2)} - \frac{3}{x+6}$

$\frac{x}{(x+6)(x-2)} - \frac{3(x-2)}{(x+6)(x-2)}$

This is the same as x/((x+6)(x-2)) - 3(x-2)/((x+6)(x-2))

Note the parenthesis around "(x+6)(x-2)"

Instead of x/(x+6)(x-2) you should write x/( (x+6)(x-2) ) to ensure that all of "(x+6)(x-2)" is in the denominator.

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