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3 years ago

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A plane made a trip to Miami and back. It flew 400mph on the way there and flew 450mph on the return trip. How long did the trip

to Miami take if the return trip took 10 hours?

1 answer:

quester [9]3 years ago

4 0

Answer:

equation: 400 + ( 450×10)= h

h= 4900.

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Step-by-step explanation:

First of all, let simplify and factorize the resulting polynomial:

$6\cdot x^{2} \geq 10 + 11\cdot x$

$6\cdot x^{2}-11\cdot x -10 \geq 0$

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$r_{1,2} = \frac{\left[-\left(-\frac{11}{6}\right)\pm \sqrt{\left(-\frac{11}{6} \right)^{2}-4\cdot (1)\cdot \left(-\frac{10}{6} \right)} \right]}{2\cdot (1)}$

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Then, the factorized form of the inequation is:

$6\cdot \left(x-\frac{5}{2}\right)\cdot \left(x+\frac{2}{3} \right)\geq 0$

By Real Algebra, there are two condition that fulfill the inequation:

a) $x-\frac{5}{2} \geq 0 \,\wedge\,x+\frac{2}{3}\geq 0$

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b) $x-\frac{5}{2} \leq 0 \,\wedge\,x+\frac{2}{3}\leq 0$

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The solution of the inequation $6\cdot x^{2} \geq 10 + 11\cdot x$ is $\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)$ .

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