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Firlakuza [10]
3 years ago
10

Which expression is equivalent to 18 1/5 - (-22 2/5) - (-40 1/5)

Mathematics
1 answer:
pogonyaev3 years ago
4 0

Answer:

option D

Step-by-step explanation:

18 \frac{1}{5} -(-22\frac{2}{5}) -(-40\frac{1}{5})

To get equivalent expression we need to remove the parenthesis

multiply negative sign inside the parenthesis

when we multiply negative and negative it becomes positive.

So the expression becomes

18 \frac{1}{5} + 22\frac{2}{5}+40\frac{1}{5}

So, option D is the equivalent expression

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Find a possible formula for a fourth degree polynomial g that has a double zero at -2, g(4) = 0, g(3) = 0, and g(0) = 12. g(x) =
astraxan [27]
<h2>Answer:</h2>

The possible formula for a fourth degree polynomial g is:

         g(x)=\dfrac{1}{4}(x^4-3x^3-12x^2+20x+48)

<h2>Step-by-step explanation:</h2>

We know that if a polynomial has zeros as a,b,c and d then the possible polynomial form is given by:

f(x)=m(x-a)(x-b)(x-c)(x-d)

Here the polynomial g  has a double zero at -2, g(4) = 0, g(3) = 0.

This means that the polynomial g(x) is given by:

g(x)=m(x-(-2))^2(x-4)(x-3)\\\\i.e.\\\\g(x)=m(x+2)^2(x-4)(x-3)\\\\i.e.\\\\g(x)=m(x^2+2^2+2\times 2\times x)(x(x-3)-4(x-3))\\\\i.e.\\\\g(x)=m(x^2+4+4x)(x^2-3x-4x+12)\\\\i.e.\\\\g(x)=m(x^2+4+4x)(x^2-7x+12)\\\\i.e.\\\\g(x)=m[x^2(x^2-7x+12)+4(x^2-7x+12)+4x(x^2-7x+12)]\\\\i.e.\\\\g(x)=m[x^4-7x^3+12x^2+4x^2-28x+48+4x^3-28x^2+48x]\\\\i.e.\\\\g(x)=m[x^4-7x^3+4x^3+12x^2+4x^2-28x^2-28x+48x+48]\\\\i.e.\\\\g(x)=m[x^4-3x^3-12x^2+20x+48]

Also,

g(0)=12

i.e.

48m=12\\\\i.e.\\\\m=\dfrac{12}{48}\\\\i.e.\\\\m=\dfrac{1}{4}

Hence, the polynomial g(x) is given by:

g(x)=\dfrac{1}{4}(x^4-3x^3-12x^2+20x+48)

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