What is the best estimate of the sum of the fraction? 31/4 +17/3 +8/18

Mathematics

1 answer:

Bogdan [553]2 years ago

3 0

The best estimate of the sum of the expression given is $\rm 13 \dfrac {31}{26}$

What is a Fraction ?

A fraction is written as p/q , where q $\rm \ne$ 0

It is asked to determine the sum of the fraction

31/4 + 17/3 + 8/18

Taking the LCM of 4 , 3 , 18

LCM of 4 , 3 ,18 is 36

Therefore

$\rm \dfrac{ 31 *9 + 17 *12 + 8 *2}{36 }$

(279+204+16) /36

499 / 36

$\rm 13 \dfrac {31}{26}$

Therefore the best estimate of the sum of the expression given is $\rm 13 \dfrac {31}{26}$ .

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Find the solutions of the equation x4 − 2x3 − x2 + 2x = 0. (Enter your answers as a comma-separated list.)

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Answer:

$S=\left \{ 0,-1,1,2 \right \}$

Step-by-step explanation:

There are several ways to solve this quartic equation. But since the coefficients, they repeat a=1,b=2,c=1,d=2, but e=0, and they are multiple of each other, then it is more convenient to work with factoring as the method of solving it.

As if it was a quadratic one.

$x^{4}-2x^{3}- x^{2} + 2x = 0\\x(x^{3}-2x^{2}-x+2)=0 \:Factoring \:out\\x[(x^{3}-2x^{2})+(-x+2)]=0 \:Grouping\\x[\mathbf{x^{2}}(x-2)+\mathbf{-1}(x+2)]=0 \:Rewriting\:the\:first\:factor\\x(x^{2}-1)(x-2)\:Expanding \:the \:first \:factor\\x(x-1)(x+1)(x-2)=0\\x=0,x=1,x=-1,x=2\\S=\left \{ 0,-1,1,2 \right \}$