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Ronch [10]
2 years ago
13

3 (3d – 2) = { (a + 5)

Mathematics
1 answer:
julia-pushkina [17]2 years ago
5 0

Step-by-step explanation:

if solving for d

-3x=2...................

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How do I do it and show my work along with it?
Rudiy27
Be kind and say please,that is being rude when you don't say it. Well, how much times does 6 go into 34? 5 times right. So then put 30 under the 34. You get 4. So then bring down the 5. How much times does 6 go into 45. 7 right. So then put 42 under 45. You get 3. Now add a decimal point after the 5 and after the 7. Add zero after the 5 . Bring down the zero. How much times does 6 go into 30? 5 times, so you put 30 under 30 and get zero. If you have any more questions,please leave them below in the comments.
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3 years ago
Determine the formula for the nth term of the sequence:<br>-2,1,7,25,79,...​
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A plausible guess might be that the sequence is formed by a degree-4* polynomial,

x_n = a n^4 + b n^3 + c n^2 + d n + e

From the given known values of the sequence, we have

\begin{cases}a+b+c+d+e = -2 \\ 16 a + 8 b + 4 c + 2 d + e = 1 \\ 81 a + 27 b + 9 c + 3 d + e = 7 \\ 256 a + 64 b + 16 c + 4 d + e = 25 \\ 625 a + 125 b + 25 c + 5 d + e = 79\end{cases}

Solving the system yields coefficients

a=\dfrac58, b=-\dfrac{19}4, c=\dfrac{115}8, d = -\dfrac{65}4, e=4

so that the n-th term in the sequence might be

\displaystyle x_n = \boxed{\frac{5 n^4}{8}-\frac{19 n^3}{4}+\frac{115 n^2}{8}-\frac{65 n}{4}+4}

Then the next few terms in the sequence could very well be

\{-2, 1, 7, 25, 79, 208, 466, 922, 1660, 2779, \ldots\}

It would be much easier to confirm this had the given sequence provided just one more term...

* Why degree-4? This rests on the assumption that the higher-order forward differences of \{x_n\} eventually form a constant sequence. But we only have enough information to find one term in the sequence of 4th-order differences. Denote the k-th-order forward differences of \{x_n\} by \Delta^{k}\{x_n\}. Then

• 1st-order differences:

\Delta\{x_n\} = \{1-(-2), 7-1, 25-7, 79-25,\ldots\} = \{3,6,18,54,\ldots\}

• 2nd-order differences:

\Delta^2\{x_n\} = \{6-3,18-6,54-18,\ldots\} = \{3,12,36,\ldots\}

• 3rd-order differences:

\Delta^3\{x_n\} = \{12-3, 36-12,\ldots\} = \{9,24,\ldots\}

• 4th-order differences:

\Delta^4\{x_n\} = \{24-9,\ldots\} = \{15,\ldots\}

From here I made the assumption that \Delta^4\{x_n\} is the constant sequence {15, 15, 15, …}. This implies \Delta^3\{x_n\} forms an arithmetic/linear sequence, which implies \Delta^2\{x_n\} forms a quadratic sequence, and so on up \{x_n\} forming a quartic sequence. Then we can use the method of undetermined coefficients to find it.

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2 years ago
Which expression is equivalent to 6w + 5 - 3w + 7
love history [14]

Answer:

the answer is B

Step-by-step explanation:

6w + 5 - 3w + 7

<h3>i) collect like terms</h3>

= 6w - 3w + 5 + 7

= 3w + 5 + 7

<h3>ii) add the numbers</h3>

= 3 w + 5 + 7

= 3w + 12

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Answer:


Step-by-step explanation:

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