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3 years ago

When a number is divided by -3, the result is 12 more than the number what is the number?

Mathematics

1 answer:

olga55 [171]3 years ago

8 0

X/-3 = 12 + x
x = -36 - 3x
4x = 36
x= = 9

The number is 9.

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Yolanda owns 4 rabbits. She expects the number of rabbits to double every year.

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R=Number of rabbits

y=Years that have passed by { y ≥ 0 }

R=f(y) --> R is a function of y.
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Note that when:

y=0, R=4 ---> Point: (0, 4)

y=1, R=8 ---> Point (1, 8)

y=2, R=16 ---> Point (2, 16)

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So the equation you want is going to form a curved graph.

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Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference

Bezzdna [24]

Since $a_1,a_2,a_3,\cdots$ are in arithmetic progression,

$a_2 = a_1 + 2$

$a_3 = a_2 + 2 = a_1 + 2\cdot2$

$a_4 = a_3+2 = a_1+3\cdot2$

$\cdots \implies a_n = a_1 + 2(n-1)$

and since $b_1,b_2,b_3,\cdots$ are in geometric progression,

$b_2 = 2b_1$

$b_3=2b_2 = 2^2 b_1$

$b_4=2b_3=2^3b_1$

$\cdots\implies b_n=2^{n-1}b_1$

Recall that

$\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n$

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

It follows that

$a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n + n(n-1)$