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andre [41]
1 year ago
8

1/3 x + 4 = x − 2 solve for x

Mathematics
1 answer:
Furkat [3]1 year ago
7 0

Step-by-step explanation:

1/3.x+4=x-2

multiplying 3 to both sides

x+12=3x-6

12+6=3x-x

18=2x

x=9

answer

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Find the value of c so that the polynomial p(x) is divisible by (x-3). p(x) =-x^3+cx^2-4x+3. c=?
Vilka [71]

Answer:

\boxed{\textsf {The value of c is $\sf \dfrac{-14}{3}$. }}

Step-by-step explanation:

A polynomial is given to us . We need to find the value of c so that it is divisible by (x-3 ) .The given polynomial to us is ,

\sf \implies p(x)=- x^3+cx^2-4x+3

And the factor is ,

\sf \implies g(x) = x + 3

Now , according to factor theorem , p(x) will be divisible by g(x) if p(-3) = 0

\sf \implies p(x)= - x^3+cx^2-4x+3 \\\\\implies\sf p(-3) = 0 \\\\\sf\implies -(-3)^3+c(-3)^2-4(-3)+3 = 0 \\\\\sf\implies 27 + 9c +12+3=0 \\\\\sf\implies 9c +42=0 \\\\\sf\implies 9c = (-42) \\\\\sf\implies c = \dfrac{-42}{9}\\\\\sf\implies \boxed{\pink{\sf c = \dfrac{-14}{3}}}

<h3><u>Hence </u><u>the </u><u>value </u><u>of </u><u>c </u><u>is </u><u>(</u><u>-</u><u>1</u><u>4</u><u>)</u><u>/</u><u>3</u><u> </u><u>.</u></h3>
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3 years ago
Calculate the arithmetic sequence in which a9=17 and the common difference is d=-2.1
jek_recluse [69]

Answer:

S_{31}=71.3


Step-by-step explanation:

The nth term of an arithmetic sequence is given by the formula,

U_n=a_1+(n-1)d


We were given that the 9th term is 17.


\Rightarrow 17=a_1+(9-1)(-2.1)


\Rightarrow 17=a_1+(8)\times(-2.1)


\Rightarrow 17=a_1-\frac{84}{5}


\Rightarrow 17+\frac{84}{5}=a_1


\Rightarrow a_1=\frac{169}{5}


The sum of the first n-terms is given by the formula,


S_n=\frac{n}{2}(2a_1+(n-1)d)


To find S_{31}, we substitute n=31, a_1=\frac{169}{5} and d=-2.1.


\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(31-1)(-2.1))


\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(30)(-2.1))



\Rightarrow S_{31}=\frac{31}{2}(\frac{23}{5})


\Rightarrow S_{31}=\frac{713}{10}


\Rightarrow S_{31}=71.3


The correct answer is D















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The regular hexagon has both reflection symmetry and rotation symmetry.

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Sedbober [7]
The answer for your question is 686
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vredina [299]

Answer:

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