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2 years ago

The sum of eight times a number and negative exceeds twelve.

Mathematics

1 answer:

11111nata11111 [884]2 years ago

6 0

Answer:8x + -4 > 12

8x > 16

x > 2

Step-by-step explanation:

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Solve the following recurrence relation: <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

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

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

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

and the pattern continues down to the first term $a_1=0$ ,

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

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

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

4 0

2 years ago

Vanyuwa [196]

Answer:5

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Can anybody please help solving this problem?

pantera1 [17]

Area of the shaded region = Area of a square - Area of a circle

Side of a square = 2r
Area of a square = (2r)² = 4r²

Area of a circle = πr²

Area of the shaded region = 4r² - πr² = r²(4-π)

7 0

3 years ago

On the same day at school, 1/6 of the students were wearing skirts and 5/8 of the students were wearing pants. The rest of the s

anastassius [24]

What you do is you find the common denominator between the two fractions given. the easiest is to just multiply them

6*8=48

and then multiply each numerator by the number it's denominator is multiplied by

1*8=8 and 5*6=30

and now you have your new fractions, add them together

8/48+30/48=38/48

this leaves 10/48 as the people who were wearing shorts, just simplify this and it's done

10/2 =5/24
48/2

4 0

2 years ago

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Find the distance between points.

SashulF [63]

Answer:

3 units

Step-by-step explanation:

Here, The distance between two points is 3 units

-TheUnknownScientist

4 0

2 years ago

The sum of eight times a number and negative exceeds twelve.​

The sum of eight times a number and negative exceeds twelve.