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2 years ago

What is the quotient of (x cubed 3 x squared minus 4 x minus 12) divided by (x squared 5 x 6)? x 2 x – 2 x – 8 x 8

Mathematics

1 answer:

snow_tiger [21]2 years ago

8 0

The quotient of the given expression is x-2. The correct option is the second option- x – 2

<h3>Simplification of fractions </h3>

From the question, we are to determine the quotient

The given expression is

$\frac{x^{3}+3x^{2} -4x-12 }{x^{2} +5x+6}$

The numerator can be expressed as

$(x-2)(x^{2} +5x+6)$

Then, the fraction becomes

$\frac{x^{3}+3x^{2} -4x-12 }{x^{2} +5x+6}$ = $\frac{(x-2)(x^{2} +5x+6)}{x^{2} +5x+6}$

Simplifying

$\frac{(x-2)(x^{2} +5x+6)}{x^{2} +5x+6} = x-2$

Hence, the quotient of the given expression is x-2. The correct option is the second option- x – 2

Learn more on Simplification of fractions here: brainly.com/question/26496816

Here is the complete and correct question:

What is the quotient of (x cubed + 3 x squared minus 4 x minus 12') divided by (x squared + 5 x + 6)? x + 2 x – 2 x – 8 x + 8

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Read 2 more answers

A sphere and a cylinder have the same radius and height. The volume of the cylinder is . Amie found the volume of the sphere. He

dezoksy [38]

Amie's error while measuring the volume of a sphere is that <u>Amie should have multiplied 54 by 2/3</u>. Thus, the <u>first option</u> is the right choice.

In the question, we are given that a sphere and a cylinder have the same radius and height.

We assume the radius of the sphere to be r, and its height to be h.

Now, the height of a sphere is its diameter, which is twice the radius.

Thus, the height of the sphere, h = 2r

Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.

The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.

Thus, the volume of the given sphere using the formula is (4/3)πr³.

The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.

Now, to compare the two volumes we take their ratios, as

Volume of the sphere/Volume of the cylinder

= {(4/3)πr³}/{2πr³}

= 2/3.

Thus, the volume of the sphere/the volume of the cylinder = 2/3,

or, the volume of the sphere = (2/3)*the volume of the cylinder.

Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.

Thus, Amie's error while measuring the volume of a sphere is that <u>Amie should have multiplied 54 by 2/3</u>. Thus, the <u>first option</u> is the right choice.

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