What is the result when 4x3 + 19x2 + 29x + 14 is divided by 4x + 7?

Mathematics

2 answers:

Orlov [11]2 years ago

6 0

Four hundred twenty thousand and sixty nine

Sergio039 [100]2 years ago

3 0

Step-by-step explanation:

4x³ + 19x² + 29x + 14

= (4x³ + 7x²) + (12x² + 21x) + (8x + 14)

= x²(4x + 7) + 3x(4x + 7) + 2(4x + 7).

= (x² + 3x + 2)(4x + 7).

Hence 4x³ + 19x² + 29x + 14 divided by 4x + 7 is x² + 3x + 2 or (x + 1)(x + 2).

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which of the following shows the graphical representation of the solution for the one-variable linear equation 2x-1=3

Andrej [43]

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$2x-1 = 3$

If we add 1 to both sides of the equation we have:

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$x = \frac {4} {2}\\x = 2$

The graph of the solution is shown in the attached figure.

Answer:

See attached image

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2 years ago

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KiRa [710]

Answer:

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If thewronskian w of f and g is 3e4t,and if f(t) = e2t,find g(t).

ehidna [41]

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We have $f(t)=e^{2t}\implies f'(t)=2e^{2t}$ , so

$W(f(t),g(t))=e^{2t}g'(t)-2e^{2t}g(t)=3e^{4t}$
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$\implies\dfrac{\mathrm d}{\mathrm dt}[e^{-2t}g(t)]=3$
$\implies e^{-2t}g(t)=\displaystyle\int3\,\mathrm dt$
$\implies e^{-2t}g(t)=3t+C$
$\implies g(t)=3te^{2t}+Ce^{2t}$

where $C$ is any arbitrary constant.