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givi [52]
3 years ago
11

Which system has no solution? Check all that appy.

Mathematics
1 answer:
Ainat [17]3 years ago
7 0
The first equation has no solution



The picture shows all the work I did, the reason I took a pic is because it is a little hard to explain by text, but I hope this helped you!

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Determine the formula for the nth term of the sequence:<br>-2,1,7,25,79,...​
rodikova [14]

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.

5 0
2 years ago
It costs $42 for 7 staplers. what is the unit rate for the stapler?
murzikaleks [220]

Answer:

The answer is 6

Step-by-step explanation:

42 divided by 7=6

5 0
3 years ago
Sovle the equation for x0.5x-4=12
Amanda [17]

Value of x is x=32

Step-by-step explanation:

We need to find the value of x of the equation 0.5x-4=12

Solving the equation and finding value of x

0.5x-4=12\\

Adding 4 on both sides

0.5x-4+4=12+4\\0.5x=16\\

Divide both sides by 0.5

\frac{0.5x}{0.5} =\frac{16}{0.5}\\ x=32

So, value of x is x=32

Keywords: Solving Equations

Learn more about Solving Equations at:

  • brainly.com/question/1563227
  • brainly.com/question/2403985
  • brainly.com/question/11229113

#learnwithBrainly

5 0
3 years ago
Whats the answer to 3+9(4x+8)30x20
AnnZ [28]

Answer:

The Answer is 1080x^21 + 2160x^20 + 3

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Evaluate please<br> 2x+(−6)∙(y+1) for x=−1.5 and y=−3
Andreyy89
First, you plug your given values in. Since x is 1.5, it will be multiples by 2x to get 3.2. Since y is -3, it will be added to 1 to get -2. Finally, the two are multiplied together to get -6.4 if I am correct. 
8 0
3 years ago
Read 2 more answers
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