Length of a rectangle is 4x²+12x and the area of the rectangle is 24x⁴+72x³, what is the width of the rectangle?

Mathematics

1 answer:

snow_lady [41]3 years ago

6 0

Answer:

The width is $6x^2$

Step-by-step explanation:

The area of a rectangle is given as : $Area=l\times w$

This implies that: $w=\frac{Area}{l}$

We have that the length is $l=4x^2+12x$ and the area is $Area=24x^4+72x^3$

We substitute to get:

$w=\frac{24x^4+72x^3}{4x^2+12x}$

$\implies w=\frac{24x^2(x^2+3x)}{4(x^2+3x)}$

We cancel out the common factors to get:

$w=6x^2$

You might be interested in

Which numbers can be placed in the blank to make the value of this expression a negative number? (-16) -

Genrish500 [490]

Answer:

All numbers greater than -16.

Step-by-step explanation:

Hello!

To keep this expression negative, we can subtract a positive number (numbers greater than or equal to 0), to give us an even smaller negative number.

Another option is to add a negative number so that the value is still negative. We can add any number that is larger than -16.

Answer: All numbers greater than -16

3 0

2 years ago

For problems 1 - 4, identify whether each figure is a point, line, or line segment. Then write its name.

Gemiola [76]

Answer:

1. Line segment 2. Point 3. Line 4. Line Segment

6 0

3 years ago

What is the equivalent trig ratio to cos 18 ?

Anika [276]

Answer:

$\sin{72^\circ}$

Step-by-step explanation:

In a right triangle, the two acute angles are complementary--they add up to 90 degrees.

Cosine is defined as the adjacent side divided by the hypotenuse. In the attached picture, $\cos{18^\circ}=\frac{a}{h}$ .

The other acute angle is 90 - 18 = 72 degrees. Looking at just that angle, side <em>a</em> is the opposite side. So the ratio a/h is opposite over hypotenuse -- the sine ratio.

Therefor, $\cos{18^\circ} = \sin{72^\circ}$