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3 years ago

Solve for x .problem down below

Mathematics

1 answer:

AleksAgata [21]3 years ago

5 0

A: no solution!

first, simplify each side of the equation.

3x + 5 - 10x simplifies to -7x + 5.
8 - 7x - 12 simplifies to -7x - 4.

then, add +7x on both sides of the equation to get the variable alone. if you add 7x to each side, you get left with 0.

so, that leaves 5 = -4 which is not true. so, that means there is no solution.

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Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

Helpppppppppppppppppp

tekilochka [14]

Answer:

5x + y = -48

Step-by-step explanation:

(y + 3)/(x + 9) =m

=> y + 3 = -5x -45

=> 5x + y + 48 = 0

4 0

2 years ago

A tortoise and a hare are competing in a race around a 1600-meter track. The arrogant hare decides to let the tortoise have a 78

Sindrei [870]

I am presuming that the question is who won or by how much did the winner win.

distance equals rate times time, or d = r*t
For the Hare d = 1600 and r = 10
1600 = 10 t
Divide both sides by 10
t = 160
The hare finished in 160 seconds

For the tortoise d = 1600 - 780 = 820 (due to the head start) and r = 5.3
820= 5.3 t
Divide both sides by 5.3
t = 154.72 (rounded to the hundredths place)

The tortoise won by 5. 28 seconds (160-154.72)

6 0

3 years ago

Read 2 more answers

Please I need Help!!! I need someone to help me do markdown's!!!

marta [7]

Answer:

The retail price is $103.6

Step-by-step explanation:

Markdowns are, to be simple, when the price goes DOWN, so the price would be less than the original rather than more. First, you must calculate what one percent of the original is, which is 1.40. As the markdown is 26 percent, you can do 1.40 x 26 to get how much was marked down, which is $36.40. To find the new price now, you must do the original minus the markdown, or 140 - 36.40 in this case. This gives you $103.6 as the retail price.

I hope this helped! :D

7 0

2 years ago

What is the missing equation N÷6=8

solong [7]

48.

N/6 = 8
48/6 = 8
8 = 8
8 does indeed equal 8

Good luck!

3 0

3 years ago

Read 2 more answers

Solve for x .problem down below ​

Solve for x .problem down below