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GalinKa [24]
3 years ago
11

What is the sum of the first 11 terms of the arithmetic series in which a1= -12 and d=5?

Mathematics
1 answer:
SVEN [57.7K]3 years ago
3 0
Hello :  
the terme general is : an = a1 +(n-1)d
 a11 = a1+(11-1)×5
a11 = -12+50
a11 = 38
<span>the sum of the first 11 terms is : S11 = (11/2)(a1+a11)
</span>S11 = (11/2)(-12+38)
S11 = 143
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Which of the values shown are potential roots of f(x) = 3x3 â€"" 13x2 â€"" 3x 45? Select all that apply.
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The potential roots of the function are, \pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45,\  \pm \dfrac{1}{3},\  \pm \dfrac{5}{3}

And the accurate root is 3 it can be determined by using rules of the rational root equation.

<h2>Given that,</h2>

Function; \rm f(x) = 3x^3 - 13x^2 -3x + 45

<h3>We have to determine,</h3>

Which of the values shown are potential roots of the given equation?

<h3>According to the question,</h3>

Potential roots of the polynomial are all possible roots of f(x).

\rm f(x) = 3x^3 - 13x^2 -3x + 45

Using rational root theorem test. We will find all the possible or potential roots of the polynomial.

\rm p=\dfrac{All\  the \ positive}{Negative\  factors \ of\  45}

\rm q=\dfrac{All\  the \ positive}{Negative\  factors \ of\  3}

The factor of the term 45 are,

\pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45

And The factor of 3 are,

\pm1, \ \pm3

All the possible roots are,

\dfrac{p}{q} = \pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45,\  \pm \dfrac{1}{3},\  \pm \dfrac{5}{3}

Now check for all the rational roots which are possible for the given function,

\rm f(x) = 3x^3 - 13x^2 -3x + 45\\\\ f(1) = 3(1)^3 - 13(1)^2 -3(1) + 45 = 3-13-3+45 = 32\neq 0\\\\ f(-1) = 3(-1)^3 - 13(-1)^2 -3(-1) + 45 =- 3-13+3+45 = 32\neq 0\\\\ f(3) = 3(3)^3 - 13(3)^2 -3(3) + 45 = 81-117-9+45 =0\\\\ f(-3) = 3(-3)^3 - 13(-3)^2 -3(-3) + 45 = -81+117+9+45 =-144\neq 0

Therefore, x = 3 is the potential root of the given function.

Hence, The potential roots of the function are, \pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45,\  \pm \dfrac{1}{3},\  \pm \dfrac{5}{3}.

For more details about Potential roots refer to the link given below.

brainly.com/question/25873992

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JulijaS [17]

Answer:

b because it is

Step-by-step explanation:

153.2 is a cool number

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