4)

Mathematics

1 answer:

Vsevolod [243]3 years ago

4 0

Answer:

if he lost 5.9 in 3.3 months he we would lost weight.

5.9* 3.3 19.47lbs

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What is the quotient (125 – 8x3) ÷ (25 + 10x + 4x2)? –2x + 5 2x – 5 –2x – 5 2x + 5

juin [17]

ANSWER

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = - 2x+5$

EXPLANATION

We have been given the quotient,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} }$
to simplify.

We need to rewrite the numerator as difference of two cubes.

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ {5}^{3} - ( {2x})^{3} }{ 25 + 10x + 4 {x}^{2} }$

We need to make use of the difference of cubes formula,

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

We now let,
$a = 5 \: and \: b = 2x$

Then the numerator becomes,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)(25 + 5 (2x) + {(2x)}^{2}) }{ 25 + 10x + 4 {x}^{2} }$

This simplifies to,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)(25 + 10x + 4 {x}^{2}) }{ 25 + 10x + 4 {x}^{2} }$

We cancel out common factors to obtain,

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = \frac{ (5 - 2x)}{ 1}$

$\frac{125 - 8 {x}^{3} }{ 25 + 10x + 4 {x}^{2} } = 5 - 2x$